Application of Mean-Field Jordan Wigner Transformation to Antiferromagnet System
|
|
- Natalie Daniel
- 6 years ago
- Views:
Transcription
1 Commun. Theor. Phys. Beijing, China pp c Chinese Physical Society Vol. 50, o. 1, July 15, 008 Application of Mean-Field Jordan Wigner Transformation to Antiferromagnet System LI Jia-Liang, 1,3 LEI Shu-Guo, and JIAG Yu-Chi 1 1 Department of Physics, Changshu Institute of Technology Changshu 15500, China Department of Applied Physics, anjing University of Technology, anjing 10009, China 3 Jiangsu Laboratory of Advanced Functional Materials, Changshu 15500, China Received August 4, 007; Revised ovember 1, 007 Abstract By using the mean-field Jordan Wigner transformation analysis, this paper studies the one-dimensional spin-1/ XYZ antiferromagnetic chain in the transverse field with uniform long-range interactions among the z- components of the spins. The thermodynamic quantities, such as Helmholtz free energy, the internal energy, the specific heat, and the isothermal susceptibility, are obtained. Under degenerating condition, our results agree with numerical results of the other literatures PACS numbers: Jm, Cx, s Key words: XYZ antiferromagnetic chain, mean-field Jordan Wigner transformation, long-range interactions 1 Introduction In recent years, the low-dimensional magnetic system, especially oxygen superconductor materials with stronger antiferromagnetic coupling, has received extensive attention from researchers in a wide range of scientific and engineering fields. So thermodynamics properties of the one-dimensional antiferromagnetic system are always one of the most activating research fields [1 3] in theory and experimentation of condensed matter physics. Studies in recent ten years also have shown that the Heisenberg chains with nonlocal quantum spin system are also used in such frontier physical fields as quantum dots and nuclear spin. [4,5] It is well nown that the Heisenberg models are frequently used to describe one-dimensional quantum spin chain. From the perspective of interaction anisotropy, there are three types of Heisenberg models named XXX, XXZ, and XYZ models respectively. They provide a good platform for studying the thermodynamic properties of low-dimensional quantum magnetic systems. Theoretically, the physical properties of spin-1/ XY chain can be studied analytically by the general Jordan Wigner transformation, which represents the spin operator to spinless Fermi operator with no interactions in the quadratic form and can be diagonalized exactly. However, the same operation is inapplicable to the isotropic spin-1/ XXX Heisenberg chain and the anisotropic spin-1/ XYZ chain because they are transformed to the interacting spinless Fermi system. Some approximate techniques are developed and applied to the model. [6] The nearest-neighbor interaction is mainly considered in the Heisenberg s model. This is because that although the nearest-neighbor interaction is not the wholly spin interaction, it is the most dominating one and its solution can also provide primary cognition and deduction for other problems. However, the effect of long range interaction as a real spin one on properties of system thermodynamics especially on phase transition of system is essential. One-dimensional finite range interaction and finite spin system have been proved by means of mathematics to have no phase transition [7] in history. The thermodynamics properties of isotropy ferromagnetic S-1/ XXZ model with uniform long range interaction are discussed by using Jordan Wigner transform and Gaussion integral transform in Refs. [8] and [9]. The phase transition of the one-dimensional antiferromagnetic Ising model with the exponential decaying long range interaction is discussed by the real space renormalization group renormalizing in Ref. [10]. The studies mentioned above show that effect of long range interaction on system thermodynamic properties is remarable, and it was also presented in Ref. [10] that the effect of long range interaction on antiferromagnetic chain is different from that on ferromagnetic chain. This paper applies a method of mean-field Jordan Wigner transformation to investigate the anisotropy S- 1/ XYZ antiferromagnetic chain with uniform long range interaction. We have found that the trend of thermodynamics quantities varying with temperature for antiferromagnetic agrees well with the result by using traditional thermodynamics integral method. Our discussion of phase transition problem is also agreeable with the viewpoint in Ref. [10]. By comparison, we have applied our method to study the ferromagnetic system, and obtained numerical result which is consistent with that in Ref. [8]. But as our focal point, the effect of anisotropy and self-consistent field on system thermodynamics properties has not been reported so far. The project supported by the Open Fund of Jiangsu Laboratory of Advanced Functional Materials under Grant o. 06KFJJ004
