Time-dependent variational principle for quantum lattices

TL;DR

This paper introduces a new, efficient algorithm for simulating quantum lattice dynamics using the time-dependent variational principle on matrix product states, avoiding Trotter errors and preserving symmetries.

Contribution

It presents a novel algorithm that is optimal, Trotter-error free, symmetry-preserving, and computationally efficient for simulating quantum lattice systems.

Findings

Algorithm effectively simulates real and imaginary time dynamics.

No Trotter decomposition required, reducing errors.

Preserves all symmetries and conservation laws.

Abstract

We develop a new algorithm based on the time-dependent variational principle applied to matrix product states to efficiently simulate the real- and imaginary time dynamics for infinite one-dimensional quantum lattice systems. This procedure: (1) is argued to be optimal; (2) does not rely on the Trotter decomposition and thus has no Trotter error; (3) explicitly preserves all symmetries and conservation laws; and (4) has low computational complexity. The algorithm is illustrated using both imaginary time and real-time examples.