Dynamical criticality and domain-wall coupling in long-range Hamiltonians

Abstract

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. arXiv:1902.08621v1 [cond-mat.stat-mech]

Out-of-equilibrium phase diagram of long-range superconductors

“…A similar discrepancy in the relevance of long-range couplings, first noticed in Ref. [70] for the β = α case, also exists in the present general case.…”

“…More intriguingly, for certain regimes of (α, β ), which we discuss in detail in Sec. IV, doubly critical cusps-which are related to two distinct critical momenta-can arise for quenches within the topologically nontrivial phase [70]. As we elaborate in Sec.…”

“…The type of nonanalyticities that occur in the wake of a quench can either be regular or anomalous [18,20]. The former are the cusps that occur for quenches crossing the dynamical critical point, while the latter can occur for arbitrarily small quenches within the ordered phase of the system, and they have been shown to be connected to local spin excitations forming the lowest-lying excitations in the spectrum of the quench Hamiltonian [24,25,70].…”

“…It has already been noticed that in the case of nearest-neighbor hopping and long-range pairing a triply critical phase can emerge with three excitation modes having p k = 1/2 for quenches across the topological phase transition [69]. More recently, the occurrence of a doubly critical dynamical phase in which two critical modes arise has been demonstrated for the case of long-range pairing and hopping with equal decay rate β = α for quenches within the topologically nontrivial phase, i.e., from [70]. It is worth noting that the properties of these peculiar dynamical phases can hardly be connected with those of equilibrium critical phenomena.…”

“…Consequently, the interest in free-fermionic models with long-range hopping or pairing has grown in recent years, as this allows the study of DQPT in an exactly solvable setting. Indeed, Dutta and Dutta [69] have recently investigated DQPT in the Kitaev chain with nearestneighbor hopping and long-range pairing, while Defenu et al [70] have employed a truncated Jordan-Wigner transformation on the so-called extended long-range Ising chain to map it onto a free-fermionic model of long-range hopping and pairing both scaling as 1/r α , with r the interspin distance and α > 1. In this paper, we investigate a Kitaev chain with gen-eralized power-law hopping and pairing profiles and draw a connection between the different dynamical phases of DQPT and the dynamic behavior of the string order parameter (SOP).…”