Critical behavior at dynamical phase transition in the generalized Bose-Anderson model

Abstract

Critical properties of the dynamical phase transition in the quenched generalized Bose-Anderson impurity model are studied in the mean-field limit of an infinite number of channels. The transition separates the evolution towards ground state and towards the branch of stable excited states. We perform numerically exact simulations of a close vicinity of the critical quench amplitude. The relaxation constant describing the asymptotic evolution towards ground state, as well as asymptotic frequency of persistent phase rotation and number of cloud particles at stable excited state are power functions of the detuning from the critical quench amplitude. The critical evolution (separatrix between the two regimes) shows a non-Lyapunov power-law instability arising after a certain critical time. The observed critical behavior is attributed to the irreversibility of the dynamics of particles leaving the cloud and to memory effects related to the low-energy behavior of the lattice density of states.The dynamics of correlated quantum systems that show phase transitions at their equilibrium became a subject of intensive investigations in the last decade. One of the key differences between the classical and quantum ensembles is that the later can emerge the undamped (persistent) excitations such as, for example, vertexes in the superfluids and superconductors [1][2][3]. Therefore, whereas a generic nonlinear classical system at finite temperature is ergodic, a quantum fluid is not necessarily. This gives rise to phase transitions seen in the asymptotic dynamics of an open quantum system: dependent on initial conditions, it can either relax to its ground state or not. The two regimes are separated by the dynamical transition point. In a wider context, dynamical transitions are singularities arising in the many body quantum dynamics. In particular, several models show a critical time t * after which an instability develops [4][5][6].The studies of how the criticality shows up in the dynamics have a long history but firstly have been mostly devoted to classical systems. It was found that the dynamical critical exponents arise (see [7,8]). The most known is the Z-index relating the correlation length ξ and the relaxation time τ via τ ∝ ξ Z [7,9]. The values of dynamical indexes cannot be expressed via static ones (that is, a dynamical effective Hamiltonian obeys larger number of relevant parameters then its static counterpart). Moreover, varying parameters of a system within the same static universality class, one can obtain different values of dynamical indexes. To describe such a situation the dynamical subclasses have been introduced [10].The dynamical quantum criticality was reported in a number of recent works [4,5,11] where the dynamics of transverse-field Ising model in low dimensions has been studied. Loschmidt echo rate scaling [5] was described using the renormalization group performed in a complex parameter space. However, universality of this procedure has been questioned in a very recent work [12]. Unfortunately the r...

Dynamical quantum phase transitions in a spin chain with deconfined quantum critical points

“…Contrary to conversional classical (quantum) phase transitions driven by temperature (magnetic field or pressure), DQPTs are considered as new types of phase transitions driven by time. There has been a lot of interest in the study of DQPTs, including critical properties [4][5][6][7][8][9][10][11] , dynamical order parameters [12][13][14][15] , and spontaneously broken symmetries [16][17][18][19][20][21] , etc. The realizations of DQPTs have been performed in a large number of experiments based on different platforms [22][23][24][25][26][27][28][29] .…”

Dynamical quantum phase transitions in systems with broken continuous time and space translation symmetries

“…Subsequently, it has been recently shown that real-time evolution of time-independent many-body systems after a quantum quench, i.e. a sudden change of a control parameter of systems, across a critical value can reveal non-analytical behavior at certain moments of time [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. The critical behavior in time evolution has been also observed for quenches within the same phase [35,36].…”