Geometric responses of Quantum Hall systems
|
|
- Winifred O’Brien’
- 5 years ago
- Views:
Transcription
1 Geometric responses of Quantum Hall systems Alexander Abanov December 14, 2015 Cologne Geometric Aspects of the Quantum Hall Effect
2 Fractional Quantum Hall state exotic fluid Two-dimensional electron gas in magnetic field forms a new type of quantum fluid It can be understood as quantum condensation of electrons coupled to vortices/fluxes Quasiparticles are gapped, have fractional charge and statistics The fluid is ideal no dissipation! Density is proportional to vorticity! Transverse transport: Hall conductivity and Hall viscosity, thermal Hall effect Protected chiral dynamics at the boundary
3 Transverse transport Signature of FQH states quantization and robustness of Hall conductance σ H j i = σ H ɛ ij E j, σ H = ν e2 h - Hall conductivity. Are there other universal transverse transport coefficients? Hall viscosity: transverse momentum transport Thermal Hall conductivity: transverse energy/heat transport What are the values of the corresponding kinetic coefficients for various FQH states? Are there corresponding protected boundary modes?
4 Acknowledgments and References A. G. Abanov and A. Gromov, Phys. Rev. B 90, (2014). Electromagnetic and gravitational responses of two-dimensional noninteracting electrons in a background magnetic field. A. Gromov and A. G. Abanov, Phys. Rev. Lett. 113, (2014). Density-Curvature Response and Gravitational Anomaly. A. Gromov and A. G. Abanov, Phys. Rev. Lett. 114, (2015). Thermal Hall Effect and Geometry with Torsion. A. Gromov, G. Cho, Y. You, A. G. Abanov, and E. Fradkin, Phys. Rev. Lett. 114, (2015). Framing Anomaly in the Effective Theory of the Fractional Quantum Hall Effect. A. Gromov, K. Jensen, and A.G. Abanov, arxiv: (2015). Boundary effective action for quantum Hall states.
5 Essential points of the talk Induced Action encodes linear responses of the system Coefficients of geometric terms of the induced action universal transverse responses. Hall conductivity, Hall viscosity, thermal Hall conductivity. These coefficients are computed for various FQH states. Framing anomaly is crucial in obtaining the correct gravitational Chern-Simons term!
6 Induced action Partition function of fermions in external e/m field A µ is: Z = DψDψ e is[ψ,ψ ;A µ] = e is ind[a µ] with S[ψ, ψ ; A µ ] = [ d 2 x dt ψ i t + ea 0 1 2m + interactions ( i e c A ) 2 ] ψ Induced action encodes current-current correlation functions j µ = δs ind δa µ, j µ j ν = δ2 S ind δa µ δa ν,... + various limits m 0, e 2 /l B,...
7 Induced action [phenomenological] Use general principles: gap+symmetries to find the form of S ind Locality expansion in gradients of A µ Gauge invariance written in terms of E and B Other symmetries: rotational, translational,... S ind = ν 4π AdA + d 2 x dt [ ɛ 2 E2 1 ] 2µ B2 + σb E +... Find responses in terms of phenomenological parameters ν, ɛ, µ, σ,... Compute these parameters from the underlying theory. For non-interacting particles in B with ν = N see AA, Gromov Any functional of E and B is gauge invariant, but...
8 Chern-Simons action S CS = ν 4π AdA
9 Linear responses from the Chern-Simons action In components S CS = ν 4π = ν 4π AdA ν d 2 x dt ɛ µνλ A µ ν A λ 4π [ ] d 2 x dt A 0 ( 1 A 2 2 A 1 ) +... Varying over A µ ρ = δs CS δa 0 = ν 2π B, j 1 = δs CS δa 1 = ν 2π E 2, We have: σ H = ν 2π and σ H = ρ B Streda formula.
10 Properties of the Chern-Simons term Gauge invariant in the absence of the boundary (allowed in the induced action) Not invariant in the presence of the boundary Leads to protected gapless edge modes First order in derivatives (more relevant than F µν F µν, B 2 or E 2 at large distances) Relativistically invariant (accidentally!!!) Does not depend on metric g µν (topological, does not contribute to the stress-energy tensor)
11 Elastic responses: Strain and Metric Deformation of solid or fluid r r + u(r) u(r) - displacement vector u ik = 1 2 ( ku i + i u k ) - strain tensor u ik plays a role of the deformation metric deformation metric g ik δ ik + 2u ik with ds 2 = g ik dx i dx k stress tensor T ij - response to the deformation metric g ij
12 Stress tensor and induced action Studying responses Microscopic model S = S[ψ] Introduce gauge field and metric background S[ψ, A, g] Integrate out matter degrees of freedom and obtain and S ind [A, g] Obtain E/M, elastic, and mixed responses from δs ind = dx dt g (j µ δa µ + 12 ) T ij δg ij Elastic responses = gravitational responses Important: stress is present even in flat space!
13 Quantum Hall in Geometric Background (by Gil Cho) e e e e = electron = magnetic field
14 Geometric background For 2+1 dimensions and spatial metric g ij we introduce spin connection ω µ so that 1 gr 2 = 1 ω 2 2 ω 1 gravi-magnetic field, E i = ω i i ω 0 gravi-electric field, For small deviations from flat space g ik = δ ik + δg ik we have explicitly ω 0 = 1 2 ɛjk δg ij ġ ik, ω i = 1 2 ɛjk j δg ik Close analogy with E/M fields A µ ω µ!
