Iridate heterostructures are gaining interest as their magnetic properties are much more sensitive to structural distortion compared to pure spin systems due to spinorbital entanglement induced by strong spin-orbit coupling. While bulk monolayer and bilayer iridates show ab-plane canted and c-axis antiferromagnetic (AFM) order, recent experiments on layered iridate superlattices (SL) have revealed striking properties, especially in the bilayer SL. A spin model is presented including the tilting induced Kitaev type interactions, which illustrates the proclivity towards ab-plane canted AFM order. A realistic Hubbard model including spin-dependent hopping terms arising from octahedral rotation and tilting is constructed for the bilayer SL in isospin space, and magnetic excitations are investigated in the self-consistently determined magnetic state. The Hubbard model analysis confirms the spin model results and shows strongly reduced magnon energy gap and an isospin reorientation transition from c-axis to ab-plane canted AFM order with increasing tilting.
We study a one-dimensional lattice model of fractional statistics in which particles have next-nearest-neighbor hopping between sites which depends on the occupation number at the intermediate site and a statistical parameter φ. The model breaks parity and time-reversal symmetries and has four-fermion interactions if φ = 0. We first analyze the model using mean field theory and find that there are four Fermi points whose locations depend on φ and the filling η. We then study the modes near the Fermi points using the technique of bosonization. Based on the quadratic terms in the bosonized Hamiltonian, we find that the low-energy modes form two decoupled Tomonaga-Luttinger liquids with different values of the Luttinger parameters which depend on φ and η; further, the right and left moving modes of each system have different velocities. A study of the scaling dimensions of the cosine terms in the Hamiltonian indicates that the terms appearing in one of the Tomonaga-Luttinger liquids will flow under the renormalization group and the system may reach a non-trivial fixed point in the long distance limit. We examine the scaling dimensions of various charge density and superconducting order parameters to find which of them is the most relevant for different values of φ and η. Finally we look at two-particle bound states that appear in this system and discuss their possible relevance to the properties of the system in the thermodynamic limit. Our work shows that the low-energy properties of this model of fractional statistics have a rich structure as a function of φ and η.
We show that the correlation functions of a class of periodically driven integrable closed quantum systems approach their steady-state value as n −(α+1)/β , where n is the number of drive cycles and α and β denote positive integers. We find that, generically, β = 2 within a dynamical phase characterized by a fixed α; however, its value can change to β = 3 or β = 4 either at critical drive frequencies separating two dynamical phases or at special points within a phase. We show that such decays are realized in both driven Su-Schrieffer-Heeger (SSH) and one-dimensional (1D) transverse field Ising models, discuss the role of symmetries of the Floquet spectrum in determining β, and chart out the values of α and β realized in these models. We analyze the SSH model for a continuous drive protocol using a Floquet perturbation theory which provides analytical insight into the behavior of the correlation functions in terms of its Floquet Hamiltonian. This is supplemented by an exact numerical study of a similar behavior for the 1D Ising model driven by a square pulse protocol. For both models, we find a crossover timescale n c which diverges at the transition. We also unravel a long-time oscillatory behavior of the correlators when the critical drive frequency, ω c , is approached from below (ω < ω c ). We tie such behavior to the presence of multiple stationary points in the Floquet spectrum of these models and provide an analytic expression for the time period of these oscillations.
In this study, we examine whether periodic driving of a model with a quasiperiodic potential can generate interesting Floquet phases that have no counterparts in the static model. Specifically, we consider the Aubry-André model, which is a one-dimensional time-independent model with an on-site quasiperiodic potential V 0 and a nearest-neighbor hopping amplitude that is taken to have a staggered form. We add a uniform hopping amplitude that varies in time either sinusoidally or as a square pulse with a frequency ω. Unlike the static Aubry-André model, which has a simple phase diagram with only two phases (only extended or only localized states), we find that the driven model has four possible phases for the Floquet eigenstates: a phase with gapless quasienergy bands and only extended states, a phase with multiple mobility gaps separating different quasienergy bands, a mixed phase with coexisting extended, multifractal, and localized states, and a phase with only localized states. The multifractal states have generalized inverse participation ratios that scale with the system size with exponents that are different from the values for both extended and localized states. In addition, we observe intricate reentrant transitions between the different kinds of states when ω and V 0 are varied. The appearance of such transitions is confirmed by the behavior of the Shannon entropy. Many of our numerical results can be understood from an analytic Floquet Hamiltonian derived using a Floquet perturbation theory that uses the inverse of the driving amplitude as the perturbation parameter. In the limit of high frequency and large driving amplitude, we find that the Floquet quasienergies match the energies of the undriven system, but the Floquet eigenstates are much more extended. We also study the spreading of a one-particle wave packet, and we find that it is always ballistic but the ballistic velocity varies significantly with the system parameters, sometimes showing a nonmonotonic dependence on V 0 that does not occur in the static model. Finally, we compare the results for the driven model, which has a static staggered hopping amplitude, with a model that has a static uniform hopping amplitude, and we find some significant differences between the two cases. All of our results are found to be independent of the driving protocol, either sinusoidal or square pulse. We conclude that the interplay of the quasiperiodic potential and driving produces a rich phase diagram that does not appear in the static model.
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