Floquet engineering of edge states in the presence of staggered potential and interactions

Abstract

We study the effects of a periodically driven electric field applied to a variety of tight-binding models in one dimension. We first consider a noninteracting system with or without a staggered on-site potential, and we find that periodic driving can generate states localized completely or partially near the ends of a finite-sized system. Depending on the system parameters, such states have Floquet eigenvalues lying either outside or inside the continuum of eigenvalues of the bulk states. In the former case, we find that these states are completely localized at the ends and are true edge states, while in the latter case, the states are not completely localized at the ends although the localization can be made almost perfect by tuning the driving parameters. We then consider a system of two bosonic particles which have an on-site Hubbard interaction and show that a periodically driven electric field can generate two-particle states which are localized at the ends of the system. We show that many of these effects can be understood using a Floquet perturbation theory which is valid in the limit of a large staggered potential or large interaction strength. Some of these effects can also be understood qualitatively by considering time-independent Hamiltonians which have a potential at the sites at the edges; Hamiltonians of these kinds effectively appear in a Floquet-Magnus analysis of the driven problem. Finally, we discuss how the edge states produced by periodic driving of a noninteracting system of fermions can be detected by measuring the differential conductance of the system.

Driven Hubbard model on a triangular lattice: Tunable Heisenberg antiferromagnet with a chiral three-spin term

“…Such systems can exhibit a wide variety interesting phenomena such as dynamical freezing [1,4,7,[10][11][12][16][17][18], the generation of nontrivial band structures and states localized at the boundaries of the system , and time crystals [30,32,85]. While periodic driving of systems of noninteracting electrons has been studied very extensively, the effects of interactions along with periodic driving have also been studied by several groups [12,[19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][48][49][50]84].…”

Effects of topological and non-topological edge states on information propagation and scrambling in a Floquet spin chain

“…However, OTOC has been studied relatively less in Floquet systems [49][50][51][52], which has also been a topic of intense research for several years. Periodic driving of quantum systems can give rise to many interesting effects such as the generation of effective models with novel properties [53][54][55][56][57], non-trivial band structures and edge states [58][59][60][61][62][63][64][65][66][67][68][69][70][71][72][73][74][75][76][77], time crystals [78][79][80][81][82][83][84][85], Floquet dynamical quantum phase transition [86][87][88][89][90][91][92], and dynamical freezing [93][94][95][96]...…”

Driven Hubbard model on a triangular lattice: tunable Heisenberg antiferromagnet with three-spin chiral term

“…Such systems can exhibit a wide variety interesting phenomena such as dynamical freezing 2,5,8,[11][12][13][17][18][19] , the generation of non-trivial band structures and states localized at the boundaries of the system , and time crystals 31,33,86 . While periodic driving of systems of non-interacting electrons has been studied very extensively, the effects of interactions along with periodic driving have also been studied by several groups 13,[20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][49][50][51]85 .…”