Quantum spin liquids and the Mott transition. T. Senthil (MIT)
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1 Quantum spin liquids and the Mott transition T. Senthil (MIT) Friday, December 9, 2011
2 Band versus Mott insulators Band insulators: even number of electrons per unit cell; completely filled bands Mott insulators: odd number of electrons per unit cell; charges localize due to Coulomb interaction. Friday, December 9, 2011
3 Physics of electronic Mott insulators Friday, December 9, 2011
4 Spin liquids and other exotica in quantum magnets Traditional quantum magnetism: Ordered ground states (Neel, spin Peierls, ) Concept of broken symmetry Modern theory (last 2 decades): Possibility of `spin liquid states in any dimension d. Eg: Mott insulators with 1 electron/unit cell with no broken symmetry Maturing theoretical understanding - extensive developments in last few years Friday, December 9, 2011
5 What is a quantum spin liquid?
6 Some natural questions Can quantum spin liquids exist in d > 1? Do quantum spin liquids exist in d > 1? Friday, December 9, 2011
7 Some natural questions Can quantum spin liquids exist in d > 1? Theoretical question Do quantum spin liquids exist in d > 1? Experimental question Friday, December 9, 2011
8 Some natural questions Can quantum spin liquids exist in d > 1? Theoretical question: YES!! Do quantum spin liquids exist in d > 1? Experimental question: Remarkable new materials possibly in spin liquid phases Friday, December 9, 2011
9 Why are quantum spin liquids interesting? 1. Exotic excitations Excitations with fractional spin (spinons), non-local emergent interactions described through gauge fields As rich in possibility if not richer than the fractional quantum Hall systems..but requires less extreme conditions (eg: no strong B-fields) Friday, December 9, 2011
10 Why are quantum spin liquids interesting? 2. Ordering not captured by concept of broken symmetry - new concepts of `topological order and generalizations Order is a global property of ground state wavefunction Possibility of encoding information non-locally.?? Useful for computing?? Friday, December 9, 2011
11 Why are quantum spin liquids interesting? 3. Platform for onset of many unusual phenomena Eg: (i) Superconductivity in doped Mott insulators?? Relevant to cuprates?? (ii) Non-fermi liquid phenomena in correlated d or f-electron metals. Friday, December 9, 2011
12 Why are quantum spin liquids interesting? 4. Excellent experimental setting for exploration of violation of long cherished notions of condensed matter physics -quasiparticles with fractional quantum numbers and unusual statistics - the very existence of a quasiparticle description - inadequacy of Landau order parameter to describe phases and phase transitions of correlated matter Friday, December 9, 2011
13 Stability of quantum spin liquids 1. Solution of concrete quantum spin models within 1/N expansions (Read, Sachdev 91) 2. Effective field theory descriptions ( Wen 91; Balents,Fisher,Nayak, 99; TS, Fisher 00,..) 3. Solution of effective models of quantum dimers (Moessner,Sondhi 01; Misguich,Serban,Pasquier 02;.) 4. Solution of various quantum spin/boson models (Kitaev 97, 06;Balents,Fisher,Girvin 02, Motrunich, TS 02, ) 5. Numerical calculations on simpler models (Misguich,Lhuillier 98; Sheng, Balents, 05; Isakov,Paramekanti,Kim,Sen,Damle 07) Friday, December 9, 2011
14 Where might we find quantum spin liquids? Geometrically frustrated quantum magnets ``Intermediate correlation regime Eg: Mott insulators that are not too deeply into the insulating regime Friday, December 9, 2011
15 Where might we find quantum spin liquids? Geometrically frustrated quantum magnets ``Intermediate correlation regime Eg: Mott insulators that are not too deeply into the insulating regime Friday, December 9, 2011
16 Wavefunctions An example
17 Other excitations
18 Full description of excitation spectrum
19 Utility of gauge theory
20 Varieties of spin liquids
21 A useful distinction: Gapped versus gapless spin spectrum
22 Best experimental candidate
23 A gapless spin liquid
24 Phase diagram
25 Summary of quantum spin liquid review Maturing theoretical understanding of quantum spin liquid phases in d > 1 Theoretically demonstrable violations of long cherished notions of condensed matter physics Interesting candidate materials exist exciting times ahead! Important general lessons for correlated metallic systems Friday, December 9, 2011
26 The Mott metal-insulator transition
27 Simple example: Mott transition of one band systems Friday, December 9, 2011
28 Some difficulties
29 Quantum spin liquids to a (partial) rescue Friday, December 9, 2011
30 Possible experimental realization of a second order Mott transition
31 How might a Fermi surface disappear?
32 Electronic structure at criticality: ``Critical Fermi surface Friday, December 9, 2011
33 Why a critical Fermi surface?
34 Evolution of single particle gap
35 Why a critical Fermi surface? Evolution of momentum distribution Friday, December 9, 2011
36 Killing a Fermi surface
37 Some obvious consequences/questions Friday, December 9, 2011
38 Some obvious consequences/questions Friday, December 9, 2011
39 Theoretical framework
40 Structure of critical theory in d = 2
41
42 Critical Fermi surface at Mott criticality
43 Approach from Fermi liquid
44 Critical thermodynamics/transport
45 Universal resistivity jump
46 Crossover out of criticality: Anderson is different (from Higgs)
47 Finite T crossovers: Marginal Fermi liquids Friday, December 9, 2011
48 Same Mott transition in three dimensions Friday, December 9, 2011
49 Summary-II Concrete theory of a continuous Mott transition in two dimensions - demonstrate critical Fermi surface - predict universal resistivity jump, emergence of marginal Fermi liquids - filling controlled transition tuned by chemical potential can also be studied. Future: Lots of challenges! Friday, December 9, 2011
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