Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2507.11914

Bose-Hubbard model in the presence of artificial magnetic fields: Ground state and thermal phase diagrams

Jaberi, Mohammadamin, Fatemeh Heydarinasab

Published Jul 16, 2025• 0 citations
arXivHTMLPDF

Abstract

We consider effects of artificial magnetic fields on the ground state of the two-dimensional Bose-Hubbard model. Using an asymmetric Bose-Hubbard model, we demonstrate that the frustrating hopping energy localizes bosons and enlarges insulators and supersolid borders. We show these increments in the presence of artificial gauge fields up to a symmetric point of the field. Moreover, our calculations exhibit the real space modulations of the superfluid and supersolid phases. The bosonic current exhibits vortices in these phases, which their configurations depend on the commensuration between the magnetic field and the lattice. Although the magnetic field breaks the translational symmetry of the square lattice explicitly, this symmetry is restored in the Mott insulator phase. The filling factor exhibits a checkerboard pattern in the density-wave and supersolid phases, regardless of the magnetic field strength. We explore thermal fluctuations and demonstrate the robustness of insulators and SS phases up to temperatures comparable to the interaction energy, which support the feasibility of observing such phases in experiments.

DOI
10.48550/arxiv.2507.11914

Related papers

Ground-state and finite-temperature phase diagrams of the Bose-Hubbard model under artificial magnetic fields

Mohammadamin Jaberi, Fatemeh Heydarinasab

We investigate the effects of artificial magnetic fields on the ground-state of the two-dimensional Bose-Hubbard model. Using an asymmetric Bose-Hubbard model, we demonstrate that anisotropic hopping amplitude localizes bosons and enlarges the insulating and supersolid regions. We show these increases in the presence of artificial gauge fields up to the symmetric point of the field. Moreover, our calculations exhibit real-space modulations of the superfluid and supersolid phases. The bosonic current exhibits vortices in these phases, whose configurations depend on the commensuration between the magnetic field and the lattice. Although the magnetic field explicitly breaks the translational symmetry of the square lattice, this symmetry is restored in the Mott insulator phase. The local densities shows a checkerboard pattern in the density-wave and supersolid phases, regardless of the magnetic field strength. We investigate thermal fluctuations and demonstrate the robustness of insulating and supersolid phases up to temperatures comparable to the interaction energy, which supports the feasibility of observing such phases in experiments.

Scientific Reports•Dec 4, 2025•0 citations

Supersolid phase of the extended Bose-Hubbard model with an artificial gauge field

Kuldeep Suthar, Hrushikesh Sable, Rukmani Bai +3 more

We examine the zero- and finite-temperature phase diagrams of soft-core bosons of the extended Bose-Hubbard model on a square optical lattice. To study various quantum phases and their transitions we employ single-site and cluster Gutzwiller mean-field theory. We have observed that the Mott insulator phase vanishes above a critical value of nearest-neighbor interaction and the supersolid phase occupies a larger region in the phase diagram. We show that the presence of an artificial gauge field enlarges the domain of the supersolid phase. The finite temperature destroys the crystalline structure of the supersolid phase and thereby favors the normal fluid--to--superfluid phase transition. The presence of an envelope harmonic potential demonstrates the coexistence of different phases, and at $z{k}_{B}T\ensuremath{\geqslant}V$, thermal energy comparable to or higher than the long-range interaction energy, the supersolidity of the system is destroyed.

arXiv:1904.12649•Physical Review A•Jul 20, 2020•32 citations

Phase diagram of the Bose-Hubbard model on a checkerboard superlattice

M. Iskin

We study the effects of an artificial gauge field on the ground-state phases of the Bose-Hubbard model on a checkerboard superlattice in two dimensions, including the superfluid phase and the Mott and alternating Mott insulators. First, we discuss the single-particle Hofstadter problem, and show that the presence of a checkerboard superlattice gives rise to a magnetic flux-independent energy gap in the excitation spectrum. Then, we consider the many-particle problem, and derive an analytical mean-field expression for the superfluid-Mott and superfluid--alternating-Mott insulator phase transition boundaries. Finally, since the phase diagram of the Bose-Hubbard model on a checkerboard superlattice is in many ways similar to that of the extended Bose-Hubbard model, we comment on the effects of magnetic field on the latter model, and derive an analytical mean-field expression for the superfluid-insulator phase transition boundaries as well.