15 Geometric terms of the induced action Terms of the lowest order in derivatives S ind = ν 4π Geometric terms: [ AdA + 2 s ωda + β ωdω]. AdA Chern-Simons term (ν: Hall conductance, filling factor) ωda Wen-Zee term ( s: orbital spin, Hall viscosity, Shift) ωdω gravitational CS term (β : Hall viscosity - curvature, thermal Hall effect, orbital spin variance) In the presence of the boundary β can be divided into chiral central charge c and s 2 (Bradlyn, Read, 2014). The latter does not correspond to an anomaly. (Gromov, Jensen, AA, 2015)
16 The Wen-Zee term Responses from the Wen-Zee term S W Z = ν s ωda. 2π Emergent spin (orbital spin) s ν (A + sω)d(a + sω) 4π Wen-Zee shift for sphere δn = νs; S = 2 s ν s 2π A 0dω δρ = ν s ν s dω δn = d 2 x gr = ν sχ = ν s(2 2g) 2π 4π Hall viscosity (per particle) η H = s 2 n e: ν s Bν s ωda 2π 2π ω s 0 = n e sω 0 = n e 2 ɛjk δg ij ġ ik
17 Hall viscosity Gradient correction to the stress tensor T ik = η H (ɛ in v nk + ɛ kn v ni ), where v ik = 1 2 ( iv k + k v i ) = 1 2ġik strain rate (a) Shear viscosity (b) η H Hall viscosity picture from Lapa, Hughes, 2013 Avron, Seiler, Zograf, 1995
18 Obtaining the effective field theory for FQH states Reduce problem to noninteracting fermions with ν - integer interacting with statistical Abelian and non-abelian gauge fields. Can be done, e.g., by flux attachment or parton construction (Zhang, Hansson, Kivelson, 1989; Wen, 1991; Cho, You, Fradkin, 2014) Integrate out fermions and obtain the effective action S[a, A, g] using the results for free fermions. (AA, Gromov, 2014) Integrate out statistical gauge fields taking into account the framing anomaly. (Gromov et al., 2015) Obtain the induced action S geom ind [A, g] and study the corresponding responses.
19 Flux attachment in geometric background Cho, You, Fradkin, 2014 Flux attachment is based on the identity: { Db Da exp i 2p bdb i 1 4π 2π adb + i L } (a + pω) Here L is a link. The last term pω is due to the framing regularization (Polyakov, 1988). Integrating over b (wrong!) { 1 Da exp i ada + i (2p)2π L } (a + pω) = 1 = 1 Integrating over b (correct!) { 1 Da exp i ada + i (a + pω) i 1 (2p)2π 48π L } ωdω = 1 Integrating over b (correct!) { 1 1 }
20 Explicit calculation for free fermions at ν = N Starting point S[ψ, ψ ; A µ, g ij ] = dt d 2 x [ g ψ i ] D t 2 2m gij (D i ψ) (D j ψ). Straightforward computation at ν = N (Gromov, AA, 2014) S (geom) eff = N 4π ( AdA + N Adω + 2N or equivalently (as a sum over Landau levels) S (geom) eff = N n=1 ) ωdω [ 1 4π (A + s nω)d(a + s n ω) c ] 48π ωdω s n = 2n 1 2, c = 1.
21 Geometric effective action for ν = 1 [ S (geom) 1 eff = (A + 12 ) 4π ω d (A + 12 ) ω 1 ] 48π ωdω Is there an intuitive way to obtain this result?
22 The Wen-Zee construction for ν = 1 Integrate out fermions but leave currents j = 1 2π da (Wen, Zee, 1992) S[a; A, ω] = 1 [ ada + 2 (A + 12 ) ] 4π ω da. (Wen, Zee, 1992) + framing anomaly: solve for a: a = ( A ω) substitute back into the action take into account framing anomaly (Gromov et.al., 2015) S ind = 1 (A + 12 ) 4π ω d (A + 12 ) ω 1 48π ωdω
23 Digression: the quantum Chern-Simons theory The partition function for Chern-Simons theory in the metric background (Witten, 1989) { Da exp i k } { c ada = exp i tr (ΓdΓ + 23 )} 4π 96π Γ3 { } c = exp i ωdω, 48π where c = sgn(k) and the last equality is correct for our background. We specialized Witten s results to the Abelian CS theory The result is obtained from the fluctuation determinant det(d) The dependence on metric comes from the gauge fixing dv φd µ a µ Action does not depend on metric, path integral does: anomaly (framing anomaly)
24 Consistency check (for ν = 1) Basic idea: two routes to effective action. Route 1: Route 2: 1 4π S 0 [ψ; A, g] 1 4π (A + 12 ) ω d (A + 12 ) ω 1 48π ωdω S 0 [ψ; A, g] S 0 [ψ; A + a + ω, g] + 1 8π ada 1 48π ωdω Introducing A = A + a + ω (A 12 ) ω d 1 4π (A + 12 ω ) d (A 12 ω ) π ωdω + 1 8π ada 1 48π ωdω (A + 12 ) ω π ωdω π ωdω Consistent only if the framing anomaly is taken into account (twice)!
25 Obtaining the effective field theory for FQH states Reduce problem to noninteracting fermions with ν - integer interacting with statistical Abelian and non-abelian gauge fields. Can be done, e.g., by flux attachment or parton construction (Zhang, Hansson, Kivelson, 1989; Wen, 1991; Cho, You, Fradkin, 2014) Integrate out fermions and obtain the effective action S[a, A, g] using the results for free fermions. (Gromov, AA, 2014) Integrate out statistical gauge fields taking into account the framing anomaly. (Gromov et al., 2015) Obtain the induced action S geom ind [A, g] and study the corresponding responses.
