Analytical Solution for the Steady States of the Driven Hubbard model

TL;DR

This paper analytically constructs correlated steady states in the driven Hubbard model, revealing how symmetries can prevent thermalization and enable long-range order under periodic driving.

Contribution

It provides an analytical method to find steady states of the driven Hubbard model considering SU(2) symmetries, predicting long-range correlations and condensate formation.

Findings

Steady states with off-diagonal long-range order are analytically derived.

Driving can induce a unique condensate with particle-hole and spin-wave order.

Symmetry preservation influences the nature of the steady states.

Abstract

Under the action of coherent periodic driving a generic quantum system will undergo Floquet heating and continously absorb energy until it reaches a featureless thermal state. The phase-space constraints induced by certain symmetries can, however, prevent this and allow the system to dynamically form robust steady states with off-diagonal long-range order. In this work, we take the Hubbard model on an arbitrary lattice with arbitrary filling and, by simultaneously diagonalising the two possible SU(2) symmetries of the system, we analytically construct the correlated steady states for different symmetry classes of driving. This construction allows us to make verifiable, quantitative predictions about the long-range particle-hole and spin-exchange correlations that these states can possess. In the case when both SU(2) symmetries are preserved in the thermodynamic limit we show how the driving can be used to form a unique condensate which simultaneously hosts particle-hole and spin-wave order.