arXiv subjects

Amit Dutta

Publications and source records attributed to Amit Dutta.

At least 55 records · Page 3Linked to original sources

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.

cond-mat.stat-mech↗

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

Slow quenches in a quantum Ising chain; dynamical phase transitions and topology

We study the slow quenching dynamics (characterized by an inverse rate, $τ^{-1}$) of a one-dimensional transverse Ising chain with nearest neighbor ferromagentic interactions across the quantum critical point (QCP) and analyze the Loschmidt overlap {measured using the subsequent temporal evolution of the final wave function (reached at the end of the quenching) with the final time-independent Hamiltonian}. Studying the Fisher zeros of the corresponding generalized "partition function", we probe non-analyticities manifested in the rate function of the return probability known as dynamical phase transitions (DPTs). In contrast to the sudden quenching case, we show that DPTs survive {in the subsequent temporal evolution following the quenching across two critical points of the model for a sufficiently slow rate; furthermore, an interesting "lobe" structure of Fisher zeros emerge.} We have also made a connection to topological aspects studying the dynamical topological order parameter ($ν_D(t)$), as a function of time ($t$) {measured from the instant when the quenching is complete. Remarkably, the time evolution of $ν_D(t)$ exhibits drastically different behavior following quenches across a single QCP and two QCPs. } {In the former case, $ν_D (t)$ increases step-wise by unity at every DPT (i.e., $Δν_D =1$). In the latter case, on the other hand, $ν_D(t)$ essentially oscillates between 0 and 1 (i.e., successive DPTs occur with $Δν_D =1$ and $Δν_D =-1$, respectively), except for instants where it shows a sudden jump by a factor of unity when two successive DPTs carry a topological charge of same sign.

cond-mat.stat-mech↗

arXiv2016

Tuning the presence of dynamical phase transitions in a generalized $XY$ spin chain

We study an integrable spin chain with three spin interactions and the staggered field ($λ$) while the latter is quenched either slowly (in a linear fashion in time ($t$) as $t/τ$ where $t$ goes from a large negative value to a large positive value and $τ$ is the inverse rate of quenching) or suddenly. In the process, the system crosses quantum critical points and gapless phases. We address the question whether there exist non-analyticities (known as dynamical phase transitions (DPTs)) in the subsequent real time evolution of the state (reached following the quench) governed by the final time-independent Hamiltonian. In the case of sufficiently slow quenching (when $τ$ exceeds a critical value $τ_1$), we show that DPTs, of the form similar to those occurring for quenching across an isolated critical point, can occur even when the system is slowly driven across more than one critical point and gapless phases. More interestingly, in the anisotropic situation we show that DPTs can completely disappear for some values of the anisotropy term ($γ$) and $τ$, thereby establishing the existence of boundaries in the $(γ-τ)$ plane between the DPT and no-DPT regions in both isotropic and anisotropic cases. Our study therefore leads to a unique situation when DPTs may not occur even when an integrable model is slowly ramped across a QCP. On the other hand, considering sudden quenches from an initial value $λ_i$ to a final value $λ_f$, we show that the condition for the presence of DPTs is governed by relations involving $λ_i$, $λ_f$ and $γ$ and the spin chain must be swept across $λ=0$ for DPTs to occur.

cond-mat.stat-mech↗

arXiv2016

Generation of concurrence between two qubits locally coupled to a one dimensional spin chain

We consider a generalized central spin model, consisting of two central qubits and an environmental spin chain (with periodic boundary condition) to which these central qubits are locally and weakly connected either at the same site or at two different sites separated by a distance $d$. Our purpose is to study the subsequent temporal generation of entanglement, quantified by concurrence, when initially the qubits are in an unentangled state. In the equilibrium situation, we show that the concurrence survives for a larger value of $d$ when the environmental spin chain is critical. Importantly, a common feature observed both in the equilibrium and the non-equilibrium situations while the latter is created by a sudden but global change of the environmental transverse field, is that the two qubits become maximally entangled for the critical quenching. Following a non-equilibrium evolution of the spin chain, our study for $d\neq 0$, indicates that there exists a threshold time above which concurrence attains a finite value. Additionally, we show that the number of independent decohering channels (DCs) is determined by $d$ as well as the local difference of the transverse field of the two underlying Hamiltonians governing the time evolution. The qualitatively similar behavior displayed by the concurrence for critical and off-critical quenches, as reported here, is characterized by analyzing the non-equilibrium evolution of these channels. The concurrence is maximum when the decoherence factor or the echo associated with the most rapidly DC decays to zero; on the contrary, the condition when the concurrence vanishes is determined non-trivially by the associated decay of one of the intermediate DCs. Analyzing the reduced density of a single qubit, we also explain the observation that the dephasing rate is always slower than the unentanglement rate.

