Quantum spin glasses and Sachdev-Ye-Kitaev models

TL;DR

This paper surveys random quantum models with infinite-range couplings, highlighting the Sachdev-Ye-Kitaev model's unique properties, its connection to black hole physics, and its extension to describe strange metallic states in correlated materials.

Contribution

It provides a comprehensive overview of the SYK model's properties, its relation to black holes, and introduces the 2dYSYK extension for understanding strange metals in quantum materials.

Findings

SYK model exhibits extensive zero-temperature entropy.

Spectral functions are 'Planckian', not particle-like.

2dYSYK model explains quantum phase transitions and strange metal behavior.

Abstract

A brief survey of some random quantum models with infinite-range couplings is presented, ranging from the quantum Ising model to the Sachdev-Ye-Kitaev model. The Sachdev-Ye-Kitaev model was the first to realize an extensive zero temperature entropy without requiring an exponentially large ground state degeneracy. This phenomenon is closely linked to the absence of a particle-like interpretation of its low energy spectrum--its spectral functions are not those of bosons or fermions but are instead "Planckian", meaning they are universal functions of energy/temperature. A remarkable consequence of these properties is that the SYK model provides an effective low energy theory of non-supersymmetric charged or rotating black holes in 3+1 dimensions, leading to new results on the density of many-body quantum states of such black holes. For applications to non-quasiparticle metallic states of quantum materials, an extension of the SYK model, known as the two-dimensional Yukawa-Sachdev-Ye-Kitaev model, is required. The 2dYSYK model describes quantum phase transitions in metals with spatial inhomogeneity in the position of the quantum critical point. This extension has led to a universal theory of the strange metal state observed in numerous correlated electron compounds, including copper-oxide based high temperature superconductors.