Effective light cone and digital quantum simulation of interacting bosons

TL;DR

This paper establishes a tight effective light cone for interacting bosons, proving finite speed of information propagation and providing an efficient simulation algorithm, thus addressing a long-standing open problem in many-body physics.

Contribution

It proves a finite speed for boson clustering, derives the shape of the effective light cone depending on dimension, and offers a provably efficient simulation method for interacting boson systems.

Findings

Established a tight effective light cone for interacting bosons

Proved finite speed for boson clustering and information propagation

Developed an efficient algorithm for simulating many-body boson systems

Abstract

The speed limit of information propagation is one of the most fundamental features in non-equilibrium physics. The region of information propagation by finite-time dynamics is approximately restricted inside the effective light cone that is formulated by the Lieb-Robinson bound. To date, extensive studies have been conducted to identify the shape of effective light cones in most experimentally relevant many-body systems. However, the Lieb-Robinson bound in the interacting boson systems, one of the most ubiquitous quantum systems in nature, has remained a critical open problem for a long time. This study reveals a tight effective light cone to limit the information propagation in interacting bosons, where the shape of the effective light cone depends on the spatial dimension. To achieve it, we prove that the speed for bosons to clump together is finite, which in turn leads to the error guarantee of the boson number truncation at each site. Furthermore, we applied the method to provide a provably efficient algorithm for simulating the interacting boson systems. The results of this study settle the notoriously challenging problem and provide the foundation for elucidating the complexity of many-body boson systems.