Density Matrix Renormalization Group Algorithm For Mixed Quantum States

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.

9 pages, 6 figures

References in corpus (13)

• The density-matrix renormalization group in the age of matrix product states
• Real time evolution using the density matrix renormalization group
• Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Efficient quantum state tomography
• Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
• Tensor network states and algorithms in the presence of a global U(1) symmetry
• Algorithms for finite Projected Entangled Pair States
• Variational Matrix Product Operators for the Steady State of Dissipative Quantum Systems
• Variational principle for steady states of dissipative quantum many-body systems
• Generic Construction of Efficient Matrix Product Operators
• Solution of the Lindblad Equation in the Kraus Representation
• Dissipatively driven strongly interacting bosons in a gauge field