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arXiv:2309.06272

Quench dynamics across the MI-SF quantum phase transition with cluster mean field theory

Gaur, Deepak, Hrushikesh Sable, D. Angom

Published Sep 12, 2023• 0 citations
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Abstract

In this work, we study the quench dynamics of quantum phases of ultracold neutral bosons trapped in optical lattices. We investigate the validity of the Kibble-Zurek (KZ) scaling laws with the single-site Gutzwiller mean-field (SGMF) and cluster Gutzwiller mean-field (CGMF) theory. With CGMF, we note the evolution of the dynamical wavefunction in the ``impulse" regime of the Kibble-Zurek mechanism. We obtain the power law scalings for the crossover time and defect density with the quench rate predicted by KZ scaling laws. The critical exponents obtained from dynamics are close to their equilibrium values. Furthermore, it is observed that the obtained dynamical critical exponent $z$ improves towards the equilibrium value with increasing cluster sizes in CGMF.

DOI
10.48550/arxiv.2309.06272

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In this work, we study the quench dynamics of quantum phases of ultracold neutral bosons trapped in optical lattices. We investigate the validity of the Kibble-Zurek (KZ) scaling laws with the single-site Gutzwiller mean-field (SGMF) and cluster Gutzwiller mean-field (CGMF) theory. With CGMF, we note the evolution of the dynamical wavefunction in the ``impulse" regime of the Kibble-Zurek mechanism. We obtain the power law scalings for the crossover time and defect density with the quench rate predicted by KZ scaling laws. The critical exponents obtained from dynamics are close to their equilibrium values. Furthermore, it is observed that the obtained dynamical critical exponent zzz improves towards the equilibrium value with increasing cluster sizes in CGMF.
We examine the quench dynamics across quantum phase transitions from a Mott insulator (MI) to a superfluid (SF) phase in a two-component bosonic mixture in an optical lattice. We show that two-component Bose mixtures exhibit qualitatively different quantum dynamics than one-component Bose gas. In addition to second-order MI-SF transitions, we investigate quench dynamics across a first-order MI-SF phase boundary. The Bose mixtures show the critical slowing down of dynamics near the critical transition point, as proposed by the Kibble-Zurek mechanism. For MI-SF transitions with homogeneous lattice-site distributions in the MI phase, the dynamical critical exponents extracted by the power-law scaling of the proposed quantities obtained via numerical simulations are in very close agreement with the mean-field predictions.
The Kibble-Zurek (KZ) hypothesis identifies the relevant time scales in out-of-equilibrium dynamics of critical systems employing concepts valid at equilibrium: It predicts the scaling of the defect formation immediately after quenches across classical and quantum phase transitions as a function of the quench speed. Here we study the crossover between the scaling dictated by a slow quench, which is ruled by the critical properties of the quantum phase transition, and the excitations due to a faster quench, where the dynamics is often well described by the classical model. We estimate the value of the quench rate that separates the two regimes and support our argument using numerical simulations of the out-of-equilibrium many-body dynamics. For the specific case of a ϕ4\phi^4ϕ4 model we demonstrate that the two regimes exhibit two different power-law scalings, which are in agreement with the KZ theory when applied to the quantum and to the classical case. This result contributes to extending the prediction power of the Kibble-Zurek mechanism and to provide insight into recent experimental observations in systems of cold atoms and ions.
We investigate the quench dynamics of the dipolar bosons in two dimensional optical lattice of square geometry using the time dependent Gutzwiller method. The system exhibits different density orders like the checkerboard and the striped pattern, depending upon the polarization angle of the dipoles. We quench the hopping parameter across the striped density wave (SDW) to striped supersolid (SSS) phase transition, and obtain the scaling laws for the correlation length and topological vortex density, as function of the quench rate. The results are reminiscent of the Kibble-Zurek mechanism (KZM). We also investigate the dynamics from the striped supersolid phase to the checkerboard supersolid phase, obtained by quenching the dipole tilt angle θθθ. This is a first order structural quantum phase transition, and we study the non-equilibrium dynamics from the perspective of the KZM. In particular, we find the number of the domains with checkerboard order follows a power law scaling with the quench rate. This indicates the applicability of the KZM to this first order quantum phase transition.
The Kibble-Zurek (KZ) hypothesis identifies the relevant time scales in out-of-equilibrium dynamics of critical systems employing concepts valid at equilibrium: It predicts the scaling of the defect formation immediately after quenches across classical and quantum phase transitions as a function of the quench speed. Here, we study the crossover between the scaling dictated by a slow quench, which is ruled by the critical properties of the quantum phase transition, and the excitations due to a faster quench, where the dynamics is often well described by the classical model. We estimate the value of the quench rate that separates the two regimes and support our argument using numerical simulations of the out-of-equilibrium many-body dynamics. For the specific case of a ϕ^{4} model we demonstrate that the two regimes exhibit two different power-law scalings, which are in agreement with the KZ theory when applied to the quantum and classical cases. This result contributes to extending the prediction power of the Kibble-Zurek mechanism and to providing insight into recent experimental observations in systems of cold atoms and ions.
We analyze mechanisms for universal out-of-equilibrium dynamics near criticality by exploring the effect of randomized quantum resetting (QR) under a finite-time quench across a quantum phase transition. Using the transverse-field Ising chain as a generic model and exploiting its exact solution, QR is found to cause a crossover of the scaling of the topological defect density with the time scale τττ of the quench, from Kibble-Zurek to anti-Kibble-Zurek scaling as τττ increases. This reflects a competition between non-adiabatic quench-driven excitations and QR, giving rise to local minima of the defect densities at optimal annealing times. These times and the corresponding local minima are shown to scale as universal power laws with the rate of QR. Additional results for the scaling of the mean excess energy suggest that a system driven across a quantum critical point exhibits the same scaling behavior under a linear quench with QR as with uncorrelated noise.
We study the non-equilibrium quench dynamics crossing a continuous phase transition between the charge density wave (CDW) and supersolid (SS) phases of a bosonic lattice gas with cavity-mediated interactions. When changing the hopping amplitude in the Hamiltonian as a function of time, we investigate the scaling behavior of the correlation length and vortex density with respect to the quench time and find that there is a threshold of the quench rate separating two distinct scaling regimes. When slowly varying the system below that threshold, we find a power-law scaling as predicted by the Kibble-Zurek mechanism (KZM). While considering fast quench above that threshold, a deviation from the KZM prediction occurs, manifested by a saturation of the defect density. We further show that such distinct scaling behaviors during different dynamic procedures can be understood through comparing the relaxation time and the quench rate.