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↗

arXiv2015

Asymptotic work statistics of periodically driven Ising chains

We study the work statistics of a periodically-driven integrable closed quantum system, addressing in particular the role played by the presence of a quantum critical point. Taking the example of a one-dimensional transverse Ising model in the presence of a spatially homogeneous but periodically time-varying transverse field of frequency $ω_0$, we arrive at the characteristic cumulant generating function $G(u)$, which is then used to calculate the work distribution function $P(W)$. By applying the Floquet theory we show that, in the infinite time limit, $P(W)$ converges, starting from the initial ground state, towards an asymptotic steady state value whose small-$W$ behaviour depends only on the properties of the small-wave-vector modes and on a few important ingredients: the time-averaged value of the transverse field, $h_0$, the initial transverse field, $h_{\rm i}$, and the equilibrium quantum critical point $h_c$, which we find to generate a sequence of non-equilibrium critical points $h_{*l}=h_c+lω_0/2$, with $l$ integer. When $h_{\rm i}\neq h_c$, we find a "universal" edge singularity in $P(W)$ at a threshold value of $W_{\rm th}=2|h_{\rm i}-h_c|$ which is entirely determined by $h_{\rm i}$. The form of that singularity --- Dirac delta derivative or square root --- depends on $h_0$ being or not at a non-equilibrium critical point $h_{*l}$. On the contrary, when $h_{\rm i}=h_c$, $G(u)$ decays as a power-law for large $u$, leading to different types of edge singularity at $W_{\rm th}=0$. Generalizing our calculations to the case in which we initialize the system in a finite temperature density matrix, the irreversible entropy generated by the periodic driving is also shown to reach a steady state value in the infinite time limit.

quant-ph↗

arXiv2015

Dynamics of decoherence: universal scaling of the decoherence factor

We study the time dependence of the decoherence factor (DF) of a qubit globally coupled to an environmental spin system (ESS) which is driven across the quantum critical point (QCP) by varying a parameter of its Hamiltonian in time $t$ as $1 -t/τ$ or $-t/τ$, to which the qubit is coupled starting at the time $t \to -\infty$; here, $τ$ denotes the inverse quenching rate. In the limit of weak coupling, we analyze the time evolution of the DF in the vicinity of the QCP (chosen to be at $t=0$) and define three quantities, namely, the generalized fidelity susceptibility $χ_F(τ)$ (defined right at the QCP), and the decay constants $α_1 (τ)$ and $α_2 (τ)$ which dictate the decay of the DF at a small but finite $t$($>0$). Using a dimensional analysis argument based on the Kibble-Zurek healing length, we show that $χ_F(τ)$ as well as $α_1 (τ)$ and $α_2(τ)$ indeed satisfy universal power-law scaling relations with $τ$ and the exponents are solely determined by the spatial dimensionality of the ESS and the exponents associated with its QCP. Remarkably, using the numerical t-DMRG method, these scaling relations are shown to be valid in both the situations when the ESS is integrable and non-integrable and also for both linear and non-linear variation of the parameter. Furthermore, when an integrable ESS is quenched far away from the QCP, there is a predominant Gaussian decay of the DF with a decay constant which also satisfies a universal scaling relation.

cond-mat.stat-mech↗

arXiv2015

Quantum phase transitions in transverse field spin models: from statistical physics to quantum information

We review quantum phase transitions of spin systems in transverse magnetic fields taking the examples of the spin-1/2 Ising and XY models in a transverse field. Beginning with an overview of quantum phase transitions, we introduce a number of model Hamiltonians. We provide exact solutions in one spatial dimension connecting them to conformal field theoretical studies. We also discuss Kitaev models and some other exactly solvable spin systems. Studies of quantum phase transitions in the presence of quenched randomness and with frustrating interactions are presented in detail. We discuss novel phenomena like Griffiths-McCoy singularities. We then turn to more recent topics like information theoretic measures of the quantum phase transitions in these models such as concurrence, entanglement entropy, quantum discord and quantum fidelity. We then focus on non-equilibrium dynamics of a variety of transverse field systems across quantum critical points and lines. After mentioning rapid quenching studies, we dwell on slow dynamics and discuss the Kibble-Zurek scaling for the defect density following a quench across critical points and its modifications for quenching across critical lines, gapless regions and multicritical points. Topics like the role of different quenching schemes, local quenching, quenching of models with random interactions and quenching of a spin chain coupled to a heat bath are touched upon. The connection between non-equilibrium dynamics and quantum information theoretic measures is presented at some length. We indicate the connection between Kibble-Zurek scaling and adiabatic evolution of a state as well as the application of adiabatic dynamics as a tool of a quantum optimization technique known as quantum annealing. The final section is dedicated to a detailed discussion on recent experimental studies of transverse Ising-like systems.

cond-mat.stat-mech↗

arXiv2015

Maximum group velocity in a one-dimensional model with a sinusoidally varying staggered potential

