Dynamics of a quantum phase transition in the Bose-Hubbard model: Kibble-Zurek mechanism and beyond

Abstract

In this paper, we study the dynamics of the Bose-Hubbard model by using time-dependent Gutzwiller methods. In particular, we vary the parameters in the Hamiltonian as a function of time, and investigate the temporal behavior of the system from the Mott insulator to the superfluid (SF) crossing a second-order phase transition. We first solve a time-dependent Schrödinger equation for the experimental setup recently done by Braun et.al. [Proc. Nat. Acad. Sci. 112, 3641 (2015)] and show that the numerical and experimental results are in fairly good agreement. However, these results disagree with the Kibble-Zurek scaling. From our numerical study, we reveal a possible source of the discrepancy. Next, we calculate the critical exponents of the correlation length and vortex density in addition to the SF order parameter for a Kibble-Zurek protocol. We show that beside the "freeze" time $\hat{t}$, there exists another important time, $t_{\mathrm{eq}}$, at which an oscillating behavior of the SF amplitude starts. From calculations of the exponents of the correlation length and vortex density with respect to a quench time $\tQ$, we obtain a physical picture of a coarsening process. Finally, we study how the system evolves after the quench. We give a global picture of dynamics of the Bose-Hubbard model.

References added. Version to appear in Phy.Rev.A

References in corpus (8)

• Many-Body Physics with Ultracold Gases
• Universal adiabatic dynamics across a quantum critical point
• Critical Dynamics of Spontaneous Symmetry Breaking in a Homogeneous Bose gas
• Emergence of coherence in a uniform quasi-two-dimensional Bose gas
• Emergence of coherence and the dynamics of quantum phase transitions
• Topology induced anomalous defect production by crossing a quantum critical point
• Defect formation beyond Kibble-Zurek mechanism and holography
• Dynamics of a quantum phase transition in the 1D Bose-Hubbard model: excitations and correlations induced by a quench

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• Quantum information scrambling in two-dimensional Bose-Hubbard lattices
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• Apparent delay of the Kibble-Zurek mechanism in quenched open systems
• Defect generation and dynamics during quenching in finite size homogeneous ion chains
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