Kibble-Zurek scaling of the one-dimensional Bose-Hubbard model at finite temperatures

Abstract

We use tensor network methods - Matrix Product States, Tree Tensor Networks, and Locally Purified Tensor Networks - to simulate the one dimensional Bose-Hubbard model for zero and finite temperatures in experimentally accessible regimes. We first explore the effect of thermal fluctuations on the system ground state by characterizing its Mott and superfluid features. Then, we study the behavior of the out-of-equilibrium dynamics induced by quenches of the hopping parameter. We confirm a Kibble-Zurek scaling for zero temperature and characterize the finite temperature behavior, which we explain by means of a simple argument.

arXiv comment13 pages, 12 figures

References in corpus (52)

• Many-Body Physics with Ultracold Gases
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• The density-matrix renormalization group in the age of matrix product states
• Cold bosonic atoms in optical lattices
• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Efficient simulation of one-dimensional quantum many-body systems
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Probing the relaxation towards equilibrium in an isolated strongly correlated 1D Bose gas
• Transition from a strongly interacting 1D superfluid to a Mott insulator
• The cold atom Hubbard toolbox
• Dynamics of a Quantum Phase Transition
• Probing the Superfluid to Mott Insulator Transition at the Single Atom Level
• Quantum entanglement in condensed matter systems
• Classical simulation of quantum many-body systems with a tree tensor network
• Quench dynamics and non equilibrium phase diagram of the Bose-Hubbard model
• The Mott insulator transition in two dimensions
• Measuring entanglement growth in quench dynamics of bosons in an optical lattice
• The one-dimensional Bose-Hubbard Model with nearest-neighbor interaction
• Phases of the one-dimensional Bose-Hubbard model
• Mott Domains of Bosons Confined on Optical Lattices
• Simulation of two-dimensional quantum systems using a tree tensor network that exploits the entropic area law
• Mott transition in one dimension
• Suppression of the critical temperature for superfluidity near the Mott transition: validating a quantum simulator
• Emergence of coherence and the dynamics of quantum phase transitions
• A positive tensor network approach for simulating open quantum many-body systems
• Cooling in strongly correlated optical lattices: prospects and challenges
• Optimal control of complex atomic quantum systems
• Condensate fraction in a 2D Bose gas measured across the Mott-insulator transition
• Boson Mott insulators at finite temperatures
• Ultracold bosons with short-range interaction in regular optical lattices
• Anti-Kibble-Zurek Behavior in Crossing the Quantum Critical Point of a Thermally Isolated System Driven by a Noisy Control Field
• Purifications of multipartite states: limitations and constructive methods
• Unconstrained Tree Tensor Network: An adaptive gauge picture for enhanced performance
• Nonequilibrium quantum criticality in open systems: The dissipation rate as an additional indispensable scaling variable
• Dynamics of an inhomogeneous quantum phase transition
• One-dimensional many-body entangled open quantum systems with tensor network methods
• One-dimensional density waves of ultracold bosons in an optical lattice
• Phases of a 2D Bose Gas in an Optical Lattice
• Lattice Thermodynamics for Ultra-Cold Atoms
• Dynamical Mean Field Theory for the Bose-Hubbard Model
• Finite temperature study of bosons in a two dimensional optical lattice
• Dynamics of a quantum phase transition in the 1D Bose-Hubbard model: excitations and correlations induced by a quench
• Light-cone and diffusive propagation of correlations in a many-body dissipative system
• Visibility of Cold Atomic Gases in Optical Lattices for Finite Temperatures
• Dynamics of a quantum phase transition in the Bose-Hubbard model: Kibble-Zurek mechanism and beyond
• Anti-Kibble-Zurek behavior of a noisy transverse-field XY chain and its quantum simulation with two-level systems
• Scaling behavior of quantum critical relaxation dynamics in a heat bath
• Bose Hubbard model in the presence of Ohmic dissipation
• Finite-temperature effects on interacting bosonic 1D systems in disordered lattices
• Quantum Critical Probing and Simulation of Colored Quantum Noise
• Scaling in driven dynamics starting in the vicinity of a quantum critical point

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• Quench dynamics of Rydberg-dressed bosons on two-dimensional square lattices
• Superfluid to Mott transition in a Bose-Hubbard ring: Persistent currents and defect formation
• Scaling Theories of Kosterlitz-Thouless Phase Transitions
• Nonequilibrium critical dynamics in the quantum chiral clock model
• Quantum information scrambling in two-dimensional Bose-Hubbard lattices
• Exploring Dynamical Phase Transitions in the XY Chain through Linear Quench: Early and Long-term Perspectives
• Finite-temperature Rydberg arrays: quantum phases and entanglement characterization
• Application of the inhomogeneous Kibble-Zurek mechanism to quench dynamics in the transition from a Mott-insulator to a superfluid in a finite system
• Is there Kibble-Zurek scaling of topological defects in first-order phase transitions?
• Solution of one-dimensional Bose Hubbard model in large-$U$ limit
• Dynamical Phase Transitions in Periodically Driving 1D Ising Model