Criticality of the excess energy cost due to the unit-flux-quantum external field for the $(2+1)$D superfluid-insulator transition

Abstract

The two-dimensional ($2$D) spin-$S=1$ $XY$ model was investigated numerically as a realization of the $(2+1)$D superfluid-Mott-insulator (SF-MI) transition. The interaction parameters are extended so as to suppress corrections to finite-size scaling. Thereby, the external field of a unit flux quantum ($\Phi =2\pi$) is applied to the 2D cluster by incorporating the phase factor $e^{i{\varphi }_{ij}}$ (${\varphi }_{ij}$: gauge angle between the $i$ and $j$ sites) into the hopping amplitudes. Taking the advantage in that the exact-diagonalization method allows us to treat such a complex-valued matrix element, we evaluated the excess energy cost $\Delta E(2\pi )$ due to the magnetic flux $\Phi =2\pi$ explicitly in the SF ($XY$) phase. As a result, we found that the amplitude ratio ${\rho }_s/\Delta E(2\pi )$ (${\rho }_s$: spin stiffness) makes sense in proximity to the critical point, exhibiting a notable plateau in the SF-phase side. The plateau height is estimated, and compared to the related studies.

References in corpus (12)

• Single-Atom Resolved Fluorescence Imaging of an Atomic Mott Insulator
• The nonperturbative functional renormalization group and its applications
• The critical exponents of the superfluid transition in He4
• Higgs amplitude mode in the vicinity of a $(2+1)$-dimensional quantum critical point: a nonperturbative renormalization-group approach
• Universal Properties of the Higgs Resonance in (2+1)-Dimensional U(1) Critical Systems
• Vortex mass in a superfluid at low frequencies
• Critical capacitance and charge-vortex duality near the superfluid to insulator transition
• A Monte Carlo study of the three-dimensional XY universality class:Universal amplitude ratios
• Spectral function of the Higgs mode in 4-\varepsilon dimensions
• Nonperturbative functional renormalization-group approach to transport in the vicinity of a $(2+1)$-dimensional O($N$)-symmetric quantum critical point
• Numerical diagonalization analysis of the criticality of the (2+1)-dimensional XY model: Off-diagonal Novotny's method
• Mass and Charge of the Quantum Vortex in the $(2+1)$-d $O(2)$ Scalar Field Theory

Cited by in corpus (1)

• End-point singularity of the $XY$-paramagnetic phase boundary for the $(2+1)$D $S=1$ square-lattice $J_1$-$J_2$ $XY$ model with the single-ion anisotropy