2 44 LI Jia-Liang, LEI Shu-Guo, and JIAG Yu-Chi Vol. 50 Model and Partition Function The Hamiltonian of the one-dimensional S-1/ antiferromagnetic chain model with uniform long-range interactions among the z-components of the spins in the external field is H = J [1 + γsj x Sj+1 x + 1 γs y j Sy j+1 ] + I j,=1 S z j S z + h Sj z, 1 where Sj α α = x, y, z is the spin operator of S = 1/ on site j, is the number of system spins, J is the nearest-neighbor exchange coupling, γ is the anisotropy parameter, I is the long range interaction parameter in z-direction, h is the transverse field parameter. Using the spin raising and lowering operators S x j = 1 S+ j + S j, Sy j = 1 i S+ j S j, and Jordan Wigner transformation, [11] S + j = [ exp ] c l c l c j, j 1 iπ l=1 S j = c j [exp iπ j 1 c l c l l=1 ], S z j = c + j c j 1, 3 equation 1 can be replaced with [ 1 H = J c j c j+1 + c j+1 c j + γ c j c j+1 + c j+1c j ] + I j,=1 c j c j j c j c jc c + h I h I. 4 The mean-field theory is applied to four-operator term in Eq. 4. Using the self-consistent field, D = c j c j, and under the mean field approximation, equation 4 can be written as H = J [c j c j+1 + c j+1 c j + γc j c j+1 + c j+1c j ] I ID h c j c j Introducing Fourier transformation, c j = 1 expijc, = πn n=1 n = 1,, 3,...,, h I ID. 5 equation 5 is transformed into H = [ Ac c + ib ] c c + c c h I ID. 6 With Bogoliubov transformation, c = U α + iv α, c = U α iv α, U K = U K, V K = V K. The Hamilton function of the system can be expressed as H = [ A + B α α 1 A + B + 1 ] A h I ID. 7 Partition function is expressed as [ β Z = exp h I + βid ] [ Tr exp [ β A + B α α 1 A + B + 1 ]] A, lnz = β h I + βid + ln1 + e βε + 1 βε 1 βa, 8 where A = J cos + h I + ID, B = Jγ sin, and ε = A + B. 3 Thermodynamics Quantities of System 3.1 Helmholtz Free Energy per Site From Eq. 8, we can obtain F = T ln1 + e βε A 1 ε h 1 ID. 9 Imposing the condition F/ D = 0, the self-consistent field D can be obtained as follows: D = 1 A βε tanh + 1 ε Internal Energy per Site From Eq. 8, we can also obtain U = 1 βε ε tanh + 1 A Specific Heat per Site h I ID. 11 According to Eq. 11, the specific heat per site can be expressed as:
3 o. 1 Application of Mean-Field Jordan Wigner Transformation to Antiferromagnet System 45 where C = I [ A βε T tanh ε + A 4 sech βε 1 ] I D β + I T D β = 1/ A/4sech βε / 1 + I/ B /ε 3 tanhβε / + βa /ε sech βε /. ε 4 sech βε + I T D D β, Magnetization per Site From Eq. 8, we can obtain 3.5 Susceptibility per Site M Z = 1 From Eq. 13, we can obtain χ = A ε 1 + e βε + 1 A = 1 A tanh ε ε βε. 13 1/ βa /4ε sech βε / + 1/ B /ε 3 tanhβε / 1 1/ IβA /ε sech βε / 1/ IB /ε 3 tanhβε /. 14 All the functions and variables i.e., A, B, ε in the above-mentioned equations satisfy Eq umerical Result and Discussion 4.1 Thermodynamics Quantities as a Function of Temperature We have solved Eqs through self-consistent method and discussed how the thermodynamics quantities vary with temperature. Figures 1a 1c show the dependence of the thermodynamic quantities on temperature in a transverse field when h/j = 0.0, γ = 0.0, and I/J = 0.8, 1.0, 1. respectively. It is also shown that with the increase of long range interaction, not only phase transition does not occur, but also the variation trends of the free energy, the internal energy and the specific heat are not changed with the increase of long range interaction. This is because that in the numerical computation by using the self-consistent approximate method which we mentioned above, D 0.5 and D/ β 0. We have found that the results are reasonable through Eqs. 9, 11, and 1 and are in good agreement with the viewpoint in Ref. [10]. Fig. 1 The free energy F a, internal energy U b and specific heat C c versus the temperature T/J with γ = 0, h/j = 0 and for different long-range interactions I/J = 0.8,1.0,1.. In order to compare the effect of long range interaction on antiferromagnetic chain with that on ferromagnetic chain, we compute the effect of long range interaction on system thermodynamic quantities in Figs. a c when h/j = 0.0, γ = 0.0, and I/J = 1.6, 1.8, respectively. The first two parts in Hamiltonian function Eq. 1 can be considered as perturbation because the value of I/J is larger. Furthermore, h/j = 0 but I/J is negative, so equation 1 describes the standard Ising ferromagnetic chain. We have solved Eqs with the help of the self-consistent approximation method, and our numerical results show that for ferromagnetic, firstly long range interaction has great effect on thermodynamics quantities, and secondly apparent phase transition occurs. The results are in good accordance with the conclusion drawn by different theoretical methods in Ref. [8].
4 46 LI Jia-Liang, LEI Shu-Guo, and JIAG Yu-Chi Vol. 50 Fig. The internal energy U a, magnetization M Z b, and specific heat C c versus the temperature T/J with γ = 0, h/j = 0 and for different long-range interactions I/J = 1.6, 1.8. Figures 3a 3c show the dependence of the thermodynamic quantities on temperature when h/j = 0.0, I/J = 1., and γ = 0., 0.5, 0.8 respectively. The numerical results show that no phase transition occurs either and the thermodynamic quantities vary with temperature apparently as anisotropy variables are increased. This is because that the first two parts in Hamilton function become larger with increasing anisotropy variables. Fig. 3 The internal energy U a, specific heat C b and susceptibility χ c versus the temperature T/J with I/J = 1., h/j = 0 and for different anisotropic γ = 0.,0.5,0.8. Figures 4a 4c show the dependence of the thermodynamic quantities on temperature when I/J = 1. and h/j = 0., 0.5, 0.8 respectively. We have found that the trend of the specific heat varying with temperature by using mean-field Jordan Wigner transformation method agrees well with the result obtained by traditional thermodynamics Bethe integral equation method. [1] Fig. 4 The free energy F a, specific heat C b, and susceptibility χ c versus the temperature T/J with γ = 0.5, I/J = 1. and for different external field h/j = 0.,0.5,0.8.
