Floquet systems
Periodically driven or the so-called Floquet systems are a class of inherent out-of-equilibirum systems which provide the arguably simplest genuine non-equilibrium setting for studying for novel phases of quantum matter. Indeed, some of the stark examples are discrete time-crystals and anomalous Floquet topological insulators. Generically, driven quantum systems heat up to featureless infinite temperature states. Localisation offers one route towards evading this heat death. Hence, the interplay of disorder and periodic driving is a question of interest. Some of my projects in this directions are:
Fate of Anderson localisation on high-d graphs to Floquet driving
Motivated by the link between Anderson localisation on high-dimensional graphs and many-body localisation, we studied the effect of periodic driving on Anderson localisation on random trees. The periodically-driven system can be mapped onto a time-independent one with an extra dimension. By analysing the localisation problem on this extended graph, we uncovered a novel localisation phase diagram. At low frequency, driving favours delocalisation as the availability of a large number of extra paths dominates over interferences. By contrast, at high frequency, it stabilises localisation compared to the static system. These lead to a unexpected regime of re-entrant localisation in the phase diagram.
Sthitadhi Roy, Roderich Moessner, and Achilleas Lazarides, "How periodic driving stabilises and destabilises Anderson localisation on random trees", [Phys. Rev. B 103, L100204 (2021) (Letter)] [arXiv:2101.00018]
Copies of the disordered graph due to the driving, and illustration of some Floquet induced hoppings
Spread of correlations in time under periodic driving of a disordered interacting spin chain.
Anomalous thermalisation in interacting Floquet systems
In the context of interacting disordered systems, there can exist a Floquet many-body localisation transition. We found signatures of anomalous thermalisation in the ergodic phases of such systems accompanied by subdiffusive transport [2]. We could explain the origin of the anomalous thermalisation by looking at the distributions of offdiagonal matrix elements of the local operators in the Floquet eigenbasis and their scalings with system size. We found that the distributions deviate from the perfect Gaussian behaviours expected in perfectly ergodic systems and the corrections to that can be connected to the subdiffusion exponent.
Sthitadhi Roy, Yevgeny Bar Lev, David J. Luitz, "Anomalous thermalization and transport in disordered interacting Floquet systems" [Phys. Rev. B 98, 060201(R) (2018)] [arXiv:1802.03401]
Floquet multifractality
One of the questions I was particualrly interested was can periodic driving lead to fundamentally new physics in terms of localisation properties. Remarkably, we found that indeed it can, and in systems with quasiperiodic potentials and mobility edges, robust multifractal states show up [1]. They are robust in the sense that the multifractal states persist over a finite range of system parameters, and hence they are fundamentally different from multifractality realised in time-independent systems as in such cases, multifractality is associated with critical points of Anderson transitions and hence naturally are fine tuned.
Sthitadhi Roy, Ivan M. Khaymovich, Arnab Das, Roderich Moessner, "Multifractality without fine-tuning in a Floquet quasiperiodic chain" [SciPost Phys. 4, 025 (2018)][arXiv:1706.05012]
Different scalings of the inverse participation ratio signalling the coexistence of delocalised, localised, and multifractal states in the Floquet spectrum
Disordered Floquet Chern insulators
Another question of interest in this regard was the effect of disorder on Floquet topological phases, for instance, in Floquet Chern insulators. We found that such systems can host anomalous Floquet topological Anderson insulators with disorder-driven topological transitions between them [3]. The topological aspects of the systems in such cases is described by a generalised winding number which takes the periodicity of the Hamiltonian into account and can be extended to the case of disordered systems in terms of flux insertions. Further we found that the phase transitions in such systems is similar to a levitation-annihilation type transition, except the levitation-annihilation does not necessarily happen at zero energy, but at the quasienergy of the topological edge modes.
Sthitadhi Roy, G. J. Sreejith, "Disordered Chern insulator with a two-step Floquet drive" [Phys. Rev. B 94, 214203 (2016) ][arXiv:1608.06302]
The levitation and annihilation mechanism for Floquet systems is shown schematically, for the case of edge modes in the (a) 0-gap and the (b) π-gap. The bulk localised, the bulk delocalised and the edge modes in the spectrum are depicted gray, orange and purple colors respectively.