Out-of-equilibrium dynamics of multiple second-order quantum phase transitions in an extended Bose-Hubbard model: Superfluid, supersolid, and density wave

Abstract

In this paper, we study the dynamics of the Bose-Hubbard model with the nearest-neighbor repulsion by using time-dependent Gutzwiller methods. Near the unit filling, the phase diagram of the model contains density wave (DW), supersolid (SS) and superfluid (SF). The three phases are separated by two second-order phase transitions. We study "slow-quench" dynamics by varying the hopping parameter in the Hamiltonian as a function of time. In the phase transitions from the DW to SS and from the DW to SF, we focus on how the SF order forms and study scaling laws of the SF correlation length, vortex density, etc. The results are compared with the Kibble-Zurek scaling. On the other hand from the SF to DW, we study how the DW order evolves with generation of the domain walls and vortices. Measurement of first-order SF coherence reveals interesting behavior in the DW regime.

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.…”

Changing the order of a dynamical phase transition through fluctuations in a quantum p-spin model

“…For example, even when a stationary state attained after a quantum quench does not reveal signatures of order as in low-dimensional systems [2][3][4], a linear ramp through a second order quantum critical point leaves universal signatures in the scaling of the number of excitations with the ramp speed [5][6][7][8], as confirmed extensively in a number of experiments [9][10][11][12][13][14][15]. Analogous signatures are left when a first order quantum phase transition is crossed [16][17][18] through the nucleation of resonant bubbles of the new phase close to the critical point [19][20][21] which leads to a modified Kibble-Zurek-like power-law scaling [22].…”