26 Example: Laughlin s states Flux attachment for Laughlin s states ν = 1 2m+1 [ 2m S 0 [ψ, A + a + mω, g] 4π bdb + 1 ] 2π adb Integrating out ψ, a, b ( S geom 1 1 ind = A + 2m + 1 ω 4π 2m Coefficients ν = ) ( d A + 2m + 1 ω 2 1 2m + 1, s =, c = 1. 2m ) 1 48π ωdω
27 Other states Geometric effective actions have been obtained for: Free fermions at ν = N Laughlin s states Jain series Arbitrary Abelian QH states Read-Rezayi non-abelian states The method can be applied to other FQH states A. Gromov et.al., PRL 114, (2015). Framing Anomaly in the Effective Theory of the Fractional Quantum Hall Effect.
28 Consequences of the gravitational CS term S gcs = c 96π tr (ΓdΓ + 23 ) Γ3 = c 48π ωdω. 1. From CS and WZ term [shift] (Wen, Zee, 1992) n = ν 2π B + ν s 4π R N = ν(n φ + sχ) From WZ and gcs term [Hall viscosity shift] (Gromov, AA, 2014 cf. Hughes, Leigh, Parrikar, 2013) η H = s 2 n c R 24 4π 2. Thermal Hall effect [from the boundary!] (Kane, Fisher, 1996; Read, Green, 2000; Cappelli, Huerta, Zemba, 2002) K H = c πk2 B T 6.
29 Some recent closely related works Geometric terms from adiabatic transport and adiabatic deformations of trial FQH wave functions (Bradlyn, Read, 2015; Klevtsov, Wiegmann, 2015) QH wave functions in geometric backgrounds (Can, Laskin, Wiegmann, 2014; Klevtsov, Ma, Marinescu, Wiegmann, 2015) Newton-Cartan geometric background and Galilean invariance (Hoyos, Son, 2011; Gromov, AA, 2014; Jensen, 2014) Thermal transport in quantum Hall systems (Geracie, Son, Wu, Wu, 2014; Gromov, AA, 2014; Bradlyn, Read, 2014)
30 Main results Response functions can be encoded in the form of the induced action for FQHE. S ind = ν [ (A + sω)d(a + sω) + βωdω] 4π c tr [ΓdΓ + 23 ] 96π Γ3 +..., where ν is the filling fraction, s is the average orbital spin, β is the orbital spin variance, and c is the chiral central charge. The coefficients ν, s, β, c are computed for various known Abelian and non-abelian FQH states. Framing anomaly is crucial in obtaining the correct gravitational Chern-Simons term!
31 Quantum Hall at the Edge (by Gil Cho)
Multipole Expansion in the Quantum Hall Effect
Multipole Expansion in the Quantum Hall Effect Andrea Cappelli (INFN and Physics Dept., Florence) with E. Randellini (Florence) Outline Chern-Simons effective action: bulk and edge Wen-Zee term: shift
More informationThe Geometry of the Quantum Hall Effect
The Geometry of the Quantum Hall Effect Dam Thanh Son (University of Chicago) Refs: Carlos Hoyos, DTS arxiv:1109.2651 DTS, M.Wingate cond-mat/0509786 Plan Review of quantum Hall physics Summary of results
More informationNematic Order and Geometry in Fractional Quantum Hall Fluids
Nematic Order and Geometry in Fractional Quantum Hall Fluids Eduardo Fradkin Department of Physics and Institute for Condensed Matter Theory University of Illinois, Urbana, Illinois, USA Joint Condensed
More informationBraid Group, Gauge Invariance and Topological Order
Braid Group, Gauge Invariance and Topological Order Yong-Shi Wu Department of Physics University of Utah Topological Quantum Computing IPAM, UCLA; March 2, 2007 Outline Motivation: Topological Matter (Phases)
More informationField Theory Description of Topological States of Matter. Andrea Cappelli INFN, Florence (w. E. Randellini, J. Sisti)
Field Theory Description of Topological States of Matter Andrea Cappelli INFN, Florence (w. E. Randellini, J. Sisti) Topological States of Matter System with bulk gap but non-trivial at energies below
More informationEffective Field Theories of Topological Insulators
Effective Field Theories of Topological Insulators Eduardo Fradkin University of Illinois at Urbana-Champaign Workshop on Field Theoretic Computer Simulations for Particle Physics and Condensed Matter
More informationGravitational response of the Quantum Hall effect
Gravitational response of the Quantum Hall effect Semyon Klevtsov University of Cologne arxiv:1309.7333, JHEP01(2014)133 () Gravitational response of QHE Bad Honnef 30.05.14 1 / 18 Gravitational response
More informationIs the composite fermion a Dirac particle?
Is the composite fermion a Dirac particle? Dam T. Son GGI conference Gauge/gravity duality 2015 Ref.: 1502.03446 Plan Plan Fractional quantum Hall effect Plan Fractional quantum Hall effect Composite fermion
More informationInteger quantum Hall effect for bosons: A physical realization
Integer quantum Hall effect for bosons: A physical realization T. Senthil (MIT) and Michael Levin (UMCP). (arxiv:1206.1604) Thanks: Xie Chen, Zhengchen Liu, Zhengcheng Gu, Xiao-gang Wen, and Ashvin Vishwanath.
More informationIs the composite fermion a Dirac particle?
