Hybrid infinite time-evolving block decimation algorithm for long-range multi-dimensional quantum many-body systems

TL;DR

This paper introduces a hybrid iTEBD algorithm that extends the simulation of quantum many-body systems to higher dimensions and long-range interactions, overcoming previous dimensional limitations.

Contribution

The authors develop a hybrid extension of iTEBD enabling the simulation of long-range, multi-dimensional quantum systems in the thermodynamic limit.

Findings

Allows simulation of higher-dimensional systems with long-range interactions

Enables studying dynamical phenomena in systems previously limited to small sizes

Facilitates validation of experimental quantum many-body physics

Abstract

In recent years, the infinite time-evolution block decimation (iTEBD) method has been demonstrated to be one of the most efficient and powerful numerical schemes for time-evolution in one-dimensional quantum many-body systems. However, a major shortcoming of the method, along with other state-of-the-art algorithms for many-body dynamics, has been their restriction to one spatial dimension. We present an algorithm based on a \textit{hybrid} extension of iTEBD where finite blocks of a chain are first locally time-evolved before an iTEBD-like method combines these processes globally. This in turn permits simulating the dynamics of many-body systems in the thermodynamic limit in $d\geq1$ dimensions including in the presence of long-range interactions. Our work paves the way for simulating the dynamics of many-body phenomena that occur exclusively in higher dimensions, and whose numerical treatments have hitherto been limited to exact diagonalization of small systems, which fundamentally limits a proper investigation of dynamical criticality. We expect the algorithm presented here to be of significant importance to validating and guiding investigations in state-of-the-art ion-trap and ultracold-atom experiments.