arXiv subjects

Utso Bhattacharya

Publications and source records attributed to Utso Bhattacharya.

52 records · Page 3Linked to original sources

arXiv2019

Fibonacci steady states in a driven integrable quantum system

We study an integrable system that is reducible to free fermions by a Jordan-Wigner transformation which is subjected to a Fibonacci driving protocol based on two non-commuting Hamiltonians. In the high frequency limit $ω\to \infty$, we show that the system reaches a non-equilibrium steady state, up to some small fluctuations which can be quantified. For each momentum $k$, the trajectory of the stroboscopically observed state lies between two concentric circles on the Bloch sphere; the circles represent the boundaries of the small fluctuations. The residual energy is found to oscillate in a quasiperiodic way between two values which correspond to the two Hamiltonians that define the Fibonacci protocol. These results can be understood in terms of an effective Hamiltonian which simulates the dynamics of the system in the high frequency limit.

cond-mat.stat-mech↗

arXiv2018

Critical phase boundaries of static and periodically kicked long-range Kitaev chain

We study the static and dynamical properties of a long-range Kitaev chain, i.e., a $p$-wave superconducting chain in which the superconducting pairing decays algebraically as $1/l^α$, where $l$ is the distance between the two sites and $α$ is a positive constant. Considering very large system sizes, we show that when $α>1$, the system is topologically equivalent to the short-range Kitaev chain with massless Majorana modes at the ends of the system; on the contrary, for $α<1$, there exist symmetry protected massive Dirac end modes. We further study the dynamical phase boundary of the model when periodic $δ$-function kicks are applied to the chemical potential; we specially focus on the case $α>1$ and analyze the corresponding Floquet quasienergies. Interestingly, we find that new topologically protected massless end modes are generated at the quasienergy $π/T$ (where $T$ is the time period of driving) in addition to the end modes at zero energies which exist in the static case. By varying the frequency of kicking, we can produce topological phase transitions between different dynamical phases. Finally, we propose some bulk topological invariants which correctly predict the number of massless end modes at quasienergies equal to 0 and $π/T$ for a periodically kicked system with $α> 1$.

cond-mat.mes-hall↗

arXiv2018

Role of topology on the work distribution function of a quenched Haldane model of graphene

We investigate the effect of equilibrium topology on the statistics of non-equilibrium work performed during the subsequent unitary evolution, following a sudden quench of the Semenoff mass of the Haldane model. We show that the resulting work distribution function for quenches performed on the Haldane Hamiltonian with broken time reversal symmetry (TRS) exhibits richer universal characteristics as compared to those performed on the time-reversal symmetric massive graphene limit whose work distribution function we have also evaluated for comparison. Importantly, our results show that the work distribution function exhibits different universal behaviors following the non-equilibrium dynamics of the system for small $ϕ$ (argument of complex next nearest neighbor hopping) and large $ϕ$ limits, although the two limits belong to the same equilibrium universality class.

cond-mat.stat-mech↗

arXiv2018

The fate of current, residual energy and entanglement entropy in aperiodic driving of one dimensional Jordan Wigner integrable models

We investigate the dynamics of two Jordan Wigner solvable models, namely, the one dimensional chain of hard-core bosons (HCB) and the one-dimensional transverse field Ising model under coin-toss like aperiodically driven staggered on-site potential and the transverse field, respectively. It is demonstrated that both the models heat up to the infinite temperature ensemble for a minimal aperiodicity in driving. Consequently, in the case of the HCB chain, we show that the initial current generated by the application of a twist vanishes in the asymptotic limit for any driving frequency. For the transverse Ising chain, we establish that the system not only reaches the diagonal ensemble but the entanglement also attains the thermal value in the asymptotic limit following initial ballistic growth. All these findings, contrasted with that of the perfectly periodic situation, are analytically established in the asymptotic limit within an exact disorder matrix formalism developed using the uncorrelated binary nature of the coin-toss aperiodicity.

cond-mat.stat-mech↗

arXiv2018

Exploring the possibilities of dynamical quantum phase transitions in the presence of a Markovian bath

We explore the possibility of dynamical quantum phase transitions (DQPTs) occurring during the temporal evolution of a quenched transverse field Ising chain coupled to a particle loss type of bath (local in Jordan-Wigner fermion space) using two versions of the Loschmidt overlap (LO), namely, the fidelity induced LO and the interferometric phase induced LO. The bath, on the one hand, dictates the dissipative evolution following a sudden quench and on the other, plays a role in dissipative mixed state preparation in the later part of the study. During a dissipative evolution following a sudden quench, no trace of DQPTs are revealed in both the fidelity and the interferometric phase approaches; however, remarkably the interferometric phase approach reveals the possibility of inter-steady state DQPTs in passage from one steady state to the other when the system is subjected to a quench after having reached the first steady state. We further probe the occurrences of DQPTs when the system evolves unitarily after being prepared in a mixed state of engineered purity by ramping the transverse field in a linear fashion in the presence of the bath. In this case though the fidelity approach fails to indicate any DQPT, the interferometric approach indeed unravels the possibility of occurrence of DQPTs which persists even up to a considerable loss of purity of the engineered initial state as long as a constraint relation involving the dissipative coupling and ramping time (rate) is satisfied. This constraint relation also marks the boundary between two dynamically inequivalent phases; in one the LO vanishes for the critical momentum mode (and hence DQPTs exist) while in the other no such critical mode can exist and hence the LO never vanishes.