Is the composite fermion a Dirac particle? Dam T. Son (University of Chicago) Cold atoms meet QFT, 2015 Ref.: 1502.03446 Plan Plan Composite fermion: quasiparticle of Fractional Quantum Hall Effect (FQHE)
More informationNon-Abelian Statistics. in the Fractional Quantum Hall States * X. G. Wen. School of Natural Sciences. Institute of Advanced Study
IASSNS-HEP-90/70 Sep. 1990 Non-Abelian Statistics in the Fractional Quantum Hall States * X. G. Wen School of Natural Sciences Institute of Advanced Study Princeton, NJ 08540 ABSTRACT: The Fractional Quantum
More informationPhysics 250 Fall 2014: Set 4 of lecture notes
Physics 250 Fall 2014: Set 4 of lecture notes Joel E. Moore, UC Berkeley and LBNL (Dated: October 13, 2014) I. FRACTIONAL QUANTUM HALL BASICS (VERY BRIEF) FQHE background: in class we gave some standard
More informationTopological Insulators in 3D and Bosonization
Topological Insulators in 3D and Bosonization Andrea Cappelli, INFN Florence (w. E. Randellini, J. Sisti) Outline Topological states of matter: bulk and edge Fermions and bosons on the (1+1)-dimensional
More information2-Group Global Symmetry
2-Group Global Symmetry Clay Córdova School of Natural Sciences Institute for Advanced Study April 14, 2018 References Based on Exploring 2-Group Global Symmetry in collaboration with Dumitrescu and Intriligator
More informationHall Viscosity of Hierarchical Quantum Hall States
M. Fremling, T. H. Hansson, and J. Suorsa ; Phys. Rev. B 89 125303 Mikael Fremling Fysikum Stockholm University, Sweden Nordita 9 October 2014 Outline 1 Introduction Fractional Quantum Hall Eect 2 Quantum
More informationConstraints on Fluid Dynamics From Equilibrium Partition Func
Constraints on Fluid Dynamics From Equilibrium Partition Function Nabamita Banerjee Nikhef, Amsterdam LPTENS, Paris 1203.3544, 1206.6499 J. Bhattacharya, S. Jain, S. Bhattacharyya, S. Minwalla, T. Sharma,
More informationSuperinsulator: a new topological state of matter
Superinsulator: a new topological state of matter M. Cristina Diamantini Nips laboratory, INFN and Department of Physics and Geology University of Perugia Coll: Igor Lukyanchuk, University of Picardie
More informationGeometric Aspects of Quantum Hall States
Geometric Aspects of Quantum Hall States ADissertationPresented by Andrey Gromov to The Graduate School in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Physics Stony
More informationCondensed Matter Physics and the Nature of Spacetime
Condensed Matter Physics and the Nature of Spacetime Jonathan Bain Polytechnic University Prospects for modeling spacetime as a phenomenon that emerges in the low-energy limit of a quantum liquid. 1. EFTs
More informationConformal Field Theory of Composite Fermions in the QHE
Conformal Field Theory of Composite Fermions in the QHE Andrea Cappelli (INFN and Physics Dept., Florence) Outline Introduction: wave functions, edge excitations and CFT CFT for Jain wfs: Hansson et al.
More informationarxiv:hep-th/ v2 31 Jul 2000
Hopf term induced by fermions Alexander G. Abanov 12-105, Department of Physics, MIT, 77 Massachusetts Ave., Cambridge, MA 02139, U.S.A. arxiv:hep-th/0005150v2 31 Jul 2000 Abstract We derive an effective
More informationFrom Luttinger Liquid to Non-Abelian Quantum Hall States
From Luttinger Liquid to Non-Abelian Quantum Hall States Jeffrey Teo and C.L. Kane KITP workshop, Nov 11 arxiv:1111.2617v1 Outline Introduction to FQHE Bulk-edge correspondence Abelian Quantum Hall States
More informationThe Dirac composite fermions in fractional quantum Hall effect. Dam Thanh Son (University of Chicago) Nambu Memorial Symposium March 12, 2016
The Dirac composite fermions in fractional quantum Hall effect Dam Thanh Son (University of Chicago) Nambu Memorial Symposium March 12, 2016 A story of a symmetry lost and recovered Dam Thanh Son (University
More informationKai Sun. University of Michigan, Ann Arbor. Collaborators: Krishna Kumar and Eduardo Fradkin (UIUC)
Kai Sun University of Michigan, Ann Arbor Collaborators: Krishna Kumar and Eduardo Fradkin (UIUC) Outline How to construct a discretized Chern-Simons gauge theory A necessary and sufficient condition for
More informationFractional quantum Hall effect and duality. Dam Thanh Son (University of Chicago) Strings 2017, Tel Aviv, Israel June 26, 2017
Fractional quantum Hall effect and duality Dam Thanh Son (University of Chicago) Strings 2017, Tel Aviv, Israel June 26, 2017 Plan Fractional quantum Hall effect Halperin-Lee-Read (HLR) theory Problem
More informationTopological Bandstructures for Ultracold Atoms
Topological Bandstructures for Ultracold Atoms Nigel Cooper Cavendish Laboratory, University of Cambridge New quantum states of matter in and out of equilibrium GGI, Florence, 12 April 2012 NRC, PRL 106,
More informationVacuum degeneracy of chiral spin states in compactified. space. X.G. Wen
Vacuum degeneracy of chiral spin states in compactified space X.G. Wen Institute for Theoretical Physics University of California Santa Barbara, California 93106 ABSTRACT: A chiral spin state is not only
More informationFractional quantum Hall effect and duality. Dam T. Son (University of Chicago) Canterbury Tales of hot QFTs, Oxford July 11, 2017
Fractional quantum Hall effect and duality Dam T. Son (University of Chicago) Canterbury Tales of hot QFTs, Oxford July 11, 2017 Plan Plan General prologue: Fractional Quantum Hall Effect (FQHE) Plan General
More informationMassive and Newton-Cartan Gravity in Action
Massive and Newton-Cartan Gravity in Action Eric Bergshoeff Groningen University The Ninth Aegean Summer School on Einstein s Theory of Gravity and its Modifications: From Theory to Observations based
More informationInti Sodemann (MIT) Séptima Escuela de Física Matemática, Universidad de Los Andes, Bogotá, Mayo 25, 2015
Inti Sodemann (MIT) Séptima Escuela de Física Matemática, Universidad de Los Andes, Bogotá, Mayo 25, 2015 Contents Why are the fractional quantum Hall liquids amazing! Abelian quantum Hall liquids: Laughlin
More informationTopological Properties of Quantum States of Condensed Matter: some recent surprises.
