Quantum critical behavior and trap-size scaling of trapped bosons in a one-dimensional optical lattice

Abstract

We study the quantum (zero-temperature) critical behaviors of confined particle systems described by the one-dimensional (1D) Bose-Hubbard model in the presence of a confining potential, at the Mott insulator to superfluid transitions, and within the gapless superfluid phase. Specifically, we consider the hard-core limit of the model, which allows us to study the effects of the confining potential by exact and very accurate numerical results. We analyze the quantum critical behaviors in the large trap-size limit within the framework of the trap-size scaling (TSS) theory, which introduces a new trap exponent theta to describe the dependence on the trap size. This study is relevant for experiments of confined quasi 1D cold atom systems in optical lattices. At the low-density Mott transition TSS can be shown analytically within the spinless fermion representation of the hard-core limit. The trap-size dependence turns out to be more subtle in the other critical regions, when the corresponding homogeneous system has a nonzero filling f, showing an infinite number of level crossings of the lowest states when increasing the trap size. At the n=1 Mott transition this gives rise to a modulated TSS: the TSS is still controlled by the trap-size exponent theta, but it gets modulated by periodic functions of the trap size. Modulations of the asymptotic power-law behavior is also found in the gapless superfluid region, with additional multiscaling behaviors.

26 pages, 34 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
• Quantum Monte Carlo simulations of confined bosonic atoms in optical lattices
• Formation of spatial shell structures in the superfluid to Mott insulator transition
• Parity effects in the scaling of block entanglement in gapless spin chains
• Exploring correlated 1D Bose gases from the superfluid to the Mott-insulator state by inelastic light scattering
• Condensate fraction in a 2D Bose gas measured across the Mott-insulator transition
• Spatial correlations of trapped 1d bosons in an optical lattice
• 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
• Simulations of ultracold bosonic atoms in optical lattices with anharmonic traps
• One-dimensional extended Bose-Hubbard model with a confining potential: a DMRG analysis
• Finite-size scaling behavior in trapped systems

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• The entanglement entropy of one-dimensional gases
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• Exact relations between particle fluctuations and entanglement in Fermi gases
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• Universal corrections to scaling for block entanglement in spin-1/2 XX chains
• Finite-size scaling at quantum transitions
• Ultracold bosons with short-range interaction in regular optical lattices
• Coherent and dissipative dynamics at quantum phase transitions
• Entanglement Entropy of Quantum Wire Junctions
• The entanglement entropy of 1D systems in continuous and homogenous space
• Entanglement and particle correlations of Fermi gases in harmonic traps
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• The Inhomogeneous Gaussian Free Field, with application to ground state correlations of trapped 1d Bose gases
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• Techniques to measure quantum criticality in cold atoms
• Quantum dynamics and entanglement of a 1D Fermi gas released from a trap
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• Corrections to scaling for block entanglement in massive spin-chains
• Surface and bulk entanglement in free-fermion chains
• 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
• Finite-size scaling at first-order quantum transitions when boundary conditions favor one of the two phases
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• One-body reduced density matrix of trapped impenetrable anyons in one dimension
• XXZ spin-1/2 representation of a finite-U Bose-Hubbard chain at half-integer filling
• Universal behavior of two-dimensional bosonic gases at Berezinskii-Kosterlitz-Thouless transitions
• Critical parameters from trap-size scaling in trapped particle systems
• Information measures for a local quantum phase transition: Lattice fermions in a one-dimensional harmonic trap
• Analytical and numerical study of trapped strongly correlated bosons in two- and three-dimensional lattices
• Universal off-diagonal long-range order behaviour for a trapped Tonks-Girardeau gas
• Anomalous behavior of the energy gap in the one-dimensional quantum XY model
• 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
• Quantum criticality of spin-1 bosons in a 1D harmonic trap
• Scaling behaviour of trapped bosonic particles in two dimensions at finite temperature
• Entanglement in composite free-fermion systems
• Entanglement in non-critical inhomogeneous quantum chains
• Scaling phenomena driven by inhomogeneous conditions at first-order quantum transitions
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• Critical dynamics in trapped particle systems
• Out-of-equilibrium quantum dynamics of fermionic gases in the presence of localized particle loss
• Quench Dynamics in Confined 1+1-Dimensional Systems