Time-evolving a matrix product state with long-ranged interactions

TL;DR

This paper presents a novel numerical algorithm for simulating the time evolution of matrix product states with long-ranged interactions, enabling studies of complex one- and two-dimensional quantum systems.

Contribution

The authors introduce a new method that overcomes the limitation to short-ranged Hamiltonians in matrix product state simulations, applicable to long-range and higher-dimensional systems.

Findings

Verified the method by reproducing theoretical predictions for the Haldane-Shastry model.

Simulated the dynamics of a 2D Bose-Hubbard model, aligning with recent experimental results.

Demonstrated the method's effectiveness for power-law and quasi-2D systems.

Abstract

We introduce a numerical algorithm to simulate the time evolution of a matrix product state under a long-ranged Hamiltonian. In the effectively one-dimensional representation of a system by matrix product states, long-ranged interactions are necessary to simulate not just many physical interactions but also higher-dimensional problems with short-ranged interactions. Since our method overcomes the restriction to short-ranged Hamiltonians of most existing methods, it proves particularly useful for studying the dynamics of both power-law interacting one-dimensional systems, such as Coulombic and dipolar systems, and quasi two-dimensional systems, such as strips or cylinders. First, we benchmark the method by verifying a long-standing theoretical prediction for the dynamical correlation functions of the Haldane-Shastry model. Second, we simulate the time evolution of an expanding cloud of particles in the two-dimensional Bose-Hubbard model, a subject of several recent experiments.