Topological Properties of Quantum States of Condensed Matter: some recent surprises. F. D. M. Haldane Princeton University and Instituut Lorentz 1. Berry phases, zero-field Hall effect, and one-way light
More informationEntanglement in Topological Phases
Entanglement in Topological Phases Dylan Liu August 31, 2012 Abstract In this report, the research conducted on entanglement in topological phases is detailed and summarized. This includes background developed
More informationUniversal phase transitions in Topological lattice models
Universal phase transitions in Topological lattice models F. J. Burnell Collaborators: J. Slingerland S. H. Simon September 2, 2010 Overview Matter: classified by orders Symmetry Breaking (Ferromagnet)
More informationA sky without qualities
A sky without qualities New boundaries for SL(2)xSL(2) Chern-Simons theory Bo Sundborg, work with Luis Apolo Stockholm university, Department of Physics and the Oskar Klein Centre August 27, 2015 B Sundborg
More informationQuantum Fields in Curved Spacetime
Quantum Fields in Curved Spacetime Lecture 3 Finn Larsen Michigan Center for Theoretical Physics Yerevan, August 22, 2016. Recap AdS 3 is an instructive application of quantum fields in curved space. The
More informationMatrix product states for the fractional quantum Hall effect
Matrix product states for the fractional quantum Hall effect Roger Mong (California Institute of Technology) University of Virginia Feb 24, 2014 Collaborators Michael Zaletel UC Berkeley (Stanford/Station
More information8.821 String Theory Fall 2008
MIT OpenCourseWare http://ocw.mit.edu 8.821 String Theory Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. 8.821 F2008 Lecture 03: The decoupling
More informationNonabelian hierarchies
Nonabelian hierarchies collaborators: Yoran Tournois, UzK Maria Hermanns, UzK Hans Hansson, SU Steve H. Simon, Oxford Susanne Viefers, UiO Quantum Hall hierarchies, arxiv:1601.01697 Outline Haldane-Halperin
More informationPreface Introduction to the electron liquid
Table of Preface page xvii 1 Introduction to the electron liquid 1 1.1 A tale of many electrons 1 1.2 Where the electrons roam: physical realizations of the electron liquid 5 1.2.1 Three dimensions 5 1.2.2
More informationThe uses of Instantons for classifying Topological Phases
The uses of Instantons for classifying Topological Phases - anomaly-free and chiral fermions Juven Wang, Xiao-Gang Wen (arxiv:1307.7480, arxiv:140?.????) MIT/Perimeter Inst. 2014 @ APS March A Lattice
More informationDeconfined Quantum Critical Points
Deconfined Quantum Critical Points Leon Balents T. Senthil, MIT A. Vishwanath, UCB S. Sachdev, Yale M.P.A. Fisher, UCSB Outline Introduction: what is a DQCP Disordered and VBS ground states and gauge theory
More informationNon-Abelian Anyons in the Quantum Hall Effect
Non-Abelian Anyons in the Quantum Hall Effect Andrea Cappelli (INFN and Physics Dept., Florence) with L. Georgiev (Sofia), G. Zemba (Buenos Aires), G. Viola (Florence) Outline Incompressible Hall fluids:
More informationThe Half-Filled Landau Level
Nigel Cooper Department of Physics, University of Cambridge Celebration for Bert Halperin s 75th January 31, 2017 Chong Wang, Bert Halperin & Ady Stern. [C. Wang, NRC, B. I. Halperin & A. Stern, arxiv:1701.00007].