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arXiv2018

Topological footprints of the 1D Kitaev chain with long range superconducting pairings at a finite temperature

We study the 1D Kitaev chain with long range superconductive pairing terms at a finite temperature where the system is prepared in a mixed state in equilibrium with a heat reservoir maintained at a constant temperature $T$. In order to probe the footprint of the ground state topological behavior of the model at finite temperature, we look at two global quantities extracted out of two geometrical constructions: the Uhlmann and the interferometric phase. Interestingly, when the long-range effect dominates, the Uhlmann phase approach fails to reproduce the topological aspects of the model in the pure state limit; on the other hand, the interferometric phase, though has a proper pure state reduction, shows a behaviour independent of the ambient temperature.

cond-mat.stat-mech↗

arXiv2018

Exact results in Floquet coin toss for driven integrable models

We study an integrable Hamiltonian reducible to free fermions which is subjected to an imperfect periodic driving with the amplitude of driving (or kicking) randomly chosen from a binary distribution like a coin-toss problem. The randomness present in the driving protocol destabilises the periodic steady state, reached in the limit of perfectly periodic driving, leading to a monotonic rise of the stroboscopic residual energy with the number of periods ($N$). We establish that a minimal deviation from the perfectly periodic driving would always result in a {\it bounded} heating up of the system with $N$ to an asymptotic finite value. Remarkably, exploiting the completely uncorrelated nature of the randomness and the knowledge of the stroboscopic Floquet operator in the perfectly periodic situation, we provide an exact analytical formalism to derive the disorder averaged expectation value of the residual energy through a {\it disorder operator}. This formalism not only leads to an immense numerical simplification, but also enables us to derive an exact analytical form for the residual energy in the asymptotic limit which is universal, i.e, independent of the bias of coin-toss and the protocol chosen. Furthermore, this formalism clearly establishes the nature of the monotonic growth of the residual energy at intermediate $N$ while clearly revealing the possible non-universal behaviour of the same.

cond-mat.stat-mech↗

arXiv2018

Dynamics of edge current in a linearly quenched Haldane model

In a finite time quantum quench of the Haldane model, the Chern number determining the topology of the bulk remains invariant, as long as the dynamics is unitary. Nonetheless, the corresponding boundary attribute, the edge current, displays interesting dynamics. For the case of sudden and adiabatic quenches the post quench edge current is solely determined by the initial and the final Hamiltonians, respectively. However for a finite time ($τ$) linear quench in a Haldane nano ribbon, we show that the evolution of the edge current from the sudden to the adiabatic limit is not monotonic in $τ$, and has a turning point at a characteristic time scale $τ=τ_c$. For small $τ$, the excited states lead to a huge unidirectional surge in the edge current of both the edges. On the other hand, in the limit of large $τ$, the edge current saturates to its expected equilibrium ground state value. This competition between the two limits lead to the observed non-monotonic behavior. Interestingly, $τ_c$ seems to depend only on the Semenoff mass and the Haldane flux. A similar dynamics for the edge current is also expected in other systems with topological phases.

cond-mat.mes-hall↗

arXiv2017

Interconnections between equilibrium topology and dynamical quantum phase transitions in a linearly ramped Haldane model

We study the behavior of Fisher Zeros (FZs) and dynamical quantum phase transitions (DQPTs) for a linearly ramped Haldane model occurring in the subsequent temporal evolution of the same and probe the intimate connection with the equilibrium topology of the model}. Here, we investigate the temporal evolution of the final state of the Haldane Hamiltonian (evolving with time-independent final Hamiltonian) reached following a linear ramping of the staggered (Semenoff) mass term from an initial to a final value, {first selecting a specific protocol}, so chosen that the system is ramped from one non-topological phase to the other through a topological phase. {We establish the existence of three possible behaviour of areas of FZs corresponding to a given sector: (i) no-DQPT, (ii) one-DQPT (intermediate) and (iii)two-DQPTs (re-entrant), depending on the inverse quenching rate $τ$. Our study also reveals that the appearance of the areas of FZs is an artefact of the non-zero (quasi-momentum dependent) Haldane mass ($M_H$), whose absence leads to an emergent one-dimensional behaviour indicated by the shrinking of the areas FZs to lines and the non-analyticity in the dynamical "free energy" itself. Moreover, the characteristic rates of crossover between the three behaviour of FZs are determined by the time-reversal invariant quasi-momentum points of the Brillouin zone where $M_H$ vanishes. Thus, we observe that through the presence or absence of $M_H$, there exists an intimate relation to the topological properties of the equilibrium model even when the ramp drives the system far away from equilibrium.

