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arXiv:2205.02285

Statistical mechanics of strange metals and black holes

Subir Sachdev A

Published May 4, 2022• 5 citations
arXivHTMLPDF

Abstract

A colloquium style review of the connections between the Sachdev-Ye-Kitaev model and strange metals without quasiparticles, and between the SYK model and the quantum properties of black holes. Along with other insights, this connection has led to an understanding of the universal form of the low energy density of states of charged black holes in asymptotically 3+1 dimensional Minkowski space.

DOI
10.48550/arxiv.2205.02285

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A colloquium style review of the connections between the Sachdev-Ye-Kitaev model and strange metals without quasiparticles, and between the SYK model and the quantum properties of black holes. Along with other insights, this connection has led to an understanding of the universal form of the low energy density of states of charged black holes in asymptotically 3+1 dimensional Minkowski space.
This review is a contribution to a book dedicated to the memory of Michael E. Fisher. The first example of a quantum many body system not expected to have any quasiparticle excitations was the Wilson-Fisher conformal field theory. The absence of quasiparticles can be established in the compressible, metallic state of the Sachdev-Ye-Kitaev model of fermions with random interactions. The solvability of the latter model has enabled numerous computations of the non-quasiparticle dynamics of chaotic many-body states, such as those expected to describe quantum black holes. We review thermodynamic properties of the SYK model, and describe how they have led to an understanding of the universal structure of the low energy density of states of charged black holes without low energy supersymmetry.
Complex many-particle quantum entanglement is a central theme in two distinct major topics in physics: the strange metal state found in numerous correlated electron compounds, and the quantum theory of black holes in Einstein gravity. The Sachdev-Ye-Kitaev model provides a solvable theory of entangled many-particle quantum states without quasiparticle excitations. This article reviews how this toy model has led to realistic universal models of strange metals, and to new insights on the quantum states of black holes.
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.
The Sachdev-Ye-Kitaev (SYK) model is a solvable model of a many-body quantum system that has stimulated interest in both condensed matter physics and quantum gravity. This review focuses on the insights provided by the SYK model, which has no quasiparticle excitations, into the physics of Planckian non-Fermi-liquid metals. This is discussed for a range of strongly correlated models and in relation to experiments on strongly correlated materials. Also included is a discussion of recent developments regarding the connections between the SYK model and the quantum theory of black holes.