Statistical properties of random matrix product states

TL;DR

This paper investigates the statistical properties of random matrix product states (RMPS), providing analytical and numerical insights into their behavior and potential as tools for approximating quantum states in statistical mechanics.

Contribution

It offers an analytical and numerical study of RMPS, demonstrating their effectiveness in approximating general quantum states and connecting them to microcanonical ensembles.

Findings

Average state of RMPS ensemble calculated and numerically validated

RMPS can accurately approximate properties of quantum random states

High-probability approximation of generalized canonical states by RMPS

Abstract

We study the set of random matrix product states (RMPS) introduced in arXiv:0908.3877 as a tool to explore foundational aspects of quantum statistical mechanics. In the present work, we provide an accurate numerical and analytical investigation of the properties of RMPS. We calculate the average state of the ensemble in the non-homogeneous case, and numerically check the validity of this result. We also suggest using RMPS as a tool to approximate properties of general quantum random states. The numerical simulations presented here support the accuracy and efficiency of this approximation. These results suggest that any generalized canonical state can be approximated with high probability by the reduced density matrix of a random MPS, if the average MPS coincide with the associated microcanonical ensemble.