In this paper we study the dynamics of long-range pairing and hopping p-wave superconducting chain after a sudden quench of chemical potential. We have shown that the quantum-classical phase transition occurs when the system is quenched to the critical point and the Loschmidt echo shows perfect periodic oscillations. Moreover we have studied the dynamical phase transition for a quench across the critical point. Our analysis shows that the dynamical phase transition occurs for the cases where the system initially prepared in the massless edge modes. While the system does not show dynamical phase transition when the system is prepared in the massive edge modes, even the quench crossing the critical point.
In this paper we study the dynamics of long-range pairing and hopping p-wave superconducting chain after a sudden quench of chemical potential. We have shown that the quantum-classical phase transition occurs when the system is quenched to the critical point and the Loschmidt echo shows perfect periodic oscillations. Moreover we have studied the dynamical phase transition for a quench across the critical point. Our analysis shows that the dynamical phase transition occurs for the cases where the system initially prepared in the massless edge modes. While the system does not show dynamical phase transition when the system is prepared in the massive edge modes, even the quench crossing the critical point.
Abstract We explore the dynamics of long-range Kitaev chain by varying pairing interaction exponent. It is well known that the distinctive features of the nonequilibrium dynamics of a closed quantum system are closely related to the equilibrium phase transitions. Specifically, the return probability (Loschmidt echo) of the system to its initial state, in the finite-size system, is expected to exhibit periodicity after a sudden quench to a quantum critical point. The time of the first revivals scales inversely with the maximum of the group velocity. We show that, contrary to expectations, the periodicity of the return probability breaks for a sudden quench to the non-trivial quantum critical point. Further, we find that the periodicity of the return probability scales inversely with the group velocity at the gap closing point for a quench to the trivial critical point of truly long-range pairing case. Also, analyzing the effect of averaging quenched disorder shows that the revivals in the short-range pairing cases are more robust against disorder than that of the long-range pairing case. We also study the effect of disorder on the non-analyticities of the rate function of the return probability which introduced as a witness of the dynamical phase transition. We show that the non-analyticities in the rate function of return probability are washed out in the presence of strong disorders.
In this paper, we have considered the extended version of the Kitaev model in one dimension, i.e., a long-range p-wave superconducting wire. In the long-range Kitaev chain, the superconducting hopping and pairing terms in the Hamiltonian decay, independently, in a power-law fashion , where l is the distance between the two sites and x is some positive constant. We have studied the appearance of Majorana zero-energy edge modes and also, massive Dirac edge modes by exact diagonalization, as well as analytical computations. Exact diagonalization indicates the existence of both kinds of massless and massive edge modes in the energy spectrum. Furthermore, we obtain the phase diagram and the topological phase transitions by calculating the winding number, which is the topological invariant.
We study the static and dynamical properties of a long-range Kitaev chain, i.e. a p -wave superconducting chain in which the superconducting pairing decays algebraically as [Formula: see text], where l is the distance between the two sites and [Formula: see text] is a positive constant. Considering very large system sizes, we show that when [Formula: see text], the system is topologically equivalent to the short-range Kitaev chain with massless Majorana modes at the ends of the system; on the contrary, for [Formula: see text], there exist symmetry protected massive Dirac end modes. We further study the dynamical phase boundary of the model when periodic [Formula: see text]-function kicks are applied to the chemical potential; we specially focus on the case [Formula: see text] and analyze the corresponding Floquet quasienergies. Interestingly, we find that new topologically protected massless end modes are generated at the quasienergy [Formula: see text] (where T is the time period of driving) in addition to the end modes at zero energies which exist in the static case. By varying the frequency of kicking, we can produce topological phase transitions between different dynamical phases. Finally, we propose some bulk topological invariants which correctly predict the number of massless end modes at quasienergies equal to 0 and [Formula: see text] for a periodically kicked system with [Formula: see text].
The nonequilibrium dynamics of long-range pairing Kitaev model with noiseless/noisy linear time dependent chemical potential, is investigated in the framework of dynamical quantum phase transitions (DQPTs). We have shown that for the ramp crossing a single quantum critical point, while the short-range pairing Kitaev model displays a single critical time scale, the long-range pairing induces a region with three DQPTs time scales. We have found that the region with three DQPTs time scales shrinks in the presence of the noise. In addition, we have uncovered that for a quench crossing two critical points, the critical sweep velocity above which the DQPTs disappear enhances by the long-range pairing exponent while decreases in the presence of the noise. On the basis of numerical simulations, we have shown that noise diminishes the long-range pairing inductions. Published by the American Physical Society 2024
Dynamical quantum phase transitions hold a deep connection to the underlying equilibrium physics of the quench Hamiltonian. In a recent study [J. C. Halimeh et al., arXiv:1810.07187] it has been numerically demonstrated that the appearance of anomalous cusps in the Loschmidt return rate coincides with the presence of bound domain walls in the spectrum of the quench Hamiltonian. Here we consider transverse-field Ising chains with power-law and exponentially decaying interactions, and show that by removing domain-wall coupling via a truncated Jordan-Wigner transformation onto a Kitaev chain with long-range hopping and pairing, anomalous dynamical criticality is no longer present. This indicates that bound domain walls are necessary for anomalous cusps to appear in the Loschmidt return rate. We also calculate the dynamical phase diagram of the Kitaev chain with long-range hopping and pairing, which in the case of power-law couplings is shown to exhibit rich dynamical criticality including a doubly critical dynamical phase.