Symmetry-enhanced Lieb-Robinson bounds for a class of Bose-Hubbard type Hamiltonians

TL;DR

This paper demonstrates that translation invariance and local p-body repulsion in Bose-Hubbard Hamiltonians can significantly slow information propagation, leading to near-linear light cones and revealing symmetry as a key factor in Lieb-Robinson bounds.

Contribution

It introduces a new symmetry-based approach to bound information spread in bosonic systems, showing how local p-body interactions can suppress propagation speed.

Findings

For large p, the propagation velocity scales as t^{D/(p - D - 1)}

Symmetry constraints can lead to near-linear light cones in bosonic systems

The derived bounds are proven to be sharp under the given assumptions

Abstract

Several recent works have derived Lieb-Robinson bounds (LRBs) for Bose-Hubbard-type Hamiltonians. For certain structured initial states, e.g., vacuum perturbations or near-stationary states, information propagates with velocity $v \leq C$ . However, for general bounded-density initial states, it was shown by the first author, Vu, and Saito that the velocity can grow in time as $v \sim t^{D-1}$, where $D$ is the spatial dimension -- demonstrating the possibility of accelerated information spreading in bosonic systems. In this work, we introduce a new perspective on this phenomenon: we show that translation invariance combined with local $p$-body repulsion ($n^p$ with $p > D+1$) qualitatively alters the propagation behavior, leading to a bound of the form $v \sim t^{\frac{D}{p - D - 1}}$ for general bounded-energy-density initial states. In particular, this establishes for an almost-linear light cone at large $p$, in stark contrast to the previously found accelerated regimes. Our result identifies symmetry-driven constraints as a new mechanism for suppressing propagation speed in bosonic systems and thereby reframes the scope of what types of LRBs can hold. We further provide matching examples showing that, under the given assumptions, this bound is sharp -- no further improvement in the power of $t$ is possible without invoking additional dynamical constraints.