5 o. 1 Application of Mean-Field Jordan Wigner Transformation to Antiferromagnet System The Magnetization as a Function of External Magnetic Field Figures 5a 5c show the dependence of the magnetization on external magnetic field. Although all variables are different, our numerical results show that with the increase of external magnetic field, the spin direction of system trends to be consistent and reaches a definite value, which agrees with the theory of thermodynamics. Fig. 5 Function of external field h/j. a For T/J = 0.0, γ = 0.0, and I/J = 0.3,0.6,0.9; b For T/J = 0.0, I/J = 0.5, and γ = 0., 0.5, 0.8; c For I/J = 0., γ = 0., and T/J = 0.05, 0.15, Summary In summary, using mean-field Jordan Wigner transform method, this paper discusses the thermodynamics properties of the system based on the S-1/ Heisenberg XYZ antiferromagnetic model with uniform long range interaction in z-direction in external magnetic field. We have placed great emphasis on studies on the effect of the competition between the anisotropic parameter and the long-range interaction parameter upon the system. Our numerical results on degenerating condition agree well with those in other papers, while the conclusion drawn under normal condition has not been reported so far. Acnowledgments We would lie to than professor Tong Pei-Qing for many important discussions and suggestions. References [1]. Laflorencie and H. Rieger, Eur. Phys. J. B [] H.H. Fu, K.L. Yao, and Z.L. Liu, Phys. Lett. A [3] H. Yoshizawa, G. Shirane, H. Shiba, and K. Hiraawa, Phys. Rev. B [4] A. Imamoglu and D.P. Divencenzo, Phys. Rev. Lett [5] S.B. Zheng and G.C. Guo, Phys. Rev. Lett [6] M. Shiroishi and M. Taahashi, Phys. Rev. Lett [7] R.B. Griffiths, Phase Transition and Critical Phenomenon, Vol. 1, Academic, London 197 pp [8] L.L. Goncalves, L.P.S. Coutinho, and J.P.de Lima, Physica A [9] Ping Lou, Phys. Rev. B [10] Zhang Jin-Shan, J. Beijing ormal University in Chinese. [11] E. Fradin, In Field Theories of Condensed Matter Systems, Addison-Wesley, Redwood City, 1991 Chap. 4. [1] A. Klumper, Eur. Phys. J. B
Lecture notes on topological insulators
Lecture notes on topological insulators Ming-Che Chang Department of Physics, National Taiwan Normal University, Taipei, Taiwan Dated: May 8, 07 I. D p-wave SUPERCONDUCTOR Here we study p-wave SC in D
More informationMonte Carlo Study of Planar Rotator Model with Weak Dzyaloshinsky Moriya Interaction
Commun. Theor. Phys. (Beijing, China) 46 (2006) pp. 663 667 c International Academic Publishers Vol. 46, No. 4, October 15, 2006 Monte Carlo Study of Planar Rotator Model with Weak Dzyaloshinsky Moriya
More informationA theoretical investigation for low-dimensional molecular-based magnetic materials
J. Phys.: Condens. Matter 10 (1998) 3003 3017. Printed in the UK PII: S0953-8984(98)87508-5 A theoretical investigation for low-dimensional molecular-based magnetic materials T Kaneyoshi and Y Nakamura
More informationSchwinger-boson mean-field theory of the Heisenberg ferrimagnetic spin chain
PHYSICAL REVIEW B VOLUME 60, UMBER 1 JULY 1999-II Schwinger-boson mean-field theory of the Heisenberg ferrimagnetic spin chain Congjun Wu Department of Physics, Peking University, Beijing 100871, China
More informationCritical Properties of Mixed Ising Spin System with Different Trimodal Transverse Fields in the Presence of Single-Ion Anisotropy
Commun. Theor. Phys. (Beijing, China) 45 (2006) pp. 111 116 c International Academic Publishers Vol. 45, No. 6, June 15, 2006 Critical Properties of Mixed Ising Spin System with Different Trimodal Transverse
More informationEffects of Different Spin-Spin Couplings and Magnetic Fields on Thermal Entanglement in Heisenberg XY Z Chain
Commun. heor. Phys. (Beijing China 53 (00 pp. 659 664 c Chinese Physical Society and IOP Publishing Ltd Vol. 53 No. 4 April 5 00 Effects of Different Spin-Spin Couplings and Magnetic Fields on hermal Entanglement
More informationDecoherence Effect in An Anisotropic Two-Qubit Heisenberg XYZ Model with Inhomogeneous Magnetic Field
Commun. Theor. Phys. (Beijing, China) 53 (010) pp. 1053 1058 c Chinese Physical Society and IOP Publishing Ltd Vol. 53, No. 6, June 15, 010 Decoherence Effect in An Anisotropic Two-Qubit Heisenberg XYZ
More informationEntanglement in the quantum Heisenberg XY model
PHYSICAL REVIEW A, VOLUME 64, 012313 Entanglement in the quantum Heisenberg XY model Xiaoguang Wang Institute of Physics and Astronomy, Aarhus University, DK-8000, Aarhus C, Denmark Received 4 January
More informationStatistical Thermodynamics Solution Exercise 8 HS Solution Exercise 8
Statistical Thermodynamics Solution Exercise 8 HS 05 Solution Exercise 8 Problem : Paramagnetism - Brillouin function a According to the equation for the energy of a magnetic dipole in an external magnetic
More informationMagnets, 1D quantum system, and quantum Phase transitions
