arXiv subjects

Amit Dutta

Publications and source records attributed to Amit Dutta.

At least 37 records · Page 2Linked to original sources

arXiv2020

Unitary preparation of many body Chern insulators: Adiabatic bulk boundary correspondence

We approach the long-standing problem of preparing an out-of-equilibrium many-body Chern insulator (CI) and associated bulk-boundary correspondence unitarily. Herein, this is addressed by constructing a dynamical many-body Chern invariant exploiting the property of the bulk macroscopic electric polarisation (Resta polarisation) of the CI. This Chern invariant defined from observable correlations is also established to topologically classify many body Chern states in equilibrium. The non-equilibrium behavior of the invariant is probed by ramping the paradigmatic Haldane model of graphene from its trivial to the topological phase. We show that a non-linear ramp may work more efficiently in approaching the topological state, thereby establishing the existence of an optimal topological state preparation. Furthermore, to ensure the near adiabatic dynamics across the quantum critical point, we propose a novel counter-diabatic scheme. The topological nature of the prepared state is firmly established by observing an emerging $U(1)$ topological charge. We also compute the edge current in the time evolved state of the system under a semi-periodic boundary condition and clearly establish an adiabatic bulk-boundary correspondence which firmly ensconces the validity of the many-body invariant.

cond-mat.stat-mech↗

arXiv2020

Dissipative preparation of many-body Floquet Chern insulators

Considering coupling to a micro-structured bath as a relaxation mechanism in a periodically driven dissipative Haldane model, we establish that the system may be tuned to a stroboscopic topological steady state at all finite temperatures. The amplitude and frequency of the periodic drive is so chosen that the Floquet Hamiltonian describing the Haldane model at stroboscopic instants of time in the unitary situation is topologically non-trivial. We establish that in the stroboscopic steady state, the system reaches a thermal state of the Floquet Hamiltonian at a controlled temperature. Further, it is observed that even with a coupling to a quasi-local bath, remarkably a Chern insulator can indeed be prepared in a Chern non-trivial pure steady state which is expected to exhibit a stroboscopic bulk-boundary correspondence. Using the non-uniqueness of the macroscopic bulk electric polarisation of a Chern insulator in its topological phase, we propose a generalised Chern invariant that reflects the topology of out-of-equilibrium many-body stroboscopic states of the Haldane model even in a dissipative ambience. The generalised topology of dynamical Chern insulators being dependent on single-particle correlations, is expected to manifest in experiments probing many-body quantum observables.

cond-mat.stat-mech↗

arXiv2020

Growth of mutual information in a quenched one-dimensional open quantum many body system

We study the temporal evolution of the mutual information (MI) in a one-dimensional Kitaev chain, coupled to a fermionic Markovian bath, subsequent to a global quench of the chemical potential. In the unitary case, the MI (or equivalently the bipartite entanglement entropy) saturates to a steady-state value (obeying a volume law) following a ballistic growth. On the contrary, we establish that in the dissipative case the MI is exponentially damped both during the initial ballistic growth as well as in the approach to the steady state. We observe that even in a dissipative system, postquench information propagates solely through entangled pairs of quasiparticles having a finite lifetime; this quasiparticle picture is further corroborated by the out-of-equilibrium analysis of two-point fermionic correlations. Remarkably, in spite of the finite lifetime of the quasiparticles, a finite steady-state value of the MI survives in asymptotic times which is an artifact of nonvanishing two-point correlations. Further, the finite lifetime of quasiparticles renders to a finite length scale in these steady-state correlations.

cond-mat.stat-mech↗

arXiv2020

Quantum magnetometry using two-stroke thermal machines

The precise estimation of small parameters is a challenging problem in quantum metrology. Here, we introduce a protocol for accurately measuring weak magnetic fields using a two-level magnetometer, which is coupled to two (hot and cold) thermal baths and operated as a two-stroke quantum thermal machine. Its working substance consists of a two-level system (TLS), generated by an unknown weak magnetic field acting on a qubit, and a second TLS arising due to the application of a known strong and tunable field on another qubit. Depending on this field, the machine may either act as an engine or a refrigerator. Under feasible conditions, determining this transition point allows to reduce the relative error of the measurement of the weak unknown magnetic field by the ratio of the temperatures of the colder bath to the hotter bath.

quant-ph↗

arXiv2019

One-dimensional quantum many body systems with long-range interactions

The presence of algebraically decaying long-range interactions may alter the critical as well as topological behaviour of a quantum many-body systems. However, when the interaction decays at a faster rate, the short-range behaviour is expected to be retrieved. Similarly, the long-range nature of interactions has a prominent signature on the out of equilibrium dynamics of these systems, e.g, in the growth of the entanglement entropy following a quench, the propagation of mutual information and non-equilibrium phase transitions. In this review, we summarize the results of long-range interacting classical and quantum Ising chains which have been studied since decades. Thereafter, we focus on the recent developments on the integrable long-range Kitaev chain emphasising the role of long-range superconducting pairing term on determining its topological phase diagram and out of equilibrium dynamics.

