Replica exchange molecular dynamics optimization of tensor network states for quantum many-body systems

Abstract

The tensor network states (TNS) methods combined with Monte Carlo (MC) techniques have been proved a powerful algorithm for simulating quantum many-body systems. However, because the ground state energy is a highly non-linear function of the tensors, it is easy to get stuck in local minima when optimizing the TNS of the simulated physical systems. To overcome this difficulty, we introduce a replica-exchange molecular dynamics optimization algorithm to obtain the TNS ground state, based on the MC sampling techniques, by mapping the energy function of the TNS to that of a classical dynamical system. The method is expected to effectively avoid local minima. We make benchmark tests on a 1D Hubbard model based on matrix product states (MPS) and a Heisenberg $J_1$-$J_2$ model on square lattice based on string bond states (SBS). The results show that the optimization method is robust and efficient compared to the existing results.

References in corpus (5)

• DMRG and periodic boundary conditions: a quantum information perspective
• Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions
• Variational quantum Monte Carlo simulations with tensor-network states
• Strings, Projected Entangled Pair States, and variational Monte Carlo methods
• Monte Carlo simulation with Tensor Network States

Cited by in corpus (1)

• Numerical Investigation of Spin Excitations in a Doped Spin Chain