Critical points of the three-dimensional Bose-Hubbard model from on-site atom number fluctuations
arXiv:1903.05936 · doi:10.1038/s41598-019-44825-9
Abstract
We discuss how positions of critical points of the three-dimensional Bose-Hubbard model can be accurately obtained from variance of the on-site atom number operator, which can be experimentally measured. The idea that we explore is that the derivative of the variance, with respect to the parameter driving the transition, has a pronounced maximum close to critical points. We show that Quantum Monte Carlo studies of this maximum lead to precise determination of critical points for the superfluid-Mott insulator transition in systems with mean number of atoms per lattice site equal to one, two, and three. We also extract from such data the correlation-length critical exponent through the finite-size scaling analysis and discuss how the derivative of the variance can be reliably computed from numerical data for the variance. The same conclusions apply to the derivative of the nearest-neighbor correlation function, which can be obtained from routinely measured time-of-flight images.
arXiv comment15 pages, corrected typos, updated references, improvements in discussion
References in corpus (33)
- Many-Body Physics with Ultracold Gases
- Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
- Cold bosonic atoms in optical lattices
- Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
- Critical Phenomena and Renormalization-Group Theory
- Bose-Einstein condensation of atoms in a uniform potential
- The ALPS project release 1.3: open source software for strongly correlated systems
- The ALPS project release 2.0: Open source software for strongly correlated systems
- Quantum phases in an optical lattice
- Non-standard Hubbard models in optical lattices: a review
- Critical behavior of the three-dimensional XY universality class
- Quantum Criticality
- Strong-coupling expansions for the pure and disordered bose Hubbard model
- Emergence of coherence in a uniform quasi-two-dimensional Bose gas
- Bose Einstein Condensate in a Box
- Homogeneous Atomic Fermi Gases
- Phase coherence of an atomic Mott insulator
- Specific Heat of Liquid Helium in Zero Gravity very near the Lambda Point
- Two-Dimensional Homogeneous Fermi Gases
- Phase diagram for a Bose-Einstein condensate moving in an optical lattice
- Condensate fraction in a 2D Bose gas measured across the Mott-insulator transition
- Superfluid Density in a Highly Underdoped YBCO Superconductor
- Recent developments in Quantum Monte-Carlo simulations with applications for cold gases
- Ultracold bosons with short-range interaction in regular optical lattices
- Nonperturbative renormalization-group approach to strongly-correlated lattice bosons
- Process chain approach to the Bose-Hubbard model: Ground-state properties and phase diagram
- Phases of a 2D Bose Gas in an Optical Lattice
- 4D-XY quantum criticality in a doped Mott insulator
- A projection operator approach to the Bose-Hubbard model
- From single-particle excitations to sound waves in a box-trapped atomic Bose-Einstein condensate
- Experimental Determination of Bose-Hubbard Energies
- Observation of atom-number fluctuations in optical lattices via quantum collapse and revival dynamics
- Quantum Critical Phenomena of 4He in Nanoporous Media
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- Evidence from on-site atom number fluctuations for a quantum Berezinskii-Kosterlitz-Thouless transition in the one-dimensional Bose-Hubbard model
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- Evidence for 4D XY Quantum Criticality in He Confined in Nanoporous Media at Finite Temperatures