•Jan 3, 2011•0 citations

Density-wave–supersolid and Mott-insulator–superfluid transitions in the presence of an artificial gauge field: A strong-coupling perturbation approach

Rashi Sachdeva, Sankalpa Ghosh

We study the effect of an artificial gauge field on the zero-temperature phase diagram of an extended Bose-Hubbard model that describes ultracold atoms in optical lattices with long-range interactions by using strong-coupling perturbation theory. We determine analytically the effect of the artificial gauge field on the density-wave--supersolid (DW-SS) and the Mott-insulator--superfluid (MI-SF) transition boundary. The momentum distribution at these two transition boundaries is also calculated in this approach. It is shown that such a momentum distribution, which can be observed in time-of-flight measurements, reveals the symmetry of the gauge potential through the formation of a magnetic Brillouin zone and clearly distinguishes between the DW-SS and MI-SF boundary. We also point out that, in a symmetric gauge, the momentum distribution structure at these transition boundaries bears distinctive signatures of vortices in supersolid and superfluid phases.

arXiv:1106.0410•Physical Review A•Jan 31, 2012•9 citations

Bose-Hubbard model in a strong effective magnetic field: Emergence of a chiral Mott insulator ground state

Arya Dhar, Maheswar Maji, Tapan Mishra +3 more

Motivated by experiments on Josephson junction arrays, and cold atoms in an optical lattice in a synthetic magnetic field, we study the ``fully frustrated'' Bose-Hubbard model with half a magnetic flux quantum per plaquette. We obtain the phase diagram of this model on a two-leg ladder at integer filling via the density matrix renormalization group approach, complemented by Monte Carlo simulations on an effective classical $XY$ model. The ground state at intermediate correlations is consistently shown to be a chiral Mott insulator (CMI) with a gap to all excitations and staggered loop currents which spontaneously break time-reversal symmetry. We characterize the CMI state as a vortex supersolid or an indirect exciton condensate, and discuss various experimental implications.

arXiv:1109.5703•Physical Review A•Apr 11, 2012•130 citations

Quantum phases for bosons in a square lattice with artificial magnetic flux

Ya-Fei Song, Shi-Jie Yang

Abstract Ground-state phases of the ultracold bosons in 2D optical lattices subject to artificial magnetic flux are studied by the inhomogeneous Gutzwiller variational method. Results show that the density of a vortex increases linearly with the magnetic flux per plaquette. For a smaller magnetic flux, no supersolid (SS) states are present. The superfluid (SF) states are vortex liquids of either particle-type or hole-type, depending on whether the average filling is greater or less than the integer number. For a larger magnetic flux, regular density-wave states, which also exhibit superfluidity of either particle-type or hole-type, appear at the boundary between the Mott insulator and the SF. Moreover, the uniform SF phases differ to the conventional SF by carrying convection super-current and coreless vorticity. The convection super-current or vorticity in the SS phases assemble in pairs or stripes, as well as checkerboards, according to the flux strength per unit cell.

Journal of Physics B Atomic Molecular and Optical Physics•Feb 20, 2019•5 citations
We consider effects of artificial magnetic fields on the ground state of the two-dimensional Bose-Hubbard model. Using an asymmetric Bose-Hubbard model, we demonstrate that the frustrating hopping energy localizes bosons and enlarges insulators and supersolid borders. We show these increments in the presence of artificial gauge fields up to a symmetric point of the field. Moreover, our calculations exhibit the real space modulations of the superfluid and supersolid phases. The bosonic current exhibits vortices in these phases, which their configurations depend on the commensuration between the magnetic field and the lattice. Although the magnetic field breaks the translational symmetry of the square lattice explicitly, this symmetry is restored in the Mott insulator phase. The filling factor exhibits a checkerboard pattern in the density-wave and supersolid phases, regardless of the magnetic field strength. We explore thermal fluctuations and demonstrate the robustness of insulators and SS phases up to temperatures comparable to the interaction energy, which support the