Thermal diffusivity and chaos in metals without quasiparticles

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Abstract

We study the thermal diffusivity \(D_T\) in models of metals without quasiparticle excitations (`strange metals'). The many-body quantum chaos and transport properties of such metals can be efficiently described by a holographic representation in a gravitational theory in an emergent curved spacetime with an additional spatial dimension. We find that at generic infra-red fixed points \(D_T\) is always related to parameters characterizing many-body quantum chaos: the butterfly velocity \(v_B\), and Lyapunov time \(\tau_L\) through \(D_T \sim v_B^2 \tau_L\). The relationship holds independently of the charge density, periodic potential strength or magnetic field at the fixed point. The generality of this result follows from the observation that the thermal conductivity of strange metals depends only on the metric near the horizon of a black hole in the emergent spacetime, and is otherwise insensitive to the profile of any matter fields.

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Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics

A Starinets, D. Son, P. Kovtun (2004)

The ratio of shear viscosity to volume density of entropy can be used to characterize how close a given fluid is to being perfect. Using string theory methods, we show that this ratio is equal to a universal value of \(\hbar/4\pi k_B\) for a large class of strongly interacting quantum field theories whose dual description involves black holes in anti--de Sitter space. We provide evidence that this value may serve as a lower bound for a wide class of systems, thus suggesting that black hole horizons are dual to the most ideal fluids.

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Comments on the Sachdev-Ye-Kitaev model

Juan Maldacena, Douglas Stanford (2016)

We study a quantum mechanical model proposed by Sachdev, Ye and Kitaev. The model consists of \(N\) Majorana fermions with random interactions of a few fermions at a time. It it tractable in the large \(N\) limit, where the classical variable is a bilocal fermion bilinear. The model becomes strongly interacting at low energies where it develops an emergent conformal symmetry. We study two and four point functions of the fundamental fermions. This provides the spectrum of physical excitations for the bilocal field. The emergent conformal symmetry is a reparametrization symmetry, which is spontaneously broken to \(SL(2,R)\), leading to zero modes. These zero modes are lifted by a small residual explicit breaking, which produces an enhanced contribution to the four point function. This contribution displays a maximal Lyapunov exponent in the chaos region (out of time ordered correlator). We expect these features to be universal properties of large \(N\) quantum mechanics systems with emergent reparametrization symmetry. This article is largely based on talks given by Kitaev \cite{KitaevTalks}, which motivated us to work out the details of the ideas described there.

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Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet

Jinwu Ye, Subir Sachdev (1992)

We examine the spin-\(S\) quantum Heisenberg magnet with Gaussian-random, infinite-range exchange interactions. The quantum-disordered phase is accessed by generalizing to \(SU(M)\) symmetry and studying the large \(M\) limit. For large \(S\) the ground state is a spin-glass, while quantum fluctuations produce a spin-fluid state for small \(S\). The spin-fluid phase is found to be generically gapless - the average, zero temperature, local dynamic spin-susceptibility obeys \(\bar{\chi} (\omega ) \sim \log(1/|\omega|) + i (\pi/2) \mbox{sgn} (\omega)\) at low frequencies. This form is identical to the phenomenological `marginal' spectrum proposed by Varma {\em et. al.\/} for the doped cuprates.