Density Matrix Renormalization Group Algorithm For Mixed Quantum States

TL;DR

This paper introduces a new positive matrix product ansatz for mixed quantum states, enabling a DMRG algorithm that preserves physicality and converges monotonically, applicable to equilibrium and non-equilibrium states.

Contribution

It proposes a novel positive matrix product ansatz and a DMRG algorithm for mixed states that guarantees physical solutions and monotonic convergence.

Findings

Successfully computes equilibrium states.

Efficiently finds non-equilibrium steady states.

Numerical demonstrations show advantages over previous methods.

Abstract

Density Matrix Renormalization Group (DMRG) algorithm has been extremely successful for computing the ground states of one-dimensional quantum many-body systems. For problems concerned with mixed quantum states, however, it is less successful in that either such an algorithm does not exist yet or that it may return unphysical solutions. Here we propose a positive matrix product ansatz for mixed quantum states which preserves positivity by construction. More importantly, it allows to build a DMRG algorithm which, the same as the standard DMRG for ground states, iteratively reduces the global optimization problem to local ones of the same type, with the energy converging monotonically in principle. This algorithm is applied for computing both the equilibrium states and the non-equilibrium steady states, and its advantages are numerically demonstrated.