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arXiv:1901.10365 · Physical review. B./Physical review. B

Floquet dynamical quantum phase transitions

Kai Yang, Longwen Zhou, Wenchao Ma, Xi Kong, Pengfei Wang, Xi Qin, Xing Rong, Ya Wang, Fazhan Shi, Jiangbin Gong, Jiangfeng Du

Published Aug 28, 2019• 108 citations
arXivHTMLPDF

Abstract

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 type of DQPTs, termed Floquet DQPTs, as intrinsic features of time-periodic systems. 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.

DOI
10.1103/physrevb.100.085308

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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 type of DQPTs, termed Floquet DQPTs, as intrinsic features of time-periodic systems. 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.
Dynamical quantum phase transitions (DQPTs) are characterized by nonanalytic behaviors of physical observables as functions of time. When a system is subject to time-periodic modulations, the nonanalytic signatures of its observables could recur periodically in time, leading to the phenomena of Floquet DQPTs. In this work, we systematically explore Floquet DQPTs in a class of periodically quenched one-dimensional system with chiral symmetry. By tuning the strength of quench, we find multiple Floquet DQPTs within a single driving period, with more DQPTs being observed when the system is initialized in Floquet states with larger topological invariants. Each Floquet DQPT is further accompanied by the quantized jump of a dynamical topological order parameter, whose values remain quantized in time if the underlying Floquet system is prepared in a gapped topological phase. The theory is demonstrated in a piecewise quenched lattice model, which possesses rich Floquet topological phases and is readily realizable in quantum simulators like the nitrogen-vacancy center in diamonds. Our discoveries thus open a new perspective for the Floquet engineering of DQPTs and the dynamical detection of topological phase transitions in Floquet systems.
Floquet dynamical quantum phase transitions (FDQPTs) are signified by recurrent nonanalytic behaviors of observables in time. In this work, we introduce a quench-free and generic approach to engineer and control FDQPTs for both pure and mixed Floquet states. By applying time-periodic modulations with two driving frequencies to a general class of spin chain model, we find multiple FDQPTs within each driving period. The model is investigated with equal, commensurate and incommensurate driving frequencies. The nonanalytic cusps of return probability form sublattice structures in time domain. Notably, the number and time locations of these cusps can be flexibly controlled by tuning the Hamiltonian parameter and the frequencies of the drive. We further employ the dynamical topological order parameter, which shows a quantized jump whenever a DQPT happens, to identify the topological feature of FDQPTs. Our findings reveal the advantage of engineering nonequilibrium phase transitions with multifrequency driving fields.
Floquet dynamical quantum phase transitions (DQPTs), which are nonanalytic phenomena recuring 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 are investigated. We analytically solve the system, and by considering the eigenstate as well as the ground state as the initial state of the Floquet dynamics, we study the corresponding multiple Floquet DQPTs emerged in the micromotion with different kicking moments. The rate function of return amplitude, the Pancharatnam geometric phase and the dynamical topological order parameter are calculated, which consistently verify the emergence of Floquet DQPTs in the system.
This work investigates dynamical quantum phase transitions (DQPTs) in a one-dimensional Ising model subjected to a periodically modulated transverse field. In contrast to sudden quenches, we demonstrate that a DQPT can be induced in two distinct ways. First, when the system remains within a given phase--ferromagnetic (FM) or paramagnetic (PM), a resonant periodic drive can trigger a DQPTs when its frequency matches the energy-level transition of the system. This DQPT is intimately connected to the emergence of Floquet topological phases. The timescale for the transition is governed by the perturbation strength λ′λ'λ′, the critical mode kck_ckc​, and its energy gap ΔkcΔ_{k_c}Δkc​​, following the scaling relation τ∝Δkcλ′−1csc⁡kcτ\proptoΔ_{k_c}λ'^{-1}\csc k_cτ∝Δkc​​λ′−1csckc​. Second, for drives across the critical point between the FM and PM phases, low frequencies can always induce DQPT, regardless of resonance. This behavior stems from the degeneracy of the energy-level at the critical point, which ensures that any drive with a frequency lower than the system's intrinsic transition frequency will inevitably excite the system. However, in the high-frequency regime, such excitation will be strongly suppressed, thereby inhibiting the occurrence of DQPTs. This study provides deeper insight into the nonequilibrium dynamics of quantum spin chains.
Non-Hermitian dynamical quantum phase transitions (DQPTs) are intrinsically sensitive to the choice of inner product under nonunitary time evolution. Although the biorthogonal formulation based on associated states provides a normalized Loschmidt echo with a probabilistic interpretation, previous studies have found biorthogonal and self-normal DQPTs to occur in the same parameter regimes, suggesting that the two forms of dynamical criticality are concomitant. Here we demonstrate that this is not the case. In an exactly solvable periodically driven non-Hermitian Su-Schrieffer-Heeger chain, we uncover a finite biorthogonal-only Floquet DQPT regime, where the biorthogonal Loschmidt rate becomes nonanalytic while the self-normal Loschmidt rate remains smooth. The critical conditions are obtained analytically, showing that the onset of biorthogonal Floquet DQPTs is locked to the exceptional lines of the effective Floquet Hamiltonian, whereas self-normal criticality has no corresponding spectral boundary. Moreover, for each critical momentum, the biorthogonal DQPT exhibits a pair of critical times within every driving period, whereas the self-normal DQPT exhibits only one. Our results establish a fundamental distinction between biorthogonal and self-normal DQPTs, thereby opening a route toward new nonequilibrium quantum phenomena in non-Hermitian systems.
Dynamical quantum phase transitions (DQPTs) manifested in the nonanalyticities in the temporal evolution of a closed quantum system generated by the time-independent final Hamiltonian, following a quench (or ramping) of a parameter of the Hamiltonian, is an emerging frontier of nonequilibrium quantum dynamics. We, here, introduce the notion of a dynamical topological order parameter (DTOP) that characterizes these DQPTs occurring in quenched (or ramped) two-dimensional closed quantum systems; this is quite a nontrivial generalization of 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. What is remarkable is that while the topology of the equilibrium model is characterized by the Chern number, the emergent topology associated with the DQPTs is characterized by a generalized winding number.