Research

My current researches are focused on

Statics and dynamics of exactly solvable models (like XY-spin chain and two-dimensional honeycomb Kitaev model)

We have explored the statics and dynamics of exactly solvable models (like XY-spin chain and two-dimensional honeycomb Kitaev model). The Loschmidt echo is studied when the spin system (the environment) is globally coupled to a central spin and is related to the decoherence of the central spin as the spin system evolves.

We then studied the Loschmidt echo in a situation where the spin system is in a non-equilibrium initial state because of a sudden quenching of one of the parameters of its Hamiltonian. We have shown that the decoherence of the central spin is markedly enhanced in the present case though the scaling of the decay constant dictating the Gaussian decay of the echo in the early time limit is unaffected (see Ref. [2]).

We have shown that the Loschmidt echo shows a sharp dip at a quantum critical point (which implies the maximum loss of coherence of the central spin) and we have proposed a scaling for the early time decay of the echo . The Echo also shows an interesting behavior within the extended gapless region appearing in the phase diagram of the Kitaev model (see Refs. [1], [2] and [3]).

Effect of marginality on the ground state fidelity and Loschmidt echo near the quantum critical point

We have studied the effect of marginality on the ground state fidelity and Loschmidt echo near the quantum critical point (QCP) of the two-dimensional Dirac Hamiltonian in the presence of a mass term tuned to zero at the Dirac point (see Ref. [4]).

Quench Dynamics of Edge States in 2-D Topological Insulator Ribbons

We have completed a study of dynamics of Dirac points appearing in the two dimensional system, topological insulator in a ribbon-geometry and observed very interesting dynamics of the edge states following a quench in the latter case (see Ref. [5])

Periodically driven quantum systems and Floquet theory

We have studied the fidelity between the initial ground state of a transverse XY spin chain and the final state generated by successive periodic driving of the transverse field. Using the Floquet theory and the notion of a decohered density matrix we have shown that the system reaches a synchronized state following an infinite number high frequency driving resulting a value of fidelity smaller than unity. We are also exploring the singularities in the rate exponent of the LE at different instants of time following a quench (see Ref. [6]).

Work-Statistics

All our observations deals with the quenching of a parameter of the Hamiltonian. The work done by the system acquires a stochastic behaviour for a non-adiabatic quenching process. We investigate how the work done appears in such case for different quenching schemes and different systems at zero and finite temperatures (see Ref. [7] and [8]).

Dynamical Phase Transition

Analogous to the non-analyticities in the free-energy density of in a thermodynamic system at the time of the phase transition at a finite temperature, one can observe the non-analyticities in the time for a quantum phase transition referred to as dynamical phase transitions (DPTs). We focus towards understanding the existence and absence of DPTs in integrable and non-integrable models (see [9] in the LOP).

Quantum Optics

We analyze self-organization of atoms in an optical lattice formed by the laser field and the interaction mediated by the cavity field. The two wavelengths (optical lattice and the standing wave field of the cavity) being incommensurate with each other gives rise to a special phase, 'Bose-Glass'. The idea is to understand the interplay between the long-range cavity mediated interaction and the short range interaction in a Bose-Hubbard model including infinitely ranged cavity potential.

Hybrid Random Quantum Circuits

We explore the out-of-equilibrium phases of a special class of system consisting of alternate layers of measurements and unitary matrices, referred to as 'Hybrid Random Quantum Circuits'. In these systems the competition between entangling nature of unitary evolution and disentangling nature of measurements leads to a volume-law to area-law transition in the scaling of entanglement entropy at a fixed non-zero value of rate of measurement. It has been shown that these phase transitions in specific analytical continual limit belongs to the Universality class of specific statistical model's phase transition. We probe the effect of different types of unitary gates and measurements, to find out what kind of phases and phase transitions we obtain in such strongly correlated systems.