Lieb-Robinson bounds with dependence on interaction strengths

TL;DR

This paper introduces new Lieb-Robinson bounds that explicitly depend on interaction strengths, revealing complex relationships between interaction parameters and information propagation speeds in quantum systems.

Contribution

It provides novel bounds on information propagation that account for multiple interaction strengths, including systems with unbounded operators and general graphs.

Findings

Lieb-Robinson speed is not always algebraic in interaction strengths.

Bounds are derived for systems with multiple bounded and certain unbounded operators.

Applicable to quantum systems on lattices and homogeneous graphs.

Abstract

We propose new Lieb-Robinson bounds (bounds on the speed of propagation of information in quantum systems) with an explicit dependence on the interaction strengths of the Hamiltonian. For systems with more than two interactions it is found that the Lieb-Robinson speed is not always algebraic in the interaction strengths. We consider Hamiltonians with any finite number of bounded operators and also a certain class of unbounded operators. We obtain bounds and propagation speeds for quantum systems on lattices and also general graphs possessing a kind of homogeneity and isotropy. One area for which this formalism could be useful is the study of quantum phase transitions which occur when interactions strengths are varied.