Approximating the long time average of the density operator: Diagonal ensemble

Abstract

For an isolated generic quantum system out of equilibrium, the long time average of observables is given by the diagonal ensemble, i.e. the mixed state with the same probability for energy eigenstates as the initial state but without coherences between different energies. In this work we present a method to approximate the diagonal ensemble using tensor networks. Instead of simulating the real time evolution, we adapt a filtering scheme introduced earlier in [Phys. Rev. B 101, 144305 (2020)] to this problem. We analyze the performance of the method on a non-integrable spin chain, for which we observe that local observables converge towards thermal values polynomially with the inverse width of the filter.

9 pages, 9 figures

References in corpus (22)

• The density-matrix renormalization group in the age of matrix product states
• Thermalization and its mechanism for generic isolated quantum systems
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• The Kernel Polynomial Method
• Quench dynamics and non equilibrium phase diagram of the Bose-Hubbard model
• Breakdown of thermalization in finite one-dimensional systems
• Interaction Quench in the Hubbard model
• Exact relaxation in a class of non-equilibrium quantum lattice systems
• Quenching the Anisotropic Heisenberg Chain: Exact Solution and Generalized Gibbs Ensemble Predictions
• Strongly correlated fermions after a quantum quench
• Operator space entanglement entropy in transverse Ising chain
• Time-step targetting methods for real-time dynamics using DMRG
• The Dynamics of 1D Quantum Spin Systems Can Be Approximated Efficiently
• Approximating Gibbs states of local Hamiltonians efficiently with PEPS
• Chebyshev matrix product state approach for spectral functions
• On entropy growth and the hardness of simulating time evolution
• Spectral functions and time evolution from the Chebyshev recursion
• Exploiting translational invariance in Matrix Product State simulations of spin chains with periodic boundary conditions
• Threshold for Chaos and Thermalization in One-Dimensional Mean-Field Bose-Hubbard Model
• Quantum quenches in the thermodynamic limit. II. Initial ground states
• Numerical linked cluster expansions for quantum quenches in one dimensional lattices

Cited by in corpus (1)

• Work statistics and symmetry breaking in an excited state quantum phase transition