Time evolution during and after finite-time quantum quenches in the  transverse-field Ising chain

Puskarov, Tatjana; Schuricht, Dirk

doi:10.21468/scipostphys.1.1.003

Cited by 49 publications

(85 citation statements)

References 77 publications

(127 reference statements)

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“…[32] and the lines of FZs were indeed found to cross the real time axis at those instants. This observation has been independently confirmed through several works on quenched one-dimensional (1D) integrable and non-integrable systems [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53]. Subsequent studies, however, have established that sudden quenching within the same phase of a system (both integrable and non-integrable) without ever encountering an equilibrium QCP may still give rise to DQPTs in some situations [54,55].…”

Section: Introductionmentioning

confidence: 83%

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

Bhattacharya

Dutta

2017

Phys. Rev. B

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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 nonzero (quasi-momentum dependent) Haldane mass (MH ), whose absence leads to an emergent onedimensional 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 MH vanishes. Thus, we observe that through the presence or absence of MH , 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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Section: Introductionmentioning

confidence: 83%

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

Bhattacharya

Dutta

2017

Phys. Rev. B

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“…Further studies, however, revealed that DQPTs can occur following a quench also within the same phase [48][49][50]. Other theoretical works have explored DQPTs in topological and mixed phases [72][73][74][75][76] and also after slow quenches ("ramps") [77][78][79].…”

Section: Dynamical Quantum Phase Transitionsmentioning

confidence: 99%

Quench dynamics and zero-energy modes: The case of the Creutz model

et al. 2019

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In most lattice models, the closing of a band gap typically occurs at high-symmetry points in the Brillouin zone. Differently, in the Creutz model − describing a system of spinless fermions hopping on a two-leg ladder pierced by a magnetic field − the gap closing at the quantum phase transition between the two topologically nontrivial phases of the model can be moved by tuning the hopping amplitudes. We take advantage of this property to examine the nonequilibrium dynamics of the model after a sudden quench of the magnetic flux through the plaquettes of the ladder. For a quench to one of the equilibrium quantum critical points we find that the revival period of the Loschmidt echo − measuring the overlap between initial and time-evolved states − is controlled by the gap closing zero-energy modes. In particular, and contrary to expectations, the revival period of the Loschmidt echo for a finite ladder does not scale linearly with size but exhibits jumps determined by the presence or absence of zero-energy modes. We further investigate the conditions for the appearance of dynamical quantum phase transitions in the model and find that, for a quench to an equilibrium critical point, such transitions occur only for ladders of sizes which host zero-energy modes. Exploiting concepts from quantum thermodynamics, we show that the average work and the irreversible work per lattice site exhibit a weak dependence on the size of the system after a quench across an equilibrium critical point, suggesting that quenching into a different phase induces effective correlations among the particles.

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“…Experimentally, DQPTs have been observed in trapped ions [3,10], cold atoms [11,12], superconducting qubits [13], nanomechanical oscillators [14], and photonic quantum walks [15,16].To date, in most studies of DQPTs, a quantum quench acts as a trigger for initiating nonequilibrium dynamics and then exposing the underlying topological features. However, DQPTs under more general nonequilibrium manipulations are still largely unexplored [17][18][19]. In particular, because the dynamics of systems under time-periodic modulations has led to fascinating discoveries like Floquet topological states [20-24] and discrete time crystals [25][26][27], it is urgent to investigate how DQPTs may occur in such Floquet systems.…”

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confidence: 99%

Floquet dynamical quantum phase transitions

et al. 2019

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Dynamical quantum phase transitions (DQPTs) are manifested by time-domain nonanalytic behaviors of many-body systems. Introducing a quench is so far understood as a typical scenario to induce DQPTs. In this work, we discover a novel type of DQPTs, termed "Floquet DQPTs", as intrinsic features of systems with periodic time modulation. Floquet DQPTs occur within each period of continuous driving, without the need for any quenches. In particular, in a harmonically driven spin chain model, we find analytically the existence of Floquet DQPTs in and only in a parameter regime hosting a certain nontrivial Floquet topological phase. The Floquet DQPTs are further characterized by a dynamical topological invariant defined as the winding number of the Pancharatnam geometric phase versus quasimomentum. These findings are experimentally demonstrated with a single spin in diamond. This work thus opens a door for future studies of DQPTs in connection with topological matter.DQPTs are often associated with quantum quenches, a protocol in which parameters of a Hamiltonian are suddenly changed [1,2]. A quantum quench across an equilibrium quantum critical point may induce a DQPT. If pre-quench and post-quench systems are in topologically distinct phases, DQPTs may also be characterized by dynamical topological invariants [3][4][5]. As a promising approach to classify quantum states of matter in nonequilibrium situations, DQPTs have been theoretically explored in both closed and open quantum systems at different physical dimensions [2,7,8]. Experimentally, DQPTs have been observed in trapped ions [3,10], cold atoms [11,12], superconducting qubits [13], nanomechanical oscillators [14], and photonic quantum walks [15,16].To date, in most studies of DQPTs, a quantum quench acts as a trigger for initiating nonequilibrium dynamics and then exposing the underlying topological features. However, DQPTs under more general nonequilibrium manipulations are still largely unexplored [17][18][19]. In particular, because the dynamics of systems under time-periodic modulations has led to fascinating discoveries like Floquet topological states [20-24] and discrete time crystals [25][26][27], it is urgent to investigate how DQPTs may occur in such Floquet systems. Along this avenue, there have been scattered studies, but still with the notion that DQPTs are best aroused by a quench to some system parameters [28,29]. Here we introduce a novel class of DQPTs, termed Floquet DQPTs, which can be regarded as intrinsic features of systems with time-periodic modulations. As schematically shown in Floquet DQPT Time Time Rate function Rate function H i H f (a) H(t) (b) Conventional DQPT T T Quench T FIG. 1. Comparison between (a) DQPTs following a quantum quench, and (b) Floquet DQPTs without any quenches.Here Hi and H f denote the Hamiltonians before and after the quench, H(t) denotes a periodically and continuously modulated Hamiltonian. Fig. 1, the Floquet DQPTs we discovered occur within each period of a continuous driving field, without the need for any...

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Time evolution during and after finite-time quantum quenches in the transverse-field Ising chain

Cited by 49 publications

References 77 publications

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

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

Quench dynamics and zero-energy modes: The case of the Creutz model

Floquet dynamical quantum phase transitions

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