Time-dependent variational principle of mixed matrix product states in the thermodynamic limit

TL;DR

This paper introduces a time evolution algorithm for infinite quantum spin chains with mixed boundary conditions, based on the time-dependent variational principle of matrix product states, applicable to both ballistic and diffusive information spreading.

Contribution

It develops a simple, inversion-free TDVP algorithm for infinite systems with different bulk parts, derived from symplectic geometry, and demonstrates its effectiveness on the quantum Ising model.

Findings

Effective simulation of quantum spin chains with mixed boundaries.

Analysis of information spread after local quenches in different regimes.

Derivation of TDVP from symplectic geometry.

Abstract

We describe a time evolution algorithm for quantum spin chains whose Hamiltonians are composed of an infinite uniform left and right bulk part, and an arbitrary finite region in between. The left and right bulk parts are allowed to be different from each other. The algorithm is based on the time-dependent variational principle (TDVP) of matrix product states. It is inversion-free and very simple to adapt from an existing TDVP code for finite systems. The importance of working in the projective Hilbert space is highlighted. We study the quantum Ising model as a benchmark and an illustrative example. The spread of information after a local quench is studied in both the ballistic and the diffusive case. We also offer a derivation of TDVP directly from symplectic geometry.