More informationA Brief Introduction to Duality Web
A Brief Introduction to Duality Web WeiHan Hsiao a a Department of Physics, The University of Chicago E-mail: weihanhsiao@uchicago.edu Abstract: This note is prepared for the journal club talk given on
More informationcan be moved in energy/momentum but not individually destroyed; in general: topological Fermi surfaces
nodes protected against gapping can be moved in energy/momentum but not individually destroyed; in general: topological Fermi surfaces physical realization: stacked 2d topological insulators C=1 3d top
More informationDefects in topologically ordered states. Xiao-Liang Qi Stanford University Mag Lab, Tallahassee, 01/09/2014
Defects in topologically ordered states Xiao-Liang Qi Stanford University Mag Lab, Tallahassee, 01/09/2014 References Maissam Barkeshli & XLQ, PRX, 2, 031013 (2012) Maissam Barkeshli, Chaoming Jian, XLQ,
More informationTopological insulators
http://www.physik.uni-regensburg.de/forschung/fabian Topological insulators Jaroslav Fabian Institute for Theoretical Physics University of Regensburg Stara Lesna, 21.8.212 DFG SFB 689 what are topological
More informationClassification of Symmetry Protected Topological Phases in Interacting Systems
Classification of Symmetry Protected Topological Phases in Interacting Systems Zhengcheng Gu (PI) Collaborators: Prof. Xiao-Gang ang Wen (PI/ PI/MIT) Prof. M. Levin (U. of Chicago) Dr. Xie Chen(UC Berkeley)
More informationTopological insulators. Pavel Buividovich (Regensburg)
Topological insulators Pavel Buividovich (Regensburg) Hall effect Classical treatment Dissipative motion for point-like particles (Drude theory) Steady motion Classical Hall effect Cyclotron frequency
More informationApplied Newton-Cartan Geometry: A Pedagogical Review
Applied Newton-Cartan Geometry: A Pedagogical Review Eric Bergshoeff Groningen University 10th Nordic String Meeting Bremen, March 15 2016 Newtonian Gravity Free-falling frames: Galilean symmetries Earth-based
More informationSpectral Action from Anomalies
Spectral Action from Anomalies Fedele Lizzi Università di Napoli Federico II and Insitut de Ciencies del Cosmo, Universitat de Barcelona Work in collaboration with A.A. Andrianov & M. Kurkov (St. Petersburg)
More informationExchange statistics. Basic concepts. University of Oxford April, Jon Magne Leinaas Department of Physics University of Oslo
University of Oxford 12-15 April, 2016 Exchange statistics Basic concepts Jon Magne Leinaas Department of Physics University of Oslo Outline * configuration space with identifications * from permutations
More informationSupersymmetric Mirror Duality and Half-filled Landau level S. Kachru, M Mulligan, G Torroba and H. Wang Phys.Rev.
Supersymmetric Mirror Duality and Half-filled Landau level S. Kachru, M Mulligan, G Torroba and H. Wang Phys.Rev. B92 (2015) 235105 Huajia Wang University of Illinois Urbana Champaign Introduction/Motivation
More informationGauge/Gravity Duality: Applications to Condensed Matter Physics. Johanna Erdmenger. Julius-Maximilians-Universität Würzburg
Gauge/Gravity Duality: Applications to Condensed Matter Physics. Johanna Erdmenger Julius-Maximilians-Universität Würzburg 1 New Gauge/Gravity Duality group at Würzburg University Permanent members 2 Gauge/Gravity
More informationField Theory Description of Topological States of Matter
Field Theory Description of Topological States of Matter Andrea Cappelli, INFN Florence (w. E. Randellini, J. Sisti) Outline Topological states of matter Quantum Hall effect: bulk and edge Effective field
More informationXiao-Gang Wen, MIT Sept., Quantum entanglement, topological order, and tensor category
Quantum entanglement, topological order, and tensor category theory Xiao-Gang Wen, MIT Sept., 2014 Topological order beyond symmetry breaking We used to believe that all phases and phase transitions are
More informationarxiv: v1 [cond-mat.str-el] 11 Dec 2011
Fractional charge and statistics in the fractional quantum spin Hall effect Yuanpei Lan and Shaolong Wan nstitute for Theoretical Physics and Department of Modern Physics University of Science and Technology
More informationChern-Simons Theory and Its Applications. The 10 th Summer Institute for Theoretical Physics Ki-Myeong Lee
Chern-Simons Theory and Its Applications The 10 th Summer Institute for Theoretical Physics Ki-Myeong Lee Maxwell Theory Maxwell Theory: Gauge Transformation and Invariance Gauss Law Charge Degrees of
More informationEmergence and Mechanism in the Fractional Quantum Hall Effect
Emergence and Mechanism in the Fractional Quantum Hall Effect Jonathan Bain Department of Technology, Culture and Society Tandon School of Engineering, New York University Brooklyn, New York 1. Two Versions
More informationarxiv: v2 [cond-mat.str-el] 3 Jan 2019
Emergent Commensurability from Hilbert Space Truncation in Fractional Quantum Hall Fluids arxiv:1901.00047v2 [cond-mat.str-el] 3 Jan 2019 Bo Yang 1, 2 1 Division of Physics and Applied Physics, Nanyang
More informationAnomalous hydrodynamics and gravity. Dam T. Son (INT, University of Washington)
Anomalous hydrodynamics and gravity Dam T. Son (INT, University of Washington) Summary of the talk Hydrodynamics: an old theory, describing finite temperature systems The presence of anomaly modifies hydrodynamics
More informationOne Loop Tests of Higher Spin AdS/CFT