134 Phys620.nb 10 Magnets, 1D quantum system, and quantum Phase transitions In 1D, fermions can be mapped into bosons, and vice versa. 10.1. magnetization and frustrated magnets (in any dimensions) Consider
More informationCritical entanglement and geometric phase of a two-qubit model with Dzyaloshinski Moriya anisotropic interaction
Chin. Phys. B Vol. 19, No. 1 010) 010305 Critical entanglement and geometric phase of a two-qubit model with Dzyaloshinski Moriya anisotropic interaction Li Zhi-Jian 李志坚 ), Cheng Lu 程璐 ), and Wen Jiao-Jin
More informationarxiv: v1 [cond-mat.stat-mech] 20 Feb 2018
Spin-1/2 anisotropic Heisenberg antiferromagnet with Dzyaloshinskii-Moriya interaction via mean-field approximation arxiv:1802.07172v1 [cond-mat.stat-mech] 20 Feb 2018 Walter E. F. Parente Universidade
More informationarxiv: v1 [quant-ph] 23 Jan 2019
Tuning the thermal entanglement in a Ising-XXZ diamond chain with two impurities I. M. Carvalho, O. Rojas,, S. M. de Souza and M. Rojas Departamento de Física, Universidade Federal de Lavras, 3700-000,
More information(Received 22 October 2009; revised manuscript received 30 December 2010)
Chin. Phys. B Vol. 19 No. 9 010) 090313 Teleportation and thermal entanglement in two-qubit Heisenberg XY Z spin chain with the Dyaloshinski Moriya interaction and the inhomogeneous magnetic field Gao
More informationTemperature Correlation Functions in the XXO Heisenberg Chain
CONGRESSO NAZIONALE DI FISICA DELLA MATERIA Brescia, 13-16 June, 1994 Temperature Correlation Functions in the XXO Heisenberg Chain F. Colomo 1, A.G. Izergin 2,3, V.E. Korepin 4, V. Tognetti 1,5 1 I.N.F.N.,
More informationBond Dilution Effects on Bethe Lattice the Spin-1 Blume Capel Model
Commun. Theor. Phys. 68 (2017) 361 365 Vol. 68, No. 3, September 1, 2017 Bond Dilution Effects on Bethe Lattice the Spin-1 Blume Capel Model Erhan Albayrak Erciyes University, Department of Physics, 38039,
More informationMAGNETISM MADE SIMPLE. An Introduction to Physical Concepts and to Some Useful Mathematical Methods. Daniel C. Mattis
THE THEORY OF MAGNETISM MADE SIMPLE An Introduction to Physical Concepts and to Some Useful Mathematical Methods Daniel C. Mattis Department of Physics, University of Utah lb World Scientific NEW JERSEY
More informationBipartite and Tripartite Entanglement in a Three-Qubit Heisenberg Model
Commun. Theor. Phys. (Beijing, China) 46 (006) pp. 969 974 c International Academic Publishers Vol. 46, No. 6, December 5, 006 Bipartite and Tripartite Entanglement in a Three-Qubit Heisenberg Model REN
More informationMagnetic ordering of local moments
Magnetic ordering Types of magnetic structure Ground state of the Heisenberg ferromagnet and antiferromagnet Spin wave High temperature susceptibility Mean field theory Magnetic ordering of local moments
More informationThermodynamics of quantum Heisenberg spin chains
PHYSICAL REVIEW B VOLUME 58, NUMBER 14 Thermodynamics of quantum Heisenberg spin chains 1 OCTOBER 1998-II Tao Xiang Research Centre in Superconductivity, University of Cambridge, Madingley Road, Cambridge
More informationarxiv: v1 [physics.optics] 30 Mar 2010
Analytical vectorial structure of non-paraxial four-petal Gaussian beams in the far field Xuewen Long a,b, Keqing Lu a, Yuhong Zhang a,b, Jianbang Guo a,b, and Kehao Li a,b a State Key Laboratory of Transient
More informationMagnetization and quadrupolar plateaus in the one-dimensional antiferromagnetic spin-3/2 and spin-2 Blume Capel model
Original Paper phys. stat. sol. (b) 243, No. 12, 2901 2912 (2006) / DOI 10.1002/pssb.200541252 Magnetization and quadrupolar plateaus in the one-dimensional antiferromagnetic spin-3/2 and spin-2 Blume
More informationA THREE-COMPONENT MOLECULAR MODEL WITH BONDING THREE-BODY INTERACTIONS
STATISTICAL PHYSICS, SOLID STATE PHYSICS A THREE-COMPONENT MOLECULAR MODEL WITH BONDING THREE-BODY INTERACTIONS FLORIN D. BUZATU Department of Theoretical Physics, National Institute of Physics and Nuclear
More informationFrequency in Middle of Magnon Band Gap in a Layered Ferromagnetic Superlattice
Commun. Theor. Phys. (Beijing, China) 54 (2010) pp. 1144 1150 c Chinese Physical Society and IOP Publishing Ltd Vol. 54, No. 6, December 15, 2010 Frequency in Middle of Magnon Band Gap in a Layered Ferromagnetic
More informationEntanglement in Many-Body Fermion Systems
Entanglement in Many-Body Fermion Systems Michelle Storms 1, 2 1 Department of Physics, University of California Davis, CA 95616, USA 2 Department of Physics and Astronomy, Ohio Wesleyan University, Delaware,
More informationDecoherence and Thermalization of Quantum Spin Systems
Copyright 2011 American Scientific Publishers All rights reserved Printed in the United States of America Journal of Computational and Theoretical Nanoscience Vol. 8, 1 23, 2011 Decoherence and Thermalization
More informationCover Page. The handle holds various files of this Leiden University dissertation.
