Trap-size scaling in confined particle systems at quantum transitions

Abstract

We develop a trap-size scaling theory for trapped particle systems at quantum transitions. As a theoretical laboratory, we consider a quantum XY chain in an external transverse field acting as a trap for the spinless fermions of its quadratic Hamiltonian representation. We discuss trap-size scaling at the Mott insulator to superfluid transition in the Bose-Hubbard model. We present exact and accurate numerical results for the XY chain and for the low-density Mott transition in the hard-core limit of the one-dimensional Bose-Hubbard model. Our results are relevant for systems of cold atomic gases in optical lattices.

Revised and greatly expanded. 15 pages, 7 figures

References in corpus (14)

• Many-Body Physics with Ultracold Gases
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• The critical exponents of the superfluid transition in He4
• Quantum Monte Carlo simulations of confined bosonic atoms in optical lattices
• Formation of spatial shell structures in the superfluid to Mott insulator transition
• Critical Behavior of a Trapped Interacting Bose Gas
• Exploring correlated 1D Bose gases from the superfluid to the Mott-insulator state by inelastic light scattering
• Universal properties of hard-core bosons confined on one-dimensional lattices
• Ground-state properties of hard-core bosons confined on one-dimensional optical lattices
• Entanglement in spin chains with gradients
• Phase Transition in Space: How Far Does a Symmetry Bend Before It Breaks?
• Simulations of ultracold bosonic atoms in optical lattices with anharmonic traps
• Gradient critical phenomena in the Ising quantum chain
• Gradient critical phenomena in the Ising quantum chain: surface behaviour

Cited by in corpus (59)

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• Fermi gases in one dimension: From Bethe Ansatz to experiments
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• Thermodynamics of the 3D Hubbard model on approach to the Neel transition
• Exact relations between particle fluctuations and entanglement in Fermi gases
• Coherent and dissipative dynamics at quantum phase transitions
• Random matrices and entanglement entropy of trapped Fermi gases
• Quantum critical behavior and trap-size scaling of trapped bosons in a one-dimensional optical lattice
• Signature of Quantum Criticality in the Density Profiles of Cold Atom Systems
• Entanglement and particle correlations of Fermi gases in harmonic traps
• Cold bosons in optical lattices: a tutorial for Exact Diagonalization
• Equilibrium and off-equilibrium trap-size scaling in 1D ultracold bosonic gases
• Interaction quench in a trapped one-dimensional Bose gas
• Criticality in Trapped Atomic Systems
• Techniques to measure quantum criticality in cold atoms
• Superfluid to normal phase transition in strongly correlated bosons in two and three dimensions
• Quantum Criticality from in-situ Density Imaging
• Surface and bulk entanglement in free-fermion chains
• Exploring quantum criticality based on ultracold atoms in optical lattices
• Scaling properties of work fluctuations after quenches at quantum transitions
• Scaling of bipartite entanglement in one-dimensional lattice systems with a trapping potential
• Renormalization-group flow and asymptotic behaviors at the Berezinskii-Kosterlitz-Thouless transitions
• One-particle density matrix of a trapped Lieb-Liniger anyonic gas
• One-body reduced density matrix of trapped impenetrable anyons in one dimension
• Universal quantum behaviors of interacting fermions in 1D traps: from few particles to the trap thermodynamic limit
• Bose-Einstein condensation and critical behavior of two-component bosonic gases
• Gradient critical phenomena in the Ising quantum chain: surface behaviour
• Universal behavior of two-dimensional bosonic gases at Berezinskii-Kosterlitz-Thouless transitions
• Critical parameters from trap-size scaling in trapped particle systems
• Universal off-diagonal long-range order behaviour for a trapped Tonks-Girardeau gas
• Analytical and numerical study of trapped strongly correlated bosons in two- and three-dimensional lattices
• Information measures for a local quantum phase transition: Lattice fermions in a one-dimensional harmonic trap
• Dynamical off-equilibrium scaling across magnetic first-order phase transitions
• Smoothly-varying hopping rates in driven flow with exclusion
• Engineering non-equilibrium quantum phase transitions via causally gapped Hamiltonians
• Phase diagram and multicritical behaviors of mixtures of 3D bosonic gases
• Exact dynamics of a one dimensional Bose gas in a periodic time-dependent harmonic trap
• Particle-number scaling of the quantum work statistics and Loschmidt echo in Fermi gases with time-dependent traps
• Interplay between temperature and trap effects in one-dimensional lattice systems of bosonic particles
• Finite-size scaling behavior in trapped systems
• OPE Coefficients of the 3D Ising model with a trapping potential
• Quasi-long-range order in trapped systems
• Three-dimensional Abelian and non-Abelian gauge Higgs theories
• Dimensional crossover of Bose-Einstein condensation phenomena in quantum gases confined within slab geometries
• Scaling behaviour of trapped bosonic particles in two dimensions at finite temperature
• One-dimensional Bose gas driven by a slow time-dependent harmonic trap
• Universal scaling of three-dimensional bosonic gases in a trapping potential
• Entanglement in composite free-fermion systems
• Universal scaling effects of a temperature gradient at first-order transitions
• Spatial Kibble-Zurek mechanism through susceptibilities: the inhomogeneous quantum Ising model case
• Information measures for a local quantum phase transition: Lattice bosons in a one-dimensional harmonic trap
• Scaling phenomena driven by inhomogeneous conditions at first-order quantum transitions
• Trap effects and continuum limit of the Hubbard model in the presence of a harmonic potential
• Critical behavior at the spatial boundary of a trapped inhomogeneous Bose-Einstein condensate
• Critical dynamics in trapped particle systems
• Out-of-equilibrium quantum dynamics of fermionic gases in the presence of localized particle loss
• Stacked quantum Ising systems and quantum Ashkin-Teller model
• Energy trapped Ising model