Local criticality and marginal Fermi liquid in a solvable model Erez Berg

Transcription

1 Local criticality and marginal Fermi liquid in a solvable model Erez Berg Y. Werman, D. Chowdhury, T. Senthil, and EB, arxiv:xxxx.xxxx

2 Yochai Werman (Weizmann Berkeley) Debanjan Chowdhury (MIT) Senthil Todadri (MIT)

3 Semiclassical theory of transport in metals " k # $ F l 1 $/( l/a 1 Drude formula: ρ = m ne 2 τ = 3π 2 h 1 e 2 k F k F l Mott-Ioffe-Regel limit ) 3, ρ 3π h 1 / 0 2 e 2 " k # F 3, 3π ) 2" # ( 3 2k F a 2 B ρ Q Quantum of Resistivity ρ Q = h e 2 a B = 136.6μΩcm

4 Resistivity of a good metal ) 3 [7Ωcm] ) = ) = >

5 Bad Metals From Caladra and Gunnarson (2003) ) 3 Bad metals: ρ T ρ Q, dρ T dt > 0 Transport without quasiparticles? Emery and Kivelson, PRL (1995)

6 Strange metals at T 0? La 2 x Sr x CuO 4 Takagi et al., PRL (1992) Planckian Bound? BC DE (Sachdev, Zaanen, Hartnoll, Blake ħ Relation to bound on quantum chaos? (Maldacena et al.) Quantum critical point? z = ( local QCP )? (Si, Varma)

7 Theoretical challenges Theory for transport in bad metal regime, ) ) 3? Model for ) = extending down to low =? Fundamental bounds on resistivity? Role of quantum criticality?

8 Outline Translationally invariant large-n model with strong e-e interactions: Fermi liquid, Marginal Fermi liquid, and non-fermi liquid Implications: transport bounds, local quantum criticality

9 Controlled Non-Fermi liquid at large N Sachdev-Ye-Kitaev Model: H = 1 σ N N 3/2 ijkl=1 U ijkl c i c j c k c l 2 ഥU ijkl = 0, U ijkl = U 2 Non-Fermi liquid behavior: G ij (ω) isgn(ω) U ω Maximally chaotic: λ L = 2πT New window into non-quasiparticle transport?

10 Higher dimensional Translationally Invariant extension Fermi surface Critical Fermi surface Aug. 23, 2017 Image from nasa.gov

11 Higher dimensional Translationally Invariant extension H = σ k σ N i=1 ε k c ki c ki + 1 N 3/2 σ r σ ijkl=1 Same U ijkl on every site N U ijkl c ri c rj c rk c rl 2 ഥU ijkl = 0, U ijkl = U 2 Disordered lattice of SYK sites: Y. Gu et al., R. Davison et al., X. Song et al. (2017)

12 One band model Σ(J, L) = Σ(L O ) P Q R L O (Σ S; FL) Σ(L O ) P T L O sgn(l O ) (Σ S; FL) ω, T W2 U ω, T W2 U D. Chowdhury, et al., In Preparation (2017)

13 One band model Σ(J, L) = D. Chowdhury, et al., In Preparation (2017)

14 Y L Y L = Conductivity + + ρ T T 2 T W 2 /U T High T regime: No FS Locally quantum critical, 4 ] Critical FS T=0 phase? D. Chowdhury, et al., In Preparation (2017)

15 Two band/kondo lattice generalization Two bands ^, _ with bandwidths S` S a H = H c + H f + 1 σ N 3/2 r σn ijkl=1 V ijkl c ri c rj f rk f rl + 1 N N 3/2 σ r σ ijkl=1 U ijkl f ri f rj f rk f rl Σ c = Σ f = + D. Chowdhury, et al., In Preparation (2017)

16 Two band/kondo lattice generalization b U f V, W f, W c Σ f Σ c ω 1/2 (SYK) S a T` d 0 0 S a Σ f U f 1/2 ω 1/2 (SYK) Σ c V2 W c U f iωlog(ω) (Marginal Fermi liquid) W 2 f /U f 0 0 Σ f Σ c iω (Fermi Liquid) D. Chowdhury, et al., In Preparation (2017)

17 Marginal Fermi Liquid (MFL) Spectral density of f fluctuations: Π f(q, ω) 1 U f atan ω T Varma et al., PRL (1989); Abbamonte et al., arxiv (2017) c fermion lifetime: 1 τ c Σ c(k, ω) V2 max ω, T U f W c ρ T, c V TlogT No apparent D. Chowdhury, et al., In Preparation (2017) Planckain bound

18 Local quantum criticality at T 0? Stability at T 0? The local quantum critical/mfl phase has S T 0 > 0 D. Chowdhury, et al., In Preparation (2017)

19 Local quantum criticality at T 0? local critical behavior (dynamical critical exponent z = ) is generically unstable at T 0. Assuming translational invariance E.g. assume that ξ log(ξ τ ) Aji, Varma (2007) i 0, j i(0,0). g e i(l = 0) 1/f(g) [f g - Level spacing] δ(l) e #L S(T 0) grows at least as L D. Chowdhury, et al., In Preparation (2017)

20 Local quantum criticality at ] n? o Local quantum critical Fermi liquid? Symmetry breaking? Spin liquid phase? = = D. Chowdhury, et al., In Preparation (2017)

21 Conclusions Large-N models: non-quasiparticle transport in a controlled setting. Fundamental Planckian bound: may apply to thermalization/chaos, but not to any particular physical quantity (e.g., current) Local quantum criticality : probably never a stable = 0 phase/qcp. Parent multi-critical point? Universality of maximally chaotic systems? Thank you.