One Loop Tests of Higher Spin AdS/CFT Simone Giombi UNC-Chapel Hill, Jan. 30 2014 Based on 1308.2337 with I. Klebanov and 1401.0825 with I. Klebanov and B. Safdi Massless higher spins Consistent interactions
More informationInfinite Symmetry in the Fractional Quantum Hall Effect
BONN-HE-93-29 hep-th/9309083 September 993 arxiv:hep-th/9309083v 5 Sep 993 Infinite Symmetry in the Fractional Quantum Hall Effect Michael Flohr and Raimund Varnhagen Physikalisches Institut der Universität
More informationNon-relativistic AdS/CFT
Non-relativistic AdS/CFT Christopher Herzog Princeton October 2008 References D. T. Son, Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry, Phys. Rev. D 78,
More informationLecture 9: RR-sector and D-branes
Lecture 9: RR-sector and D-branes José D. Edelstein University of Santiago de Compostela STRING THEORY Santiago de Compostela, March 6, 2013 José D. Edelstein (USC) Lecture 9: RR-sector and D-branes 6-mar-2013
More informationHydrodynamics of the superfluid CFL phase and r-mode instabilities
Hydrodynamics of the superfluid CFL phase and r-mode instabilities Cristina Manuel Instituto de Ciencias del Espacio (IEEC-CSIC) Barcelona Hirschegg 2009 Outline Introduction Superfluid hydrodynamics Hydrodynamics
More informationSPT order - new state of quantum matter. Xiao-Gang Wen, MIT/Perimeter Taiwan, Jan., 2015
Xiao-Gang Wen, MIT/Perimeter Taiwan, Jan., 2015 Symm. breaking phases and topo. ordered phases We used to believe that all phases and phase transitions are described by symmetry breaking Counter examples:
More informationHydrodynamics. Stefan Flörchinger (Heidelberg) Heidelberg, 3 May 2010
Hydrodynamics Stefan Flörchinger (Heidelberg) Heidelberg, 3 May 2010 What is Hydrodynamics? Describes the evolution of physical systems (classical or quantum particles, fluids or fields) close to thermal
More informationInstantons and Sphalerons in a Magnetic Field
Stony Brook University 06/27/2012 GB, G.Dunne & D. Kharzeev, arxiv:1112.0532, PRD 85 045026 GB, D. Kharzeev, arxiv:1202.2161, PRD 85 086012 Outline Motivation & some lattice results General facts on Dirac
More informationPoS(LAT2005)324. D-branes and Topological Charge in QCD. H. B. Thacker University of Virginia
D-branes and Topological Charge in QCD University of Virginia E-mail: hbt8r@virginia.edu The recently observed long-range coherent structure of topological charge fluctuations in QCD is compared with theoretical
More informationOptical Flux Lattices for Cold Atom Gases
for Cold Atom Gases Nigel Cooper Cavendish Laboratory, University of Cambridge Artificial Magnetism for Cold Atom Gases Collège de France, 11 June 2014 Jean Dalibard (Collège de France) Roderich Moessner
More informationarxiv:hep-th/ v1 15 Aug 2000
hep-th/0008120 IPM/P2000/026 Gauged Noncommutative Wess-Zumino-Witten Models arxiv:hep-th/0008120v1 15 Aug 2000 Amir Masoud Ghezelbash,,1, Shahrokh Parvizi,2 Department of Physics, Az-zahra University,
More informationSpinning strings and QED
Spinning strings and QED James Edwards Oxford Particles and Fields Seminar January 2015 Based on arxiv:1409.4948 [hep-th] and arxiv:1410.3288 [hep-th] Outline Introduction Various relationships between
More informationThe Quantum Hall Effects
The Quantum Hall Effects Integer and Fractional Michael Adler July 1, 2010 1 / 20 Outline 1 Introduction Experiment Prerequisites 2 Integer Quantum Hall Effect Quantization of Conductance Edge States 3
More informationIrrational anyons under an elastic membrane
Irrational anyons under an elastic membrane Claudio Chamon Collaborators: Siavosh Behbahani Ami Katz Euler Symposium on Theoretical and Mathematical Physics D.I. Diakonov Memorial Symposium Fractionalization
More informationRecovering General Relativity from Hořava Theory
Recovering General Relativity from Hořava Theory Jorge Bellorín Department of Physics, Universidad Simón Bolívar, Venezuela Quantum Gravity at the Southern Cone Sao Paulo, Sep 10-14th, 2013 In collaboration
More informationFourth Aegean Summer School: Black Holes Mytilene, Island of Lesvos September 18, 2007
Fourth Aegean Summer School: Black Holes Mytilene, Island of Lesvos September 18, 2007 Central extensions in flat spacetimes Duality & Thermodynamics of BH dyons New classical central extension in asymptotically
More informationSpectral action, scale anomaly. and the Higgs-Dilaton potential
Spectral action, scale anomaly and the Higgs-Dilaton potential Fedele Lizzi Università di Napoli Federico II Work in collaboration with A.A. Andrianov (St. Petersburg) and M.A. Kurkov (Napoli) JHEP 1005:057,2010
More informationarxiv: v1 [cond-mat.other] 20 Apr 2010
Characterization of 3d topological insulators by 2d invariants Rahul Roy Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford, OX1 3NP, UK arxiv:1004.3507v1 [cond-mat.other] 20 Apr 2010
More informationChern-Simons gauge theory The Chern-Simons (CS) gauge theory in three dimensions is defined by the action,
Lecture A3 Chern-Simons gauge theory The Chern-Simons (CS) gauge theory in three dimensions is defined by the action, S CS = k tr (AdA+ 3 ) 4π A3, = k ( ǫ µνρ tr A µ ( ν A ρ ρ A ν )+ ) 8π 3 A µ[a ν,a ρ
More informationEntanglement Chern numbers for random systems
POSTECH, Korea, July 31 (2015) Ψ = 1 D D Entanglement Chern numbers for random systems j Ψ j Ψj Yasuhiro Hatsugai Institute of Physics, Univ. of Tsukuba Ref: T. Fukui & Y. Hatsugai, J. Phys. Soc. Jpn.
