Transient phases and dynamical transitions in the post-quench evolution of the generalized Bose-Anderson model

Chichinadze, Dmitry V.; Ribeiro, Pedro; Shchadilova, Yulia E.; Rubtsov, A. N.

doi:10.1103/physrevb.94.054301

Cited by 7 publications

(14 citation statements)

References 62 publications

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“…In order to understand this behaviour we proceeded as in the closed case and consider the quench to be a small perturbation δM/M (∞) 1, with δM = M (∞) − M eq , where M eq is the equilibrium value of the magnetization at U = U f . The solution of the equations of motion (12) is assumed to be of the form τ k (t) = τ k eq +s k (t), and M (t) = M eq − δ(t), where τ k eq is equilibrium value of pseudo-spin for U = U f . Expanding Eq.…”

Section: Open Systemmentioning

confidence: 99%

Post-quench dynamics and suppression of thermalization in an open half-filled Hubbard layer

2017

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We study the time evolution of an half-filled Hubbard layer coupled to a magnon bath after a quench of the Hubbard interaction. Qualitatively different regimes, regarding the asymptotic long time dynamics, are identified and characterized within the mean-field approximation. In the absence of the bath, the dynamics of the closed system is similar to that of a quenched BCS condensate. Though the presence of the bath introduces an additional relaxation mechanism, our numerical results and analytical arguments show that equilibration with the bath is not necessarily attained within approximations used. Instead, non-equilibrium states, similar to the ones observed in the closed system, can emerge at long times as a consequence of the competition between intrinsic relaxation mechanism (Landau damping, for example), and the bath-induced dissipation.

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Section: Open Systemmentioning

confidence: 99%

Post-quench dynamics and suppression of thermalization in an open half-filled Hubbard layer

2017

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“…In our recent paper [20], we have shown that impurity models can exhibit dynamical phase transitions as well. We have studied the generalized Bose-Anderson model, in which N identical nonlinear oscillators are connected to the same lattice site.…”

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confidence: 96%

“…The equilibrium phase diagram of the model is shown in the lower panel of Figure 1. We study a type of quenches for which a dynamical transition was reported in [20]. They correspond to a sudden lowering −ε 0 within the lBEC domain for the system initially prepared in its ground state.…”

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confidence: 99%

“…Possible asymptotic states of the system described by (5) are either the new equilibrium state, or the stable excited state with a persistently rotating phase a(t) = a ∞ e iωt . The value of a ∞ can be found by switching to the rotation frame [20], where the chemical potential appears to be shifted; ε 0 → ε 0 + ω, k → k + ω. After this shift is accounted, a ∞ satisfies the "equilibrium" equations (3,4).…”

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confidence: 99%

“…Our conclusions allow to estimate how the number of particles asymptotically remaining in the lBEC cloud N lBEC scales with δε 0 . The rotation-frame analysis [20] gives the expression N lBEC ∝ d 3 k (ω+ k ) 2 . It leads to the divergence N lBEC ∝ ω −1/2 .…”

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

Chichinadze

Rubtsov

2017

Phys. Rev. B

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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...

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Dynamical quantum phase transitions in non-Hermitian lattices

et al. 2018

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In closed quantum systems, a dynamical phase transition is identified by nonanalytic behaviors of the return probability as a function of time. In this work, we study the nonunitary dynamics following quenches across exceptional points in a non-Hermitian lattice realized by optical resonators. Dynamical quantum phase transitions with topological signatures are found when an isolated exceptional point is crossed during the quench. A topological winding number defined by a real, noncyclic geometric phase is introduced, whose value features quantized jumps at critical times of these phase transitions and remains constant elsewhere, mimicking the plateau transitions in quantum Hall effects. This work provides a simple framework to study dynamical and topological responses in non-Hermitian systems.Introduction.-Dynamical quantum phase transitions (DQPTs) are characterized by nonanalytic behavior of physical observables as functions of time [1,2]. These transitions happen in general if the system is ramped through a quantum critical point. As a promising framework to classify quantum dynamics of nonequilibrium many-body systems, DQPTs have been studied intensively in recent years [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. The generality and topological feature of DQPTs were demonstrated in both lattice and continuum systems [20], across different spatial dimensions [21][22][23][24][25], and under various dynamical protocols [26][27][28]. The defining features of DQPTs have also been observed in recent experiments [29][30][31].Following the initial proposal, most studies on DQPTs focus on closed quantum systems undergoing unitary time evolution. Efforts have been made to generalize DQPTs to systems prepared in mixed states [32,33]. However, DQPTs in systems with gain and loss, and therefore subject to nonunitary evolution are largely unexplored. One such class of open systems can be descried by a non-Hermitian Hamiltonian. This type of system, realizable in various platforms like photonic lattice [34], phononic media [35], LRC circuits [36] and cold atoms [37,38], has attracted great attention in recent years due to their nontrivial dynamical [39][40][41][42][43][44][45][46][47][48], topological [49][50][51][52][53][54][55][56][57][58][59][60][61][62] and transport properties [63][64][65][66][67][68][69][70]. Many of these features can be traced back to non-Hermitian degeneracy (i.e. exceptional) points mediating gap closing and reopening transitions on the complex plane [71][72][73][74][75][76]. In this work, we explore DQPTs in non-Hermitian systems, with a focus on topological signatures in nonunitary evolution following quenches across exceptional points (EPs).Theory.-We start by summarizing the theoretical framework of DQPTs for systems described by non-Hermitian lattice Hamiltonians. The nonunitary time evolution of the system is governed by a Schrödinger equation i d dt |Ψ(t) = H|Ψ(t) . For concreteness, we present the formalism with a one-dimensional twoband lattice model in mind, while the g...

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Transient phases and dynamical transitions in the post-quench evolution of the generalized Bose-Anderson model

Cited by 7 publications

References 62 publications

Post-quench dynamics and suppression of thermalization in an open half-filled Hubbard layer

Post-quench dynamics and suppression of thermalization in an open half-filled Hubbard layer

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

Dynamical quantum phase transitions in non-Hermitian lattices

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