Dynamical quantum phase transitions in the spin-boson model

Abstract

We study dynamical quantum phase transitions in a 2-qubit system interacting with a transverse field and a quantized bosonic environment in the context of open quantum systems. By applying the stochastic Schrödinger equation approach, the model with a spin-boson type of coupling can be solved numerically. It is observed that the dynamics of the rate function of the Loschmidt echo in a 2-qubit system within a finite size of Hilbert space exhibit nonanalyticity when the direction of the transverse field coupled to the system is under a sudden quench. Moreover, we demonstrate that the memory time of the environment and the coupling strength between the system and the transverse field can jointly impact the dynamics of the rate function. We also supply a semi-classical explanation to bridge the dynamical quantum phase transitions in many-body systems and the non-Markovian dynamics of open quantum systems.

Characterization of Quantum and Classical Critical Points for an Integrable Two-Qubit Spin–Boson Model

“…We point out that with respect to the previous works [37,39,45], we obtain a different critical value of α for which we observe the occurrence of QPTs in the TISBM, e.g., the K-T transition. However, it must be remembered that our TISBM is different from those analyzed to date: the absence of an external actual transverse field applied to the spin-pair is crucial and causes a remarkable difference.…”

“…We point out that the present model profoundly differs from those studied until now [37][38][39][40][41][42][43][44][45][46][47][48][49][50]. The latter can be classified as direct generalizations of the single-spin-boson model.…”

“…The interest towards decoherence and dissipation, as well as quantum phase transitions (QPTs) in two-impurity spin-boson models (TISBMs) with competing interactions, has remarkably grown in the last two decades [37][38][39][40][41][42][43][44][45][46][47][48][49][50]. The TISBM is currently under attention to determine the existence of critical points and then the presence of quantum and/or classical phase transitions [38,39].…”

“…We point out that, until now, the TISBMs considered [37,39,45] have been mainly focused on the effects stemming from the application of external (longitudinal and transverse) magnetic fields, taking into account the simplest spin-spin coupling. In the present work, instead, the attention has been focused on the physical properties of a two-spin/bath system related to the internal parameters that characterize the system itself: a nontrivial spin-spin coupling (anisotropic Heisenberg interaction) and the spin-bath coupling(s).…”

Dynamical quantum phase transitions in Stark quantum spin chains

“…3 DQPTs studied intensively in many models such as transverse field Ising model, 1 anisotropic XY model, 4 quantum Potts chain, 5 Hubbard and Falicov-Kimball models, 6 two-band topological systems, [7][8][9][10] flat band networks, 11 and bosonic models. 12,13 DQPTs were also studied in inhomogeneous models such as the random energy model, 14,15 the Anderson model, 16 as well as quasiperiodic potential in the context of the Aubry-Andre model. 17,18 Exploring DQPTs in higher dimensions reported on models such as the integrable two-dimensional Kitaev honeycomb, 19 two-dimensional Haldane, 20,21 three-dimensional O(N) 22 models, and twodimensional transverse field Ising model.…”