Dynamics of the quantum phase transition in the one-dimensional Bose-Hubbard model: Excitations and correlations induced by a quench

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

doi:10.1103/physrevb.95.104306

Cited by 40 publications

(45 citation statements)

References 97 publications

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“…By fitting power-laws to the equilibrium quantities in the appropriate interval of J, we obtain ν eff = 2.32 ± 0.2 and [zν] eff = 1.54 ± 0.1 which is compatible with the numbers reported in Ref. [63]. Inserting these values into Eq.…”

Section: A Quenches At Zero Temperaturesupporting

confidence: 87%

Kibble-Zurek scaling of the one-dimensional Bose-Hubbard model at finite temperatures

et al. 2018

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We use tensor network methods -Matrix Product States, Tree Tensor Networks, and Locally Purified Tensor Networks -to simulate the one-dimensional Bose-Hubbard model for zero and finite temperatures in experimentally accessible regimes. We first explore the effect of thermal fluctuations on the system ground state by characterizing its Mott and superfluid features. Then, we study the behavior of the out-of-equilibrium dynamics induced by quenches of the hopping parameter. We confirm a Kibble-Zurek scaling for zero temperature and characterize the finite temperature behavior, which we explain by means of a simple argument.

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Section: A Quenches At Zero Temperaturesupporting

confidence: 87%

Kibble-Zurek scaling of the one-dimensional Bose-Hubbard model at finite temperatures

et al. 2018

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“…(ii) Non-equilibrium dynamics of arbitrary QMB states under unitary Hamiltonian evolution. The Hamiltonian itself can be time-dependent, thus encompassing quenches [114,115], quasi-adiabatic regimes [116,117], and even optimal control [118]. The most common strategies to perform such dynamics on the TN states rely either on a Suzuki-Trotter decomposition of the unitary evolution (TEBD, tDMRG) [48,49] or on a time-dependent variational principle (TDVP) on the TN class [51], however, alternative routes are known [119][120][121][122].…”

Section: Typically Addressed Problemsmentioning

confidence: 99%

The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems

Silvi

Tschirsich

Gerster

et al. 2019

SciPost Phys. Lect. Notes

118

110

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We present a compendium of numerical simulation techniques, based on tensor network methods, aiming to address problems of many-body quantum mechanics on a classical computer. The core setting of this anthology are lattice problems in low spatial dimension at finite size, a physical scenario where tensor network methods, both Density Matrix Renormalization Group and beyond, have long proven to be winning strategies. Here we explore in detail the numerical frameworks and methods employed to deal with low-dimension physical setups, from a computational physics perspective. We focus on symmetries and closed-system simulations in arbitrary boundary conditions, while discussing the numerical data structures and linear algebra manipulation routines involved, which form the core libraries of any tensor network code. At a higher level, we put the spotlight on loop-free network geometries, discussing their advantages, and presenting in detail algorithms to simulate low-energy equilibrium states. Accompanied by discussions of data structures, numerical techniques and performance, this anthology serves as a programmer's companion, as well as a self-contained introduction and review of the basic and selected advanced concepts in tensor networks, including examples of their applications.

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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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Dynamics of the quantum phase transition in the one-dimensional Bose-Hubbard model: Excitations and correlations induced by a quench

Cited by 40 publications

References 97 publications

Kibble-Zurek scaling of the one-dimensional Bose-Hubbard model at finite temperatures

Kibble-Zurek scaling of the one-dimensional Bose-Hubbard model at finite temperatures

The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems

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

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