Cover Page The handle http://hdl.handle.net/1887/49403 holds various files of this Leiden University dissertation. Author: Keesman, R. Title: Topological phases and phase transitions in magnets and ice
More informationThe Mermin-Wagner Theorem
June 24, 2010 Conclusion In one and two dimensions, continuous symmetries cannot be spontaneously broken at finite temperature in systems with sufficiently short-range interactions. Contents 1 How symmetry
More informationarxiv:quant-ph/ v2 24 Dec 2003
Quantum Entanglement in Heisenberg Antiferromagnets V. Subrahmanyam Department of Physics, Indian Institute of Technology, Kanpur, India. arxiv:quant-ph/0309004 v2 24 Dec 2003 Entanglement sharing among
More informationThe Mott Metal-Insulator Transition
Florian Gebhard The Mott Metal-Insulator Transition Models and Methods With 38 Figures Springer 1. Metal Insulator Transitions 1 1.1 Classification of Metals and Insulators 2 1.1.1 Definition of Metal
More informationarxiv: v2 [cond-mat.mes-hall] 19 Nov 2018
Entanglement entropy distribution in the strongly disordered one-dimensional Anderson model B. Friedman and R. Berkovits Department of Physics, Jack and Pearl Resnick Institute, Bar-Ilan University, Ramat-Gan
More informationThermal quantum discord in Heisenberg models with Dzyaloshinski Moriya interaction
Thermal quantum discord in Heisenberg models with Dzyaloshinski Moriya interaction Wang Lin-Cheng(), Yan Jun-Yan(), and Yi Xue-Xi() School of Physics and Optoelectronic Technology, Dalian University of
More informationThe mixed-spins 1/2 and 3/2 Blume Capel model with a random crystal field
The mixed-spins 1/2 and 3/2 Blume Capel model with a random crystal field Erhan Albayrak Erciyes University, Department of Physics, 38039, Kayseri, Turkey (Received 25 August 2011; revised manuscript received
More informationPhase Transitions in Condensed Matter Spontaneous Symmetry Breaking and Universality. Hans-Henning Klauss. Institut für Festkörperphysik TU Dresden
Phase Transitions in Condensed Matter Spontaneous Symmetry Breaking and Universality Hans-Henning Klauss Institut für Festkörperphysik TU Dresden 1 References [1] Stephen Blundell, Magnetism in Condensed
More informationThermal Bias on the Pumped Spin-Current in a Single Quantum Dot
Commun. Theor. Phys. 62 (2014) 86 90 Vol. 62, No. 1, July 1, 2014 Thermal Bias on the Pumped Spin-Current in a Single Quantum Dot LIU Jia ( ) 1,2, and CHENG Jie ( ) 1 1 School of Mathematics, Physics and
More informationThe continuum limit of the integrable open XYZ spin-1/2 chain
arxiv:hep-th/9809028v2 8 Sep 1998 The continuum limit of the integrable open XYZ spin-1/2 chain Hiroshi Tsukahara and Takeo Inami Department of Physics, Chuo University, Kasuga, Bunkyo-ku, Tokyo 112-8551
More informationarxiv: v3 [cond-mat.str-el] 15 Jun 2018
Quantum entanglement in the neighborhood of pseudo-transition for a spin-/ Ising-XYZ diamond chain I. M. Carvalho, J. Torrico, S. M. de Souza, M. Rojas and O. Rojas. Departamento de Física, Universidade
More information8.334: Statistical Mechanics II Problem Set # 4 Due: 4/9/14 Transfer Matrices & Position space renormalization
8.334: Statistical Mechanics II Problem Set # 4 Due: 4/9/14 Transfer Matrices & Position space renormalization This problem set is partly intended to introduce the transfer matrix method, which is used
More informationPhase Transitions of Random Binary Magnetic Square Lattice Ising Systems
I. Q. Sikakana Department of Physics and Non-Destructive Testing, Vaal University of Technology, Vanderbijlpark, 1900, South Africa e-mail: ike@vut.ac.za Abstract Binary magnetic square lattice Ising system
More informationDielectric Properties and Lattice Distortion in Rhombohedral Phase Region and Phase Coexistence Region of PZT Ceramics
Commun. Theor. Phys. (Beijing, China) 43 (2005) pp. 855 860 c International Academic Publishers Vol. 43, No. 5, May 15, 2005 Dielectric Properties and Lattice Distortion in Rhombohedral Phase Region and
More informationS j H o = gµ o H o. j=1
LECTURE 17 Ferromagnetism (Refs.: Sections 10.6-10.7 of Reif; Book by J. S. Smart, Effective Field Theories of Magnetism) Consider a solid consisting of N identical atoms arranged in a regular lattice.
More informationSimulation of the temperature-dependent resistivity of La 1 x Te x MnO 3
phys stat sol (a) 202, No 14, 2776 2780 (2005) / DOI 101002/pssa200520093 Simulation of the temperature-dependent resistivity of La 1 x Dong-yi Guan, Qing-li Zhou, Kui-juan Jin *, Guo-tai Tan, Zheng-hao
More informationarxiv:cond-mat/ v1 12 Jan 2001
Jordan Wigner fermionization for spin 1 systems in two dimensions: A brief review arxiv:cond-mat/0101188v1 1 Jan 001 Oleg Derzho Institute for Condensed Matter Physics 1 Svientsitsii Street, L viv 11,
More informationComment on Conjectures on exact solution of three-dimensional (3D) simple orthorhombic Ising lattices
arxiv:0811.1802v2 [cond-mat.stat-mech] 22 Nov 2008 Comment on Conectures on exact solution of three-dimensional (3D) simple orthorhombic Ising lattices Jacques H.H. Perk 145 Physical Sciences, Oklahoma
More informationQuantum Phase Transition
Quantum Phase Transition Guojun Zhu Department of Physics, University of Illinois at Urbana-Champaign, Urbana IL 61801, U.S.A. (Dated: May 5, 2002) A quantum system can undergo a continuous phase transition