cond-mat.stat-mech↗

arXiv2019

Dynamical Quantum Phase Transitions in Extended Toric-Code Models

We study the nonequilibrium dynamics of the extended toric code model (both ordered and disordered) to probe the existence of the dynamical quantum phase transitions (DQPTs). We show that in the case of the ordered toric code model, the zeros of Loschmidt overlap (generalized partition function) occur at critical times when DQPTs occur, which is confirmed by the nonanalyticities in the dynamical counter-part of the free-energy density. Moreover, we show that DQPTs occur for any non-zero field strength if the initial state is the excited state of the toric code model. In the disordered case, we show that it is imperative to study the behavior of the first time derivative of the dynamical free-energy density averaged over all the possible configurations, to characterize the occurrence of a DQPTs in the disordered toric code model since the disorder parameter itself acts as a new artificial dimension. We also show that for the case where anyonic excitations are present in the initial state, the conditions for a DQPTs to occur are the same as what happens in the absence of any excitation.

cond-mat.stat-mech↗

arXiv2019

Dynamical preparation of a topological state and out of equilibrium bulk boundary correspondence in a SSH chain under periodic driving

Exploiting the possibility of temporal variation of the winding number, we have prepared a SSH chain in its {\it stroboscopic} topological state, starting from the trivial one, by application of a periodic perturbation. The periodic driving, we employ here, is adiabatically switched on to break the particle-hole symmetry and generate a chiral mass term in the effective Floquet Hamiltonian; consequently the Floquet Hamiltonian also gets deformed without crossing the gapless quantum critical point. The particle hole symmetry is subsequently restored in the Floquet Hamiltonian by adiabatically switching off a part of the periodic potential. Thereafter, the Floquet Hamiltonian develops a symmetry protected non-trivial topological winding number. Furthermore, we also observe stroboscopic topologically protected localised edge states in a long open chain and show that a bulk boundary correspondence survives a unitary non-equilibrium situation in 1D BDI Hamiltonians. Moreover, considering an extended SSH chain with higher neighbour hoppings, we dynamically prepare the system in a stroboscopic out-of-equilibrium topological insulator state starting from a metallic regime. At the same time, we establish the dynamical preparation of higher winding phases in an extended SSH chain with stroboscopic bulk-boundary correspondence in the non-equilibrium state of the system.

cond-mat.mes-hall↗

arXiv2019

Temporal variation in the winding number due to dynamical symmetry breaking and associated transport in a driven SSH chain

Considering a BDI symmetric one-dimensional SSH model, we explore the fate of the bulk topological invariant, namely, the winding number under a generic time dependent perturbation; the effective Hamiltonian, that generates the temporal evolution of the initial (ground) state of the completely symmetric initial Hamiltonian, may have the same or different symmetries. To exemplify, we consider the following protocols, namely (i) a perfectly periodic protocol (ii) a periodic protocol with noisy perturbations and also (iii) sudden changes in the parameters of the initial Hamiltonian. We establish that the topological invariant may change in some cases when the effective Hamiltonian (or the Floquet Hamiltonian in the periodic situation when observed stroboscopically) does not respect all BDI symmetries; this is manifested in the associated particle (polarisation) or heat current in the bulk. Our results establish a strong connection between the time evolution of the winding number (thus, the associated transport of currents) and the symmetry of the Hamiltonian generating the time evolution which has been illustrated considering an exhaustive set of possibilities.

cond-mat.stat-mech↗

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.

cond-mat.stat-mech↗

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

Dynamical Quantum Phase Transitions in Extended Transverse Ising Models

We study the dynamical quantum phase transitions (DQPTs) manifested in the subsequent unitary dynamics of an extended Ising model with additional three spin interactions following a sudden quench. Revisiting the equilibrium phase diagram of the model where different quantum phases are characterised by different winding numbers, we show that in some situations the winding number may not change across a gap closing point in the energy spectrum. Although, usually there exists a one-to-one correspondence between the change in winding number and the number of critical time scales associated with DQPTs, we show that the extended nature of interactions may lead to unusual situations. Importantly, we show that in the limit of the cluster Ising model, three critical modes associated with DQPTs become degenerate and thereby leading to a single critical time scale for a given sector of Fisher zeros.

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

Probing the role of long-range interactions in the dynamics of a long-range Kitaev Chain

We study the role of long-range interactions on the non-equilibrium dynamics considering a long-range Kitaev chain in which superconducting term decays with distance between two sites in a power-law fashion characterised by an exponent $α$. We show that the Kibble-Zurek scaling exponent, dictating the power-law decay of the defect density in the final state reached following a slow quenching of the chemical potential ($μ$) across a quantum critical point, depends non-trivially on the exponent $α$ as long as $α<2$; on the other hand, for $α>2$, one finds that the exponent saturates to the corresponding well-know value of $1/2$ expected for the short-range model. Furthermore, studying the dynamical quantum phase transitions manifested in the non-analyticities in the rate function of the return possibility ($I(t)$) in subsequent temporal evolution following a sudden change in $μ$, we show the existence of a new region; in this region, we find three instants of cusp singularities in $I(t)$ associated with a single sector of Fisher zeros. Notably, the width of this region shrinks as $α$ increases and vanishes in the limit $α\to 2$.

cond-mat.stat-mech↗