Critical parameters from trap-size scaling in trapped particle systems

Abstract

We investigate the critical behavior of trapped particle systems at the low-temperature superfluid transition. In particular, we consider the three-dimensional Bose-Hubbard model in the presence of a trapping harmonic potential coupled with the particle density, which is a realistic model of cold bosonic atoms in optical lattices. We present a numerical study based on quantum Monte Carlo simulations, analyzed in the framework of the trap-size scaling (TSS). We show how the critical parameters can be derived from the trap-size dependences of appropriate observables, matching them with TSS. This provides a systematic scheme which is supposed to exactly converge to the critical parameters of the transition in the large trap-size limit. Our numerical analysis may provide a guide for experimental investigations of trapped systems at finite-temperature and quantum transitions, showing how critical parameters may be determined by looking at the scaling of the critical modes with respect to the trap size, i.e. by matching the trap-size dependence of the experimental data with the expected TSS Ansatz.

14 pages, few corrections

References in corpus (23)

• Many-Body Physics with Ultracold Gases
• Theory of ultracold Fermi gases
• Spatial quantum noise interferometry in expanding ultracold atom clouds
• Observation of scale invariance and universality in two-dimensional Bose gases
• The critical exponents of the superfluid transition in He4
• Imaging the Mott Insulator Shells using Atomic Clock Shifts
• 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
• Critical Point of an Interacting Two-Dimensional Atomic Bose Gas
• Universal properties of hard-core bosons confined on one-dimensional lattices
• Ground-state properties of hard-core bosons confined on one-dimensional optical lattices
• The trapped two-dimensional Bose gas: from Bose-Einstein condensation to Berezinskii-Kosterlitz-Thouless physics
• Kosterlitz-Thouless transition of the quasi two-dimensional trapped Bose gas
• Criterion for bosonic superfluidity in an optical lattice
• Superfluid to normal phase transition in strongly correlated bosons in two and three dimensions
• Quantum Criticality from in-situ Density Imaging
• Critical properties of a trapped interacting Bose gas
• Exploring quantum criticality based on ultracold atoms in optical lattices
• Critical Behaviour in Trapped Strongly Interacting Fermi Gases
• Finite-size scaling behavior in trapped systems
• Comment on "Direct Mapping of the Finite Temperature Phase Diagram of Strongly Correlated Quantum Models" by Q. Zhou, Y. Kato, N. Kawashima, and N. Trivedi, Phys. Rev. Lett. 103, 085701 (2009)
• Scaling behaviour of trapped bosonic particles in two dimensions at finite temperature

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