Phase transitions and metastability in the distribution of the bipartite entanglement of a large quantum system

TL;DR

This paper analyzes the distribution of bipartite entanglement in large quantum systems using statistical mechanics, revealing phase transitions and metastable states related to entanglement properties.

Contribution

It introduces a novel approach applying statistical mechanics to quantum entanglement, identifying phase transitions and metastable states in the distribution of Schmidt coefficients.

Findings

Identification of two phase transitions at positive and negative temperatures.

Discovery of metastable states related to 2-D quantum gravity.

Finite size corrections to the saddle point solution.

Abstract

We study the distribution of the Schmidt coefficients of the reduced density matrix of a quantum system in a pure state. By applying general methods of statistical mechanics, we introduce a fictitious temperature and a partition function and translate the problem in terms of the distribution of the eigenvalues of random matrices. We investigate the appearance of two phase transitions, one at a positive temperature, associated to very entangled states, and one at a negative temperature, signalling the appearance of a significant factorization in the many-body wave function. We also focus on the presence of metastable states (related to 2-D quantum gravity) and study the finite size corrections to the saddle point solution.