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arXiv2017

Mixed state dynamical quantum phase transition and emergent topology

Preparing an integrable system in a mixed state described by a thermal density matrix , we subject it to a sudden quench and explore the subsequent unitary dynamics. Defining a version of the generalised Loschmidt overlap amplitude (GLOA) through the purifications of the time evolved density matrix, we claim that non-analyiticies in the corresponding "dynamical free energy density" persist and is referred to as mixed state dynamical quantum phase transitions (MSDQPTs). Furthermore, these MSDQPTs are uniquely characterised by a topological index constructed by the application of the Pancharatnam geometry on the purifications of the thermal density matrix; the quantization of this index however persists up to a critical temperature. These claims are corroborated analysing the non-equilibrium dynamics of a transverse Ising chain initially prepared in a thermal state and subjected to a sudden quench of the transverse field.

cond-mat.stat-mech↗

arXiv2017

Quenching in Chern insulators with satellite Dirac points: The fate of edge states

We perform a sudden quench on the Haldane model with long range interactions, more specifically generalising to the next to next nearest neighbour hopping, referred to as the $N3$ model in our work. Such a model possesses both isotropic and multiple anisotropic (satellite) Dirac points which lead to a rich topological phase diagram consisting of phases with higher Chern number ($C$). Quenches between the topological and the non-topological phases of such an infinite system probe the effect of the presence of the anisotropic Dirac points on the non-equilibrium response of the topological system. Interestingly, the Chern number remains the same before and after the quench for both the quenching protocols, even when the quench of the system is carried out between two different topological phases. {However, for a finite system, we establish that the initial edge current asymptotically decays to zero when the system is quenched to the non-topological phase although the Chern number for the corresponding periodically wrapped system remains unaltered; what is remarkable is that when the Hamiltonian is quenched from $|C|=2$ phase to the non-topological phase the edge current associated with the inner channel decays at a faster rate than the outer channel resembling a situation in which the system passes through the phase with $|C|=1$ before ending up in the phase $C=0$.

cond-mat.stat-mech↗

arXiv2017

Emergent topology and dynamical quantum phase transitions in two-dimensional closed quantum systems

We introduce the notion of a dynamical topological order parameter (DTOP) that characterises dynamical quantum phase transitions (DQPTs) occurring in the subsequent temporal evolution of "two dimensional" closed quantum systems, following a quench (or ramping) of a parameter of the Hamiltonian, {which generalizes the notion of DTOP introduced in Budich and Heyl, Phys. Rev. B 93, 085416 (2016) for one-dimensional situations}. This DTOP is obtained from the "gauge-invariant" Pancharatnam phase extracted from the Loschmidt overlap, i.e., the modulus of the overlap between the initially prepared state and its time evolved counterpart reached following a temporal evolution generated by the time-independent final Hamiltonian. This generic proposal is illustrated considering DQPTs occurring in the subsequent temporal evolution following a sudden quench of the staggered mass of the topological Haldane model on a hexagonal lattice where it stays fixed to zero or unity and makes a discontinuous jump between these two values at critical times at which DQPTs occur.

cond-mat.stat-mech↗

arXiv2016

Dynamical manipulation of Dirac points in the Kitaev honeycomb model

We study the effect of a half wave rectified sinusoidal electromagnetic (EM) wave on the Kitaev honeycomb model with an additional magneto-electric coupling term {arising due to induced polarization of the bonds. Within the framework of Floquet analysis, we show that merging of a pair of Dirac points in the gapless region of the Kitaev model leading to a semi-Dirac spectrum is indeed possible} by externally varying the amplitude and the phase of the EM field.

cond-mat.stat-mech↗

arXiv2016

Effects of periodic kicking on dispersion and wave packet dynamics in graphene

We study the effects of $δ$-function periodic kicks on the Floquet energy-momentum dispersion in graphene. We find that a rich variety of dispersions can appear depending on the parameters of the kicking: at certain points in the Brillouin zone, the dispersion can become linear but anisotropic, linear in one direction and quadratic in the perpendicular direction, gapped with a quadratic dispersion, or completely flat (called dynamical localization). We show all these results analytically and demonstrate them numerically through the dynamics of wave packets propagating in graphene. We propose experimental methods for producing these effects.

cond-mat.mes-hall↗

arXiv2014

Phase Transition in the periodically pulsed Dicke Model

We study the effect of pulsed driving and kicked driving of the interaction term on the non-equilibrium phase transition in the Dicke Model. Within the framework of Floquet theory, we observe the emergence of new non-trivial phases on impingement by such periodic pulses. Notably, our study reveals that a greater control over the dynamical quantum criticality is possible through the variation of multiple parameters related to the pulse, as opposed to a single parameter control in a monochromatic drive. Furthermore, the probability of the system remaining trapped in a metastable state during the observed first order transition from the super-radiant to normal phase is found to be higher for small number of kicks (or pulses) in comparison to the sinusoidal perturbation.

cond-mat.stat-mech↗

arXiv2014

Exploring chaos in Dicke Model using ground state fidelity and Loschmidt echo

We study the quantum critical behaviour of the Dicke Hamiltonian, with finite number of atoms and explore the signature of quantum chaos using measures like the ground state fidelity and the Loschmidt echo. We show that both these quantities clearly point to the chaotic nature of the system in the super-radiant phase.

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