Abstract
The Mott insulator-to-superfluid transition exhibited by the Bose–Hubbard model on a two-dimensional square lattice occurs for any value of the chemical potential, but becomes critical at the tips of the so-called Mott lobes only. Employing a numerical approach based on a combination of high-order perturbation theory and hypergeometric analytic continuation we investigate how quantum critical properties manifest themselves in computational practice. We consider two-dimensional triangular lattices and three-dimensional cubic lattices for comparison, providing accurate parametrizations of the phase boundaries at the tips of the respective first lobes. In particular, we lend strong support to a recently suggested inequality which bounds the divergence exponent of the one-particle correlation function in terms of that of the two-particle correlation function, and which sharpens to an equality if and only if a system becomes critical.
Highlights
The application of the theory of critical phenomena [1,2,3] to the description of the lambda transition undergone by liquid helium at about 2.18 K is still confronting physicists with a seemingly minor, yet annoying challenge: Owing to measurements performed under zero-gravity conditions in Earth orbit in order to reduce the rounding of the transition caused by gravitationally induced pressure gradients, the critical exponent α describing the singularity of the specific heat could be determined with exceptional accuracy [4], resulting in the value αex = −0.0127 ± 0.0003
It is of interest to observe that the quantum phase transition exhibited at zero temperature by the Bose-Hubbard model [10] may contribute to solving this long-standing puzzle
The comparatively simple 2-dimensional Bose-Hubbard model belongs to the 3-dimensional XY universality class, the same class which covers the lambda transition of liquid helium
Summary
The currently most accurate theoretical value has been reported by Campostrini et al [8], based on finite-size scaling analyses of high-statistics Monte Carlo simulations and resummations of 22nd-order high-temperature expansions for the φ4 lattice model and the dynamically diluted XY model, giving αth = −0.0151 ± 0.0003. Since this comparison of measurement with calculation constitutes a core test of the renormalization group theory, the remaining discrepancy needs to be taken seriously. As an essential consistency check we consider the Bose-Hubbard model on a 3-dimensional cubic lattice, which falls into the 4-dimensional XY class and should not become critical at all
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Journal of Physics A: Mathematical and Theoretical
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
