Engineering Floquet dynamical quantum phase transitions

Naji, J.; Jafari, R.; Zhou, Longwen; Langari, A.

doi:10.1103/physrevb.106.094314

Cited by 19 publications

(6 citation statements)

References 93 publications

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“…It can be verified that the effective time-independent Hamiltonian undergoes quantum phase transitions at h c = ±J − ω/2, where the energy gap closes at k = 0, π [16,91]. Therefore the critical points of the effective Hamiltonian can be displaced by tuning the driven frequency.…”

Section: Model and Exact Solutionmentioning

confidence: 93%

“…It should be mentioned that, when the magnetic field is time-independent h(t) = h, the Floquet Hamiltonian in the rotating frame given by the unitary transformation 85,87,[89][90][91], is transformed to the time-independent Hamiltonian…”

Section: Model and Exact Solutionmentioning

confidence: 99%

“…As the equilibrium phase transition is signaled by non-analyticities in the thermal free energy, the DQPT is revealed through the nonanalytical behavior of dynamical free energy, where the real-time plays the role of the control parameter [41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60]. DQPT displays a phase transition between dynamically emerging quantum phases, that takes place during the nonequilibrium coherent quantum time evolution under sudden/ramped quench or timeperiodic modulation of Hamiltonian [16,[85][86][87][88][89][90][91]. In addition, a dynamical topological order parameter (DTOP) has been proposed to capture DQPTs [92,93], analogous to order parameters at equilibrium quantum phase transition.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Scaling and universality at ramped quench dynamical quantum phase transitions

Zamani,

Naji,

Jafari

et al. 2024

J. Phys.: Condens. Matter

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The nonequilibrium dynamics of a periodically driven extended XY model, in the presence oflinear time dependent magnetic filed, is investigated using the notion of dynamical quantum phasetransitions (DQPTs). Along the similar lines to the equilibrium phase transition, the main purposeof this work is to search the fundamental concepts such as scaling and universality at the rampedquench DQPTs. We have shown that the critical points of the model, where the gap closing occurs,can be moved by tuning the driven frequency and consequently the presence/absence of DQPTscan be flexibly controlled by adjusting the driven frequency. We have uncovered that, for a rampacross the single quantum critical point, the critical mode at which DQPTs occur is classified intothree regions: the Kibble-Zurek (KZ) region, where the critical mode scales linearly with the squareroot of the sweep velocity, pre-saturated (PS) region, and the saturated (S) region where the criticalmode makes a plateau versus the sweep velocity. While for a ramp that crosses two critical points,the critical modes disclose just KZ and PS regions. On the basis of numerical simulations, we findthat the dynamical free energy scales linerly with time, as approaches to DQPT time, with theexponent ν = 1 ± 0.01 for all sweep velocities and driven frequencies.

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Section: Model and Exact Solutionmentioning

confidence: 93%

Section: Model and Exact Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Scaling and universality at ramped quench dynamical quantum phase transitions

Zamani,

Naji,

Jafari

et al. 2024

J. Phys.: Condens. Matter

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“…[35][36][37][38] The Floquet engineering technique serves as an effective method for creating high-dimensional synthetic spaces without the need to physically introduce extra spatial degrees of freedom, addressing a challenge encountered in traditional systems. [39,40] The application of Floquet synthetic systems in quantum simulation provides an ideal platform to investigate rich physics, such as topologically protected transport, [41,42] dynamical phase transition [43,44] and time crystals. [45,46] Interestingly, one can realize the synthetic space with controllable dimensions by adding quasi-periodical driven potential with incommensurate frequencies to the kicked rotor model, and observe the Anderson metal-insulator transition in different effective dimensions.…”

Section: Introductionmentioning

confidence: 99%

Dynamical localization in a non-Hermitian Floquet synthetic system

Ke 可,

Zhang 张,

Huo 霍

et al. 2024

Chinese Phys. B

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We investigate the non-Hermitian effects on quantum diffusion in a kicked rotor model where the complex kicking potential is quasi-periodically modulated in time domain. The synthetic space with arbitrary dimension can be created by incorporating incommensurate frequencies in the quasi-periodical modulation. In Hermitian case, strong kicking induces the chaotic diffusion in the four-dimension momentum space characterized by linear growth of mean energy. We find that the quantum coherence in deep non-Hermitian regime can effectively suppress the chaotic diffusion and hence result in the emergence of dynamical localization. Moreover, the extent of dynamical localization is dramatically enhanced by increasing the non-Hermitian parameter. Interestingly, the quasi-energies become complex when the non-Hermitian parameter exceeds a certain threshold value. The quantum state will finally evolve to a quasi-eigenstate for which the imaginary part of its quasi-energy is large most. The exponential localization length decreases with the increase of the non-Hermitian parameter, unveiling the underlying mechanism of the enhancement of the dynamical localization by non-Hermiticity.

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“…[46][47][48][49][50] As an extended research area of DQPTs, richer non-equilibrium phases and intrinsic features have been revealed in timeperiodic driven quantum systems and experimentally verified for Floquet DQPTs, and the related problems have become one of the most attractive areas of developing nonequilibrium research topics. Research of Floquet DQPTs has been extended to various quantum systems, such as the spin chain model, [47,49] synchronized periodic driving systems, [51] dissipative systems, [52] periodically driven topological systems, [53,54] and periodic quenching topological systems. [50] Many non-equilibrium phases have been revealed in time-periodic driven quantum systems and experimentally verified.…”

Section: Introductionmentioning

confidence: 99%

Floquet dynamical quantum phase transitions in transverse XY spin chains under periodic kickings

2023

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Floquet dynamical quantum phase transitions(DQPTs), which are nonanalytic phenomena recur periodically in time-periodic driven quantum many body systems, have been widely studied in recent years. In this article, the Floquet DQPTs in transverse XY spin-chains under the modulation of δ-function periodic kickings have been investigated. We analytically solved the system, and by considering the eigenstate as well as the ground state as the initial state of the Floquet dynamics, we studied the corresponding multiple Floquet DQPTs emerged in the micromotion with different kicking moments, respectively. The rate function of return amplitude, the Pancharatnam geometric phase and the dynamical topological order parameter have been calculated, which consistently verified the emergence of Floquet DQPTs in the system.

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Engineering Floquet dynamical quantum phase transitions

Cited by 19 publications

References 93 publications

Scaling and universality at ramped quench dynamical quantum phase transitions

Scaling and universality at ramped quench dynamical quantum phase transitions

Dynamical localization in a non-Hermitian Floquet synthetic system

Floquet dynamical quantum phase transitions in transverse XY spin chains under periodic kickings

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