The nonequilibrium dynamics of two-dimensional Su-Schrieffer-Heeger model, in the presence of staggered chemical potential, is investigated using the notion of dynamical quantum phase transition. We contribute to expanding the systematic understanding of the interrelation between the equilibrium quantum phase transition and the dynamical quantum phase transition (DQPT). Specifically, we find that dynamical quantum phase transition relies on the existence of massless propagating quasiparticles as signaled by their impact on the Loschmidt overlap. These massless excitations are a subset of all gapless modes, which leads to quantum phase transitions. The underlying two-dimensional model reveals gapless modes, which do not couple to the dynamical quantum phase transitions, while relevant massless quasiparticles present periodic nonanalytic signatures on the Loschmidt amplitude. The topological nature of DQPT is verified by the quantized integer values of the topological order parameter, which gets even values. Moreover, we have shown that the dynamical topological order parameter truly captures the topological phase transition on the zero Berry curvature line, where the Chern number is zero and the two-dimensional Zak phase is not the proper indicator.
The nonequilibrium dynamics of two-dimensional Su-Schrieffer-Heeger model, in the presence of staggered chemical potential, is investigated using the notion of dynamical quantum phase transition. We contribute to expanding the systematic understanding of the interrelation between the equilibrium quantum phase transition and the dynamical quantum phase transition (DQPT). Specifically, we find that dynamical quantum phase transition relies on the existence of massless propagating quasiparticles as signaled by their impact on the Loschmidt overlap. These massless excitations are a subset of all gapless modes, which leads to quantum phase transitions. The underlying two-dimensional model reveals gapless modes, which do not couple to the dynamical quantum phase transitions, while relevant massless quasiparticles present periodic nonanalytic signatures on the Loschmidt amplitude. The topological nature of DQPT is verified by the quantized integer values of the topological order parameter, which gets even values. Moreover, we have shown that the dynamical topological order parameter truly captures the topological phase transition on the zero Berry curvature line, where the Chern number is zero and the two-dimensional Zak phase is not the proper indicator.
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.
Dynamical quantum phase transitions (DQPTs), which refer to the criticality in time of a quantum many-body system, have attracted much theoretical and experimental research interest recently. Despite that DQPTs are defined and signaled by the nonanalyticities in the Loschmidt rate, its interrelation with various correlation measures such as the equilibrium order parameters of the system remains unclear. In this work, by considering the quench dynamics in an interacting topological model, we find that the equilibrium order parameters of the model in general exhibit signatures around the DQPT, in the short time regime. The first extrema of the equilibrium order parameters are connected to the first Loschmidt rate peak. By studying the unequal-time two-point correlation, we also find that the correlation between the nearest neighbors decays while that with neighbors further away builds up as time grows in the noninteracting case, and upon the addition of repulsive intracell interactions. On the other hand, the intercell interaction tends to suppress the two-site correlations. These findings could provide us insights into the characteristic of the system around DQPTs, and pave the way to a better understanding of the dynamics in nonequilibrium quantum many-body systems.
The quench dynamics in type-I inversion-symmetric Weyl semimetals (WSM) is explored in this work which, due to the form of the Hamiltonian, may be readily extended to two-dimensional Chern insulators. We analyze the role of equilibrium topological properties characterized by the Chern number of the prequench ground state in dictating the nonequilibrium dynamics of the system, specifically, the emergence of dynamical quantum phase transitions (DQPT). By investigating the ground-state fidelity, it is found that a change in the signed Chern number constitutes a sufficient but not necessary condition for the occurrence of DQPTs. Depending on the ratio of the transverse and longitudinal hopping parameters, DQPTs may also be observed for quenches lying entirely within the initial Chern phase. Additionally, we analyze the zeros of the boundary partition function discovering that while the zeros generally form two-dimensional structures resulting in one-dimensional critical times, infinitesimal quenches may lead to one-dimensional zeros with zero-dimensional critical times, provided the quench distance scales appropriately with the system size. This is strikingly manifested in the nature of nonanalyticities of the dynamical free energy, revealing a logarithmic singularity. Moreover, we show that these zero-dimensional critical times may be detected only by a direct observation of the dynamical free energy. Finally, following recent advances in observing the dynamical zeros of the Loschmidt overlap through azimuthal Bloch phase vortices, we rigorously investigate the same in WSMs, demonstrating that only one-dimensional critical times arising from two-dimensional manifolds of zeros of the boundary partition function lead to dynamical vortices.
We know that a one-dimensional (1D) modulated system can simulate 2D topological states by expanding the dimension. This scenario provides a justifiable avenue to test the dilatation of the dynamical quantum phase transition (DQPT). Through a generalized Su-Schrieffer-Heeger model, we have shown how the Loschmidt echo, Fisher zero, and Dynamical topological order parameter (DTOP) transit from one to two dimensions. Owing to the introduced pseudomomentum, the derivative of the return rate does not always capture the DQPT well, but the Fisher zero and the DTOP can be treated as faithful indicators. A topology-independent parameter will also affect the occurrence of the DQPTs for quenches inside a given phase. Moreover, a comparison with the Haldane model owning the same phase diagram implies that a pair of fixed points will lead to different critical momentum distributions, thus different robustness, further reminding us that the correspondences between the equilibrium and dynamical phases transitions are multifarious.
Dynamical quantum phase transitions (DQPTs) probe the nonequilibrium evolution of quantum systems, unveiling their geometric and topological characteristics. In this study, we introduce the concepts of parallel quench and dynamic geometrical order parameter (DGOP) for nonband models without momentum-space structure, where these quantities capture the geometric shifts associated with DQPTs. At zero temperature, the DGOP corresponds to the Pancharatnam geometric phase, while at finite temperatures, it extends to the interferometric geometric phase. We further generalize the dynamic topological order parameter (DTOP) to finite-temperature band models, examining its behavior in the Su-Schrieffer-Heeger model. Our analysis shows that thermal fluctuations and boundary effects at finite temperatures disrupt the quantization of the DTOP, yet it retains signatures of topological transitions. These findings deepen the understanding of geometric and topological properties in quantum dynamics, illuminating DQPTs across both nonband and band frameworks.
Dynamical quantum phase transitions occur in dynamically evolving quantum systems when nonanalyticities occur at critical times in the return rate, a dynamical analog of the free energy. This extension of the concept of phase transitions can be brought into contact with another, namely, that of topological phase transitions in which the phase transition is marked by a change in a topological invariant. Following a quantum quench dynamical quantum phase transitions can happen in topological matter, a fact which has already been explored in one-dimensional topological insulators and in two-dimensional Chern insulators. Additionally, in one-dimensional systems a dynamical bulk boundary correspondence has been seen, related to the periodic appearance of zero modes of the Loschmidt echo itself. Here we extend both of these concepts to two-dimensional higher-order topological matter in which the topologically protected boundary modes are corner modes. We consider a minimal model which encompasses all possible forms of higher-order topology in two-dimensional topological band structures. We find that dynamical quantum phase transitions can still occur, and can occur for quenches which cross both bulk and boundary gap closings. Furthermore, a dynamical bulk boundary correspondence is also found, which takes a different form to that in one dimension.