Signatures of the superfluid to Mott insulator transition in equilibrium and in dynamical ramps

Abstract

We investigate the equilibrium and dynamical properties of the Bose-Hubbard model and the related particle-hole symmetric spin-1 model in the vicinity of the superfluid to Mott insulator quantum phase transition. We employ the following methods: exact-diagonalization, mean field (Gutzwiller), cluster mean-field, and mean-field plus Gaussian fluctuations. In the first part of the paper we benchmark the four methods by analyzing the equilibrium problem and give numerical estimates for observables such as the density of double occupancies and their correlation function. In the second part, we study parametric ramps from the superfluid to the Mott insulator and map out the crossover from the regime of fast ramps, which is dominated by local physics, to the regime of slow ramps with a characteristic universal power law scaling, which is dominated by long wavelength excitations. We calculate values of several relevant physical observables, characteristic time scales, and an optimal protocol needed for observing universal scaling.

23 pages, 13 figures

References in corpus (9)

• Single-Atom Resolved Fluorescence Imaging of an Atomic Mott Insulator
• Universal adiabatic dynamics across a quantum critical point
• The `Higgs' Amplitude Mode at the Two-Dimensional Superfluid-Mott Insulator Transition
• Breakdown of the adiabatic limit in low dimensional gapless systems
• Supplementary Information to the paper ``Breakdown of the adiabatic limit in low dimensional gapless systems''
• Dynamical properties of ultracold bosons in an optical lattice
• Quantum quenches in a spinor condensate
• Spectral functions of the Higgs mode near two-dimensional quantum critical points
• The Higgs mode in a two-dimensional superfluid

Cited by in corpus (19)

• Amplitude / Higgs Modes in Condensed Matter Physics
• Emergence of coherence and the dynamics of quantum phase transitions
• Entanglement entropy across the superfluid-insulator transition : a signature of bosonic criticality
• Gaussian time dependent variational principle for the Bose-Hubbard model
• Quenching from superfluid to free bosons in two dimensions: entanglement, symmetries, and quantum Mpemba effect
• Composite Boson Mapping for Lattice Boson Systems
• Observation of many-body quantum phase transitions beyond the Kibble-Zurek mechanism
• Collective modes at a disordered quantum phase transition
• Phases and collective modes of bosons in a triangular lattice at finite temperature: A cluster mean field study
• Novel quantum phases of two-component bosons with pair hopping in synthetic dimension
• Inhomogeneous mean-field approach to collective excitations in disordered interacting bosons
• Non-local correlation and entanglement of ultracold bosons in the two-dimensional Bose-Hubbard lattice at finite temperature
• Bose-Hubbard model with occupation-parity couplings
• Bose-Fermi-Hubbard model in the truncated Hilbert space limit
• Formation of paired phases of bosons and their excitations in a square lattice
• Topological Higgs Amplitude Modes in Strongly Interacting Superfluids
• Critical Behavior and Collective Modes at the Superfluid Transition in Amorphous Systems
• Finite temperature phases and excitations of bosons on a square lattice: A cluster mean field study
• Suppression of coherent light scattering in a three-dimensional atomic array