Matrix Product Density Operators: Simulation of finite-T and dissipative systems

TL;DR

This paper introduces a novel method for simulating the dynamics and thermal states of one-dimensional quantum systems using matrix product density operators, enabling efficient handling of dissipation and finite-temperature effects.

Contribution

It extends matrix product state techniques to mixed states and develops a variational algorithm for simulating real and imaginary time evolution of these states.

Findings

Enables simulation of dissipative quantum dynamics.

Allows thermal equilibrium state computation.

Applicable to finite and inhomogeneous systems.

Abstract

We show how to simulate numerically both the evolution of 1D quantum systems under dissipation as well as in thermal equilibrium. The method applies to both finite and inhomogeneous systems and it is based on two ideas: (a) a representation for density operators which extends that of matrix product states to mixed states; (b) an algorithm to approximate the evolution (in real or imaginary time) of such states which is variational (and thus optimal) in nature.