More informationMomentum Distribution of a Fragment and Nucleon Removal Cross Section in the Reaction of Halo Nuclei
Commun. Theor. Phys. Beijing, China) 40 2003) pp. 693 698 c International Academic Publishers Vol. 40, No. 6, December 5, 2003 Momentum Distribution of a ragment and Nucleon Removal Cross Section in the
More informationIntroduction to the Mathematics of the XY -Spin Chain
Introduction to the Mathematics of the XY -Spin Chain Günter Stolz June 9, 2014 Abstract In the following we present an introduction to the mathematical theory of the XY spin chain. The importance of this
More information九州工業大学学術機関リポジトリ. Title Chain System: F5PNN in a Magnetic = 1/2 A. Author(s) Hosokoshi, Y; Inoue, K. Issue Date
九州工業大学学術機関リポジトリ Title Specific Heat Study of an S Chain System: F5PNN in a Magnetic = 1/ A F Author(s) Yoshida, Y; Tateiwa, N; Mito, Masak Hosokoshi, Y; Inoue, K Issue Date 005 URL http://hdl.handle.net/108/67
More informationarxiv:cond-mat/ v1 [cond-mat.str-el] 11 Jul 2002
The spin-/2 anisotropic Heisenberg-chain in longitudinal and transversal magnetic fields: a DMRG study. arxiv:cond-mat/27279v [cond-mat.str-el] Jul 22 Felicien Capraro and Claudius Gros Universität des
More informationAn introduction to magnetism in three parts
An introduction to magnetism in three parts Wulf Wulfhekel Physikalisches Institut, Karlsruhe Institute of Technology (KIT) Wolfgang Gaede Str. 1, D-76131 Karlsruhe 0. Overview Chapters of the three lectures
More informationM. A. Gusmão IF-UFRGS
M. A. Gusmão IF-UFRGS - 217 1 FIP164-217/2 Text 9 Mean-field approximation - II Heisenberg Hamiltonian in wave-vector space As we saw in Text 8, the uniform susceptibility does not diverge in the case
More informationFormation Mechanism and Binding Energy for Icosahedral Central Structure of He + 13 Cluster
Commun. Theor. Phys. Beijing, China) 42 2004) pp. 763 767 c International Academic Publishers Vol. 42, No. 5, November 5, 2004 Formation Mechanism and Binding Energy for Icosahedral Central Structure of
More informationStatistical Thermodynamics
Statistical Thermodynamics Basic Theory and Equations: A White Paper Alianna J. Maren, Ph.D. Themasis December, 2013 THM TR2013-001(ajm) 1 Goal of This Paper Identify and present basic equations from statistical
More informationarxiv:cond-mat/ v4 [cond-mat.stat-mech] 19 Jun 2007
arxiv:cond-mat/060065v4 [cond-mat.stat-mech] 9 Jun 007 Restoration of Isotropy in the Ising Model on the Sierpiński Gasket Naoto Yajima Graduate School of Human and Environmental Studies, Kyoto University,
More informationNumerical Analysis of 2-D Ising Model. Ishita Agarwal Masters in Physics (University of Bonn) 17 th March 2011
Numerical Analysis of 2-D Ising Model By Ishita Agarwal Masters in Physics (University of Bonn) 17 th March 2011 Contents Abstract Acknowledgment Introduction Computational techniques Numerical Analysis
More informationPhase transitions and critical phenomena
Phase transitions and critical phenomena Classification of phase transitions. Discontinous (st order) transitions Summary week -5 st derivatives of thermodynamic potentials jump discontinously, e.g. (
More informationSolving the sign problem for a class of frustrated antiferromagnets
Solving the sign problem for a class of frustrated antiferromagnets Fabien Alet Laboratoire de Physique Théorique Toulouse with : Kedar Damle (TIFR Mumbai), Sumiran Pujari (Toulouse Kentucky TIFR Mumbai)
More informationarxiv: v1 [cond-mat.stat-mech] 8 Jul 2017
The boundary effects of transverse field Ising model Yan He College of Physical Science and Technology, arxiv:177.24v1 [cond-mat.stat-mech] 8 Jul 217 Sichuan University, Chengdu, Sichuan 6164, China Hao
More informationProblem set for the course Skálázás és renormálás a statisztikus fizikában, 2014
1 Problem set for the course Skálázás és renormálás a statisztikus fizikában, 014 Rules: You can choose at wish from problems having the same main number (i.e. from a given section), but you can collect
More informationQuantum spin systems - models and computational methods
Summer School on Computational Statistical Physics August 4-11, 2010, NCCU, Taipei, Taiwan Quantum spin systems - models and computational methods Anders W. Sandvik, Boston University Lecture outline Introduction
More informationCritical Values for Electron Pairing in t U J V and t J V Models
Vol. 114 (2008) ACTA PHYSICA POLONICA A No. 1 Proceedings of the XIII National School of Superconductivity, L adek Zdrój 2007 Critical Values for Electron Pairing in t U J V and t J V Models M. Bak Institute
More informationMetropolis Monte Carlo simulation of the Ising Model
Metropolis Monte Carlo simulation of the Ising Model Krishna Shrinivas (CH10B026) Swaroop Ramaswamy (CH10B068) May 10, 2013 Modelling and Simulation of Particulate Processes (CH5012) Introduction The Ising
More informationPhys Midterm. March 17
Phys 7230 Midterm March 17 Consider a spin 1/2 particle fixed in space in the presence of magnetic field H he energy E of such a system can take one of the two values given by E s = µhs, where µ is the
More informationAndreas Kreisel. Institut für Theoretische Physik Johann Wolfgang Goethe Universität Frankfurt am Main. July,
