Quantum transport in d-dimensional lattices

TL;DR

This paper analytically demonstrates that uniform d-dimensional lattices of fermions and bosons exhibit ballistic transport due to their reduction to independent one-dimensional modes, with spin lattices showing both ballistic and non-ballistic behaviors.

Contribution

It provides a novel analytical framework for understanding quantum transport in high-dimensional lattices and extends the analysis to spin systems using Jordan-Wigner transformation.

Findings

Fermionic and bosonic lattices are reducible to independent 1D modes.

Uniform fermionic and bosonic lattices exhibit always ballistic transport.

Spin lattices can have both ballistic and non-ballistic subspaces depending on excitations.

Abstract

We prove analytically that both fermionic and bosonic uniform d-dimensional lattices can be reduced to a set of independent one-dimensional modes. This reduction leads to the conclusion that the dynamics in uniform fermionic and bosonic lattices is always ballistic. By the use of the Jordan-Wigner transformation we extend our analysis to spin lattices, proving the existence of both ballistic and non-ballistic subspaces in any dimension and for any system size. We then relate the nature of transport with the number of excitations in the spin lattice, indicating that a single excitation propagates always ballistically and that the non-ballistic behavior of uniform spin lattices is a consequence of the interaction between different excitations.