Long-time dynamics of quantum chains: transfer-matrix renormalization group and entanglement of the maximal eigenvector

Abstract

By using a different quantum-to-classical mapping from the Trotter-Suzuki decomposition, we identify the entanglement structure of the maximal eigenvectors for the associated quantum transfer matrix. This observation provides a deeper insight into the problem of linear growth of the entanglement entropy in time evolution using conventional methods. Based on this observation, we propose a general method for arbitrary temperatures using the biorthonormal transfer-matrix renormalization group. Our method exhibits a competitive accuracy with a much cheaper computational cost in comparison with two recent proposed methods for long-time dynamics based on a folding algorithm [Phys. Rev. Lett. 102, 240603 (2009)] and a modified time-dependent density-matrix renormalization group [Phys. Rev. Lett. 108, 227206 (2012)].

References in corpus (8)

• Real time evolution using the density matrix renormalization group
• Conservation laws, integrability and transport in one-dimensional quantum systems
• Matrix Product States for dynamical simulation of infinite chains
• Spectral functions in one-dimensional quantum systems at T>0
• Tensor network techniques for the computation of dynamical observables in 1D quantum spin systems
• Real-time dynamics at finite temperature by DMRG: A path-integral approach
• Temperature driven crossover phenomena in the correlation lengths of the one-dimensional t-J model
• Accurate computation of low-temperature thermodynamics for quantum spin chains

Cited by in corpus (11)

• Transfer Matrices and Excitations with Matrix Product States
• An efficient method for quantum impurity problems out of equilibrium
• Non-equilibrium quantum impurity problems via matrix-product states in the temporal domain
• Series-Expansion Thermal Tensor Network Approach for Quantum Lattice Models
• Reorthonormalization of Chebyshev matrix product states for dynamical correlation functions
• Bilayer Linearized Tensor Renormalization Group Approach for Thermal Tensor Networks
• Two-dimensional coherent spectrum of interacting spinons from matrix-product states
• Dynamical correlation functions from complex time evolution
• TNSPackage: A Fortran2003 library designed for tensor network state methods
• Summing Real Time Feynman Paths of Lattice Polaron with Matrix Product States
• Process Tensor Approaches to Non-Markovian Quantum Dynamics