Quantum many-body systems in thermal equilibrium

TL;DR

This paper provides a comprehensive, rigorous overview of the universal features, mathematical properties, and computational aspects of quantum many-body systems in thermal equilibrium, emphasizing locality and quantum information tools.

Contribution

It offers a pedagogical, mathematically rigorous summary of the key features and complexity of thermal quantum states, integrating quantum information theory insights.

Findings

Bounds on correlations in thermal states

Characterization of subsystem structures

Analysis of classical and quantum algorithm performance

Abstract

The thermal or equilibrium ensemble is one of the most ubiquitous states of matter. For models comprised of many locally interacting quantum particles, it describes a wide range of physical situations, relevant to condensed matter physics, high energy physics, quantum chemistry and quantum computing, among others. We give a pedagogical overview of some of the most important universal features about the physics and complexity of these states, which have the locality of the Hamiltonian at its core. We focus on mathematically rigorous statements, many of them inspired by ideas and tools from quantum information theory. These include bounds on their correlations, the form of the subsystems, various statistical properties, and the performance of classical and quantum algorithms. We also include a summary of a few of the most important technical tools, as well as some self-contained proofs.