Space and time renormalization in phase transition dynamics

Francuz, Anna; Dziarmaga, Jacek; Gardas, Bartłomiej; Zurek, Wojciech H.

doi:10.1103/physrevb.93.075134

Cited by 90 publications

(142 citation statements)

References 95 publications

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“…To study dynamics of quantum-many-body systems, the parameters in the Hamiltonian are varied through a quantum phase transition (QPT), i.e., the quantum quench [13][14][15][16][17][18][19][20][21][22][23][24][25][26], and the system evolution is observed. Experiments on this problem have been already done using the various ultra-cold atomic gases [27][28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of first-order quantum phase transitions in extended Bose–Hubbard model: from density wave to superfluid and vice versa

et al. 2018

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In this paper, we study the nonequilibrium dynamics of the Bose-Hubbard model with the nearestneighbor repulsion by using time-dependent Gutzwiller (GW) methods. In particular, we vary the hopping parameters in the Hamiltonian as a function of time, and investigate the dynamics of the system from the density wave (DW) to the superfluid (SF) crossing a first-order phase transition and vice versa. From the DW to SF, we find scaling laws for the correlation length and vortex density with respect to the quench time. This is a reminiscence of the Kibble-Zurek scaling for continuous phase transitions and contradicts the common expectation. We give a possible explanation for this observation. On the other hand from SF to DW, the system evolution depends on the initial SF state. When the initial state is the ground state obtained by the static GW methods, a coexisting state of the SF and DW domains forms after passing through the critical point. Coherence of the SF order parameter is lost as the system evolves. This is a phenomenon similar to the glass transition in classical systems. When the state starts from the SF with small local phase fluctuations, the system obtains a large size DW domain structure with thin domain walls. them, works in [27, 28] questioned the applicability of the KZ scaling theory to the QPT, whereas [29,30] concluded that the observed results were in good agreement with the KZ scaling law.In this paper, we focus on the two-dimensional (2D) Bose-Hubbard model (BHM) [33,34], which is a canonical model of the bosonic ultra-cold atomic gas systems in an optical lattice. In particular, we add nearestneighbor (NN) repulsions between atoms. Then, the resultant system is described by an extended Bose-Hubbard model (EBHM). As a result, a parameter region corresponding to the density wave (DW) appears in the ground-state phase diagram, in addition to the Mott insulator and SF. Near the half filling, there exists a firstorder phase transition between the SF and DW [35]. We shall study the quench dynamics of the EBHM on passing across the SF and DW phase boundary. There are only a few works for the dynamical properties of quantum systems at first-order phase transitions under a quench [36][37][38], and therefore detailed study on that problem is desired.This paper is organized as follows. In section 2, we introduce the EBHM and explain the Gutzwiller (GW) methods, which are used in the present work. In section 3, quench dynamics of the first-order phase transition from the DW to SF is studied. Behavior of SF and DW orders are investigated by solving the Schrödinger equation by means of time-dependent GW (tGW) methods. We focus on the order parameters, correlation length, vortex number, etc, in particular, scaling laws of these quantities with respect to the quench time τ Q . Contrary to the common expectation, we find that scaling laws hold for the correlation length and vortex density. In section 4, we give a possible explanation of the observed results from viewpoint of the SF-bubblenucleation process. W...

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Section: Introductionmentioning

confidence: 99%

Dynamics of first-order quantum phase transitions in extended Bose–Hubbard model: from density wave to superfluid and vice versa

et al. 2018

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“…An exactly solvable model on a lattice will be useful to address these issues. Progress in this direction has been made recently in [34] analyzing the KibbleZurek scaling in the transverse Ising model. We have recently found exactly solvable quench protocols in several spin models and studied the dependence on the quench rate: the results will appear in a separate communication [23].…”

Section: Jhep05(2016)164mentioning

confidence: 99%

Quantum quenches in free field theory: universal scaling at any rate

Das

Galante

Myers

2016

J. High Energ. Phys.

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Quantum quenches display universal scaling in several regimes. For quenches which start from a gapped phase and cross a critical point, with a rate slow compared to the initial gap, many systems obey Kibble-Zurek scaling. More recently, a different scaling behaviour has been shown to occur when the quench rate is fast compared to all other physical scales, but still slow compared to the UV cutoff. We investigate the passage from fast to slow quenches in scalar and fermionic free field theories with time dependent masses for which the dynamics can be solved exactly for all quench rates. We find that renormalized one point functions smoothly cross over between the regimes.

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“…In particular we would like to understand possible universal scaling of the entropy as a function of the quench rate. While some results about such scaling behavior are known in solvable and integrable field theories [28][29][30][31][32] , very little is known in strongly coupled systems. In the past, holographic methods have been useful to understand scaling of one point functions in various regimes…”

Section: Jhep09(2017)016mentioning

confidence: 99%

Holographic entanglement entropy of a 1 + 1 dimensional p-wave superconductor

Das

Fujita

Kim

2017

J. High Energ. Phys.

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We examine the behavior of entanglement entropy S EEA of a subsystem A in a fully backreacted holographic model of a 1 + 1 dimensional p wave superconductor across the phase transition. For a given temperature, the system goes to a superconducting phase beyond a critical value of the charge density. The entanglement entropy, considered as a function of the charge density at a given temperature, has a cusp at the critical point. In addition, we find that there are three different behaviors in the condensed phase, depending on the subsystem size. For a subsystem size l smaller than a critical size l c1 , S EE A continues to increase as a function of the charge density as we cross the phase transition. When l lies between l c1 and another critical size l c2 the entanglement entropy displays a nonmonotonic behavior, while for l > l c2 it decreases monotonically. At large charge densities S EE A appears to saturate. The non-monotonic behavior leads to a novel phase diagram for this system.

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Space and time renormalization in phase transition dynamics

Cited by 90 publications

References 95 publications

Dynamics of first-order quantum phase transitions in extended Bose–Hubbard model: from density wave to superfluid and vice versa

Dynamics of first-order quantum phase transitions in extended Bose–Hubbard model: from density wave to superfluid and vice versa

Quantum quenches in free field theory: universal scaling at any rate

Holographic entanglement entropy of a 1 + 1 dimensional p-wave superconductor

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