BEC of magnons and spin wave interactions in QAF Andreas Kreisel Institut für Theoretische Physik Johann Wolfgang Goethe Universität Frankfurt am Main July, 18 2007 collaborators: N. Hasselmann, P. Kopietz
More informationShape Coexistence and Band Termination in Doubly Magic Nucleus 40 Ca
Commun. Theor. Phys. (Beijing, China) 43 (2005) pp. 509 514 c International Academic Publishers Vol. 43, No. 3, March 15, 2005 Shape Coexistence and Band Termination in Doubly Magic Nucleus 40 Ca DONG
More informationSpin Superfluidity and Graphene in a Strong Magnetic Field
Spin Superfluidity and Graphene in a Strong Magnetic Field by B. I. Halperin Nano-QT 2016 Kyiv October 11, 2016 Based on work with So Takei (CUNY), Yaroslav Tserkovnyak (UCLA), and Amir Yacoby (Harvard)
More informationarxiv:cond-mat/ v1 30 Jun 1997
Coupled Cluster Treatment of the XY model D.J.J. Farnell, S.E. Krüger and J.B. Parkinson arxiv:cond-mat/9706299v1 30 Jun 1997 Department of Physics, UMIST, P.O.Box 88, Manchester M60 1QD. Abstract We study
More informationSpin Peierls Effect in Spin Polarization of Fractional Quantum Hall States. Surface Science (2) P.1040-P.1046
Title Author(s) Spin Peierls Effect in Spin of Fractional Quantum Hall States Sasaki, Shosuke Citation Surface Science. 566-568(2) P.1040-P.1046 Issue Date 2004-09-20 Text Version author URL http://hdl.handle.net/11094/27149
More informationDecay of correlations in 2d quantum systems
Decay of correlations in 2d quantum systems Costanza Benassi University of Warwick Quantissima in the Serenissima II, 25th August 2017 Costanza Benassi (University of Warwick) Decay of correlations in
More informationWORLD SCIENTIFIC (2014)
WORLD SCIENTIFIC (2014) LIST OF PROBLEMS Chapter 1: Magnetism of Free Electrons and Atoms 1. Orbital and spin moments of an electron: Using the theory of angular momentum, calculate the orbital
More informationPhysics 127b: Statistical Mechanics. Landau Theory of Second Order Phase Transitions. Order Parameter
Physics 127b: Statistical Mechanics Landau Theory of Second Order Phase Transitions Order Parameter Second order phase transitions occur when a new state of reduced symmetry develops continuously from
More informationReal-Space Renormalization Group (RSRG) Approach to Quantum Spin Lattice Systems
WDS'11 Proceedings of Contributed Papers, Part III, 49 54, 011. ISBN 978-80-7378-186-6 MATFYZPRESS Real-Space Renormalization Group (RSRG) Approach to Quantum Spin Lattice Systems A. S. Serov and G. V.
More informationDepartment of Physics, Princeton University. Graduate Preliminary Examination Part II. Friday, May 10, :00 am - 12:00 noon
Department of Physics, Princeton University Graduate Preliminary Examination Part II Friday, May 10, 2013 9:00 am - 12:00 noon Answer TWO out of the THREE questions in Section A (Quantum Mechanics) and
More informationQuantum Correlation in Matrix Product States of One-Dimensional Spin Chains
Commun. Theor. Phys. 6 (015) 356 360 Vol. 6, No. 3, September 1, 015 Quantum Correlation in Matrix Product States of One-Dimensional Spin Chains ZHU Jing-Min ( ) College of Optoelectronics Technology,
More informationThermodynamic and transport properties of infinite U Hubbard model
Journal of Physics: Conference Series Thermodynamic and transport properties of infinite U Hubbard model To cite this article: R Kishore and A K Mishra 200 J. Phys.: Conf. Ser. 200 02085 View the article
More informationarxiv: v2 [quant-ph] 12 Aug 2008
Complexity of thermal states in quantum spin chains arxiv:85.449v [quant-ph] Aug 8 Marko Žnidarič, Tomaž Prosen and Iztok Pižorn Department of physics, FMF, University of Ljubljana, Jadranska 9, SI- Ljubljana,
More informationConstructing Landau Formalism for Topological Order: Spin Chains and Ladders
Constructing Landau Formalism for Topological Order: Spin Chains and Ladders Gennady Y. Chitov Laurentian University Sudbury, Canada Talk at Washington University in St. Louis, October 20, 2016 Collaborators:
More informationThermal conductivity of anisotropic spin ladders
Thermal conductivity of anisotropic spin ladders By :Hamed Rezania Razi University, Kermanshah, Iran Magnetic Insulator In one dimensional is a good candidate for thermal conductivity due to magnetic excitation
More informationQuantum Effect in a Diode Included Nonlinear Inductance-Capacitance Mesoscopic Circuit
Commun. Theor. Phys. (Beijing, China) 52 (2009) pp. 534 538 c Chinese Physical Society and IOP Publishing Ltd Vol. 52, No. 3, September 15, 2009 Quantum Effect in a Diode Included Nonlinear Inductance-Capacitance
More informationDecimation Technique on Sierpinski Gasket in External Magnetic Field
Egypt.. Solids, Vol. (), No. (), (009 ) 5 Decimation Technique on Sierpinski Gasket in External Magnetic Field Khalid Bannora, G. Ismail and M. Abu Zeid ) Mathematics Department, Faculty of Science, Zagazig
More informationRational Form Solitary Wave Solutions and Doubly Periodic Wave Solutions to (1+1)-Dimensional Dispersive Long Wave Equation
Commun. Theor. Phys. (Beijing, China) 43 (005) pp. 975 98 c International Academic Publishers Vol. 43, No. 6, June 15, 005 Rational Form Solitary Wave Solutions and Doubly Periodic Wave Solutions to (1+1)-Dimensional
More informationThe Quantum Heisenberg Ferromagnet
