Ultra‐Fast Control of Magnetic Relaxation in a Periodically Driven Hubbard Model

Abstract

Motivated by cold atom and ultra-fast pumpprobe experiments we study the melting of longrange antiferromagnetic order of a perfect Néel state in a periodically driven repulsive Hubbard model. The dynamics is calculated for a Bethe lattice in infinite dimensions with non-equilibrium dynamical mean-field theory. In the absence of driving melting proceeds differently depending on the quench of the interactions to hopping ratio U /ν 0 from the atomic limit. For U ≫ ν 0 decay occurs due to mobile charge-excitations transferring energy to the spin sector, while for ν 0 U it is governed by the dynamics of residual quasi-particles. Here we explore the rich effects that strong periodic driving has on this relaxation process spanning three frequency ω regimes: (i) high-frequency ω ≫ U , ν 0 , (ii) resonant l ω = U > ν 0 with integer l , and (iii) ingap U > ω > ν 0 away from resonance. In case (i) we can quickly switch the decay from quasiparticle to charge-excitation mechanism through the suppression of ν 0 . For (ii) the interaction can be engineered, even allowing an effective U = 0 regime to be reached, giving the reverse switch from a charge-excitation to quasi-particle decay mechanism. For (iii) the exchange interaction can be controlled with little effect on the decay. By combining these regimes we show how periodic driving could be a potential pathway for controlling magnetism in antiferromagnetic materials.Finally, our numerical results demonstrate the accuracy and applicability of matrix product state techniques to the Hamiltonian DMFT impurity problem subjected to strong periodic driving.

Method for Finding the Exact Effective Hamiltonian of Time‐Driven Quantum Systems

“…To insure that U A [α(0)] = 1, the initial condition α(0) = 0 must be applied. Determining α(t) allows us to fully express the evolution operator in the form (4). In order to find the effective Hamiltonian, obtained evolution operator must be put in the form of U B .…”

“…Finding the relation between α(t) and β(t) is then essential to derive the effective Hamiltonian. To obtain such a relation, we start by assuming that both forms of the evolution operator, (4) and (5), coincide. This equality should be preserved if we introduce a dependence on an auxiliary parameter λ by making…”

“…By following the previously detailed method, we may obtain the evolution operator even for non-periodical Hamiltonians. Moreover, the expressions for the parameters α and β are valid for any time t. Therefore, the evolution operator in either form, (4) or (5), can be used to describe the dynamics of the system at any instant, giving information about its micromotion. [5] In Section 3.4, we present examples where the micromotion of the system is calculated explicitly.…”

“…[39]. The previous explicit expressions for the three coefficients completely determine the evolution operator in the form (4).…”

“…In recent years, there has been a remarkable interest in time-driven quantum systems [1][2][3][4][5] (TDQS). Among the reasons for this are the possibility of tailoring time-driven potentials using cold atoms, [6][7][8][9][10][11] creating topologically protected edge states, [12,13] other interesting topological phases, [14][15][16] and dynamically generating quantum entanglement [17] as well as global quantum-quenching.…”