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

Abstract

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...

Fine-grained domain counting and percolation analysis in 2D lattice systems with linked-lists

“…This is consistent with the Kibble-Zurek mechanism (KZM) [18][19][20][21][22]. It is to be mentioned that recent works on ultracold atoms have reported similar results in quantum quenches across different quantum phases [23][24][25][26]. Further, as to be expected, we show that the dependence of the defect density on the quench rate has the same power-law exponent as the number of domains.…”

“…The same scaling law is also applicable to the defect density N v . For the MI-SF transition the defects are the vortices and their density is given by [23][24][25]43]…”

Quench dynamics of Rydberg-dressed bosons on two-dimensional square lattices

“…This has paved new ways to explore non-equilibrium dynamics in addition to static properties. Inspired by this, recent theoretical and experimental works have investigated Landau-Zener transition [35][36][37], Kibble-Zurek mechanism [38][39][40][41][42][43][44], transport [45][46][47], Higgs/Goldstone modes [48,49].…”

“…Such situation has been examined extensively using atoms with weak magnetic or electric dipole moments [60][61][62][63][64][65][66][67][68], where the dominant interaction is between nearest neighbour sites. When quenching eBHMs, the nearest-neighbour interaction will bring extra time scales [42,43]. It was found that vortex nucleation and correlation lengths exhibit different scaling laws other than that in BHMs.…”

Observation of generalized Kibble-Zurek mechanism across a first-order quantum phase transition in a spinor condensate

“…Different from the second-order quantum phase transition, multiple phases coexist at the transition point for the first-order one. Similar to the former, numerical simulations have suggested that scaling laws may also exist in the dynamics of several first-order phase transitions (15,(17)(18)(19)(20)(21). However, while the KZM is very successful in the former, some direct application of the KZM to the first-order transition cannot give a satisfied description of the scaling law compared to the numerical simulation results, such as in an extended Bose-Hubbard model (21).…”