The Quantum Heisenberg Ferromagnet Soon after Schrödinger discovered the wave equation of quantum mechanics, Heisenberg and Dirac developed the first successful quantum theory of ferromagnetism W. Heisenberg,
More informationPHYSICAL REVIEW LETTERS
PHYSICAL REVIEW LETTERS VOLUME 76 4 MARCH 1996 NUMBER 10 Finite-Size Scaling and Universality above the Upper Critical Dimensionality Erik Luijten* and Henk W. J. Blöte Faculty of Applied Physics, Delft
More informationScaling Theory. Roger Herrigel Advisor: Helmut Katzgraber
Scaling Theory Roger Herrigel Advisor: Helmut Katzgraber 7.4.2007 Outline The scaling hypothesis Critical exponents The scaling hypothesis Derivation of the scaling relations Heuristic explanation Kadanoff
More informationarxiv:quant-ph/ v1 21 Nov 2003
Analytic solutions for quantum logic gates and modeling pulse errors in a quantum computer with a Heisenberg interaction G.P. Berman 1, D.I. Kamenev 1, and V.I. Tsifrinovich 2 1 Theoretical Division and
More informationJ ij S i S j B i S i (1)
LECTURE 18 The Ising Model (References: Kerson Huang, Statistical Mechanics, Wiley and Sons (1963) and Colin Thompson, Mathematical Statistical Mechanics, Princeton Univ. Press (1972)). One of the simplest
More informationPhase transitions in the complex plane of physical parameters
Phase transitions in the complex plane of physical parameters Bo-Bo Wei, Shao-Wen Chen, Hoi-Chun Po & Ren-Bao Liu* Department of Physics, Centre for Quantum Coherence, and nstitute of Theoretical Physics,
More informationBilliard ball model for structure factor in 1-D Heisenberg anti-ferromagnets
Billiard ball model for structure factor in 1-D Heisenberg anti-ferromagnets Shreyas Patankar 1 Chennai Mathematical Institute August 5, 2010 1 Project with Prof. Kedar Damle, TIFR and Girish Sharma, Satyasai
More informationarxiv:cond-mat/ Jan 2000
arxiv:cond-mat/0001144 11 Jan 000 Macroscopic Quantum Phase Interference in Antiferromagnetic Particles Yi-Hang Nie 1,Yan-Hong Jin 1 5, J.-Q.Liang 1 3,H.J.W.Muller-Kirsten 3,D.K.Park 3 4,F.-C.Pu 5 6 1
More informationNumerical diagonalization studies of quantum spin chains
PY 502, Computational Physics, Fall 2016 Anders W. Sandvik, Boston University Numerical diagonalization studies of quantum spin chains Introduction to computational studies of spin chains Using basis states
More informationBose Description of Pauli Spin Operators and Related Coherent States
Commun. Theor. Phys. (Beijing, China) 43 (5) pp. 7 c International Academic Publishers Vol. 43, No., January 5, 5 Bose Description of Pauli Spin Operators and Related Coherent States JIANG Nian-Quan,,
More informationVIC Effect and Phase-Dependent Optical Properties of Five-Level K-Type Atoms Interacting with Coherent Laser Fields
Commun. Theor. Phys. (Beijing China) 50 (2008) pp. 741 748 c Chinese Physical Society Vol. 50 No. 3 September 15 2008 VIC Effect and Phase-Dependent Optical Properties of Five-Level K-Type Atoms Interacting
More informationPhase diagrams of mixtures of flexible polymers and nematic liquid crystals in a field
PHYSICAL REVIEW E VOLUME 58, NUMBER 5 NOVEMBER 998 Phase diagrams of mixtures of flexible polymers and nematic liquid crystals in a field Zhiqun Lin, Hongdong Zhang, and Yuliang Yang,, * Laboratory of
More information74 JIN Meng and LI Jia-Rong Vol. 39 From the path integral principle, the partition function can be written in the following form [13] = [d ][d ][d][d
Commun. Theor. Phys. (Beijing, China) 39 (23) pp. 73{77 c International Academic Publishers Vol. 39, No. 1, January 15, 23 Inuence of Vacuum Eect on Behavior of Hot/Dense Nulcear Matter JIN Meng y and
More informationOptical time-domain differentiation based on intensive differential group delay
Optical time-domain differentiation based on intensive differential group delay Li Zheng-Yong( ), Yu Xiang-Zhi( ), and Wu Chong-Qing( ) Key Laboratory of Luminescence and Optical Information of the Ministry
More information4 Surfaces and Interfaces
Sction 4 Surfaces and Interfaces Chapter 1 Statistical Mechanics of Surface Systems and Quantum- Correlated Systems Chapter 2 Synchrotron X-Ray Studies of Surface Disordering Chapter 3 Chemical Reaction
More informationarxiv: v1 [quant-ph] 2 Nov 2018
Entanglement and Measurement-induced quantum correlation in Heisenberg spin models arxiv:1811.733v1 [quant-ph] 2 Nov 218 Abstract Indrajith V S, R. Muthuganesan, R. Sankaranarayanan Department of Physics,
More informationarxiv:cond-mat/ v1 [cond-mat.stat-mech] 14 Mar 2006
Condensed Matter Physics, 2?, Vol.?, No?, pp. 1?? arxiv:cond-mat/63377v1 [cond-mat.stat-mech] 14 Mar 26 1. Introduction The effect of uniaxial crystal-field anisotropy on magnetic properties of the superexchange
More informationarxiv:cond-mat/ v1 [cond-mat.str-el] 7 Dec 2006
Nature of the Quantum Phase Transition in Quantum Compass Model Han-Dong Chen Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 6181 Chen Fang and iangping Hu Department of
More informationarxiv: v1 [cond-mat.stat-mech] 22 Sep 2009
Phase diagram and critical behavior of the square-lattice Ising model with competing nearest- and next-nearest-neighbor interactions Junqi Yin and D. P. Landau Center for Simulational Physics, University
More information