Generalized quantum microcanonical ensemble from random matrix product states

TL;DR

This paper introduces a tensor network algorithm for sampling quantum states from a generalized microcanonical ensemble, enabling efficient analysis of energy-specific properties in quantum many-body systems.

Contribution

It adapts the power method to a new ensemble of random matrix product states, allowing for efficient sampling without equal statistical weights of energy eigenstates.

Findings

Magnetization curves differ from canonical ensemble results due to microcanonical constraints

Algorithm successfully applied to the Heisenberg model with external magnetic field

Potential applications in studying quantum quenches in isolated systems

Abstract

We propose a tensor network algorithm for the efficient sampling of quantum pure states belonging to a generalized microcanonical ensemble. The algorithm consists in an adaptation of the power method to a recently introduced ensemble of random matrix product states. The microcanonical ensemble that we consider is characterized by the fact that the participating energy eigenstates are not required to have identical statistical weight. To test the method we apply it to the Heisenberg model with an external magnetic field, and we find that the magnetization curves, due to the microcanonical constraint, are qualitatively different from those obtained in the canonical ensemble. Possible future applications include the study of isolated quantum systems evolving after a quantum quench.