More informationTopological Electromagnetic and Thermal Responses of Time-Reversal Invariant Superconductors and Chiral-Symmetric band insulators
Topological Electromagnetic and Thermal Responses of Time-Reversal Invariant Superconductors and Chiral-Symmetric band insulators Satoshi Fujimoto Dept. Phys., Kyoto University Collaborator: Ken Shiozaki
More informationTopological Defects inside a Topological Band Insulator
Topological Defects inside a Topological Band Insulator Ashvin Vishwanath UC Berkeley Refs: Ran, Zhang A.V., Nature Physics 5, 289 (2009). Hosur, Ryu, AV arxiv: 0908.2691 Part 1: Outline A toy model of
More informationSingle particle Green s functions and interacting topological insulators
1 Single particle Green s functions and interacting topological insulators Victor Gurarie Nordita, Jan 2011 Topological insulators are free fermion systems characterized by topological invariants. 2 In
More informationWiring Topological Phases
1 Wiring Topological Phases Quantum Condensed Matter Journal Club Adhip Agarwala Department of Physics Indian Institute of Science adhip@physics.iisc.ernet.in February 4, 2016 So you are interested in
More informationHund s rule for monopole harmonics, or why the composite fermion picture works
PERGAMON Solid State Communications 110 (1999) 45 49 Hund s rule for monopole harmonics, or why the composite fermion picture works Arkadiusz Wójs*, John J. Quinn The University of Tennessee, Knoxville,
More informationIntroduction to String Theory ETH Zurich, HS11. 9 String Backgrounds
Introduction to String Theory ETH Zurich, HS11 Chapter 9 Prof. N. Beisert 9 String Backgrounds Have seen that string spectrum contains graviton. Graviton interacts according to laws of General Relativity.
More informationChiral sound waves from a gauge theory of 1D generalized. statistics. Abstract
SU-ITP # 96/ Chiral sound waves from a gauge theory of D generalized statistics Silvio J. Benetton Rabello arxiv:cond-mat/9604040v 6 Apr 996 Department of Physics, Stanford University, Stanford CA 94305
More informationProximity-induced magnetization dynamics, interaction effects, and phase transitions on a topological surface
Proximity-induced magnetization dynamics, interaction effects, and phase transitions on a topological surface Ilya Eremin Theoretische Physik III, Ruhr-Uni Bochum Work done in collaboration with: F. Nogueira
More informationBoundary Degeneracy of Topological Order
Boundary Degeneracy of Topological Order Juven Wang (MIT/Perimeter Inst.) - and Xiao-Gang Wen Mar 15, 2013 @ PI arxiv.org/abs/1212.4863 Lattice model: Toric Code and String-net Flux Insertion What is?
More informationGRAVITATION F10. Lecture Maxwell s Equations in Curved Space-Time 1.1. Recall that Maxwell equations in Lorentz covariant form are.
GRAVITATION F0 S. G. RAJEEV Lecture. Maxwell s Equations in Curved Space-Time.. Recall that Maxwell equations in Lorentz covariant form are. µ F µν = j ν, F µν = µ A ν ν A µ... They follow from the variational
More informationarxiv:cond-mat/ v1 [cond-mat.mes-hall] 19 Sep 1998
Persistent Edge Current in the Fractional Quantum Hall Effect Kazusumi Ino arxiv:cond-mat/989261v1 cond-mat.mes-hall] 19 Sep 1998 Institute for Solid State Physics, University of Tokyo, Roppongi 7-22-1,
More informationBeyond the unitarity bound in AdS/CFT
Beyond the unitarity bound in AdS/CFT Tomás Andrade in collaboration with T. Faulkner, J. Jottar, R. Leigh, D. Marolf, C. Uhlemann October 5th, 2011 Introduction 1 AdS/CFT relates the dynamics of fields
More informationHolography for non-relativistic CFTs
Holography for non-relativistic CFTs Herzog, Rangamani & SFR, 0807.1099, Rangamani, Son, Thompson & SFR, 0811.2049, SFR & Saremi, 0907.1846 Simon Ross Centre for Particle Theory, Durham University Liverpool
More informationΨ({z i }) = i<j(z i z j ) m e P i z i 2 /4, q = ± e m.
Fractionalization of charge and statistics in graphene and related structures M. Franz University of British Columbia franz@physics.ubc.ca January 5, 2008 In collaboration with: C. Weeks, G. Rosenberg,
More informationLaughlin quasiparticle interferometer: Observation of Aharonov-Bohm superperiod and fractional statistics
Laughlin quasiparticle interferometer: Observation of Aharonov-Bohm superperiod and fractional statistics F.E. Camino, W. Zhou and V.J. Goldman Stony Brook University Outline Exchange statistics in 2D,
More informationExamining the Viability of Phantom Dark Energy
Examining the Viability of Phantom Dark Energy Kevin J. Ludwick LaGrange College 12/20/15 (11:00-11:30) Kevin J. Ludwick (LaGrange College) Examining the Viability of Phantom Dark Energy 12/20/15 (11:00-11:30)
More informationSymmetric Surfaces of Topological Superconductor
Symmetric Surfaces of Topological Superconductor Sharmistha Sahoo Zhao Zhang Jeffrey Teo Outline Introduction Brief description of time reversal symmetric topological superconductor. Coupled wire model
More informationQuantum Quenches in Chern Insulators
Quantum Quenches in Chern Insulators Nigel Cooper Cavendish Laboratory, University of Cambridge CUA Seminar M.I.T., November 10th, 2015 Marcello Caio & Joe Bhaseen (KCL), Stefan Baur (Cambridge) M.D. Caio,
More informationComposite Dirac liquids
Composite Dirac liquids Composite Fermi liquid non-interacting 3D TI surface Interactions Composite Dirac liquid ~ Jason Alicea, Caltech David Mross, Andrew Essin, & JA, Physical Review X 5, 011011 (2015)
More information