We use Floquet theory to study the maximum value of the stroboscopic group velocity in a one-dimensional tight-binding model subjected to an on-site staggered potential varying sinusoidally in time. The results obtained by numerically diagonalizing the Floquet operator are analyzed using a variety of analytical schemes. In the low frequency limit we use adiabatic theory, while in the high frequency limit the Magnus expansion of the Floquet Hamiltonian turns out to be appropriate. When the magnitude of the staggered potential is much greater or much less than the hopping, we use degenerate Floquet perturbation theory; we find that dynamical localization occurs in the former case when the maximum group velocity vanishes. Finally, starting from an "engineered" initial state where the particles (taken to be hard core bosons) are localized in one part of the chain, we demonstrate that the existence of a maximum stroboscopic group velocity manifests in a light cone like spreading of the particles in real space.

cond-mat.stat-mech↗

arXiv2015

Quenches and dynamical phase transitions in a non-integrable quantum Ising model

We study quenching dynamics of a one-dimensional transverse Ising chain with nearest neighbor antiferromagentic interactions in the presence of a longitudinal field which renders the model non-integrable. The dynamics of the spin chain is studied following a slow (characterized by a rate) or sudden quenches of the longitudinal field; the residual energy, as obtained numerically using a t-DMRG scheme, is found to satisfy analytically predicted scaling relations in both the cases. However, analyzing the temporal evolution of the Loschmidt overlap, we find different possibilities of the presence (or absence) of dynamical phase transitions (DPTs) manifested in the non-analyticities of the rate function. Even though the model is non-integrable, there are {periodic} occurrences of DPTs when the system is slowly ramped across the quantum critical point (QCP) as opposed to the ferromagnetic (FM) version of the model; this numerical finding is qualitatively explained by mapping the original model to an effective integrable spin model which is appropriate for describing such slow quenches. Furthermore, concerning the sudden quenches, our numerical results show that in some cases, DPTs can be present even when the spin chain is quenched within the same phase or even to the QCP while in some other situations they completely disappear even after quenching across the QCP. These observations lead us to the conclusion that it is the change in the nature of the ground state that determines the presence of DPTs following a sudden quench.

cond-mat.stat-mech↗

arXiv2015

One and two-dimensional quantum models: quenches and the scaling of irreversible entropy

Using the scaling relation of the ground state quantum fidelity, we propose the most generic scaling relations of the irreversible work (the residual energy) of a closed quantum system at absolute zero temperature when one of the parameters of its Hamiltonian is suddenly changed; we consider two extreme limits namely, the heat susceptibility limit and the thermodynamic limit. It is then argued that the irreversible entropy generated for a thermal quench at low enough temperature when the system is initially in a Gibbs state, is likely to show a similar scaling behavior. To illustrate this proposition, we consider zero-temperature and thermal quenches in one and two-dimensional Dirac Hamiltonians where the exact estimation of the irreversible work and the irreversible entropy is indeed possible. Exploiting these exact results, we then establish: (i) the irreversible work at zero temperature indeed shows an appropriate scaling in the thermodynamic limit; (ii) the scaling of the irreversible work in the 1D Dirac model at zero-temperature shows logarithmic corrections to the scaling which is a signature of a marginal situation. (iii) Furthermore, remarkably the logarithmic corrections do indeed appear in the scaling of the entropy generated if temperature is low enough while disappears for high temperatures. For the 2D model, no such logarithmic correction is found to appear.

cond-mat.stat-mech↗

arXiv2015

Possibility of adiabatic transport of a Majorana edge state through an extended gapless region

In the context of slow quenching dynamics of a $p$-wave superconducting chain, it has been shown that a Majorana edge state can not be adiabatically transported from one topological phase to the other separated by a quantum critical line. On the other hand, the inclusion of a phase factor in the hopping term, that breaks the extended time reversal invariance, results in an extended gapless region between two topological phases. We show that for a finite chain with an open boundary condition there exists a non-zero probability that an edge Majorana can be adiabatically transported from one topological phase to the other across this gapless region following a slow quench of the superconducting term; this happens for an optimum transit time, that is proportional to the system size and diverges for a thermodynamically large chain. We attribute this phenomenon to the mixing of the Majorana only with low-lying inverted bulk states.

cond-mat.mes-hall↗

arXiv2015

Universal scaling in quenches across a discontinuity critical point

We study slow variation (both spatial as well as temporal) of a parameter of a system in the vicinity of discontinuous quantum phase transitions, in particular, a discontinuity critical point (DCP) (or a first-order critical point). We obtain the universal scaling relations of the density of defects and the residual energy after a temporal quench, while we also unravel the scaling of the characteristic length scale associated with a spatial quench of a symmetry breaking field. Considering a spin-1/2 XXZ chain we establish how these scaling relations get modified when the DCP is located at the boundary of a gapless critical phase; these predictions are also confirmed numerically.

cond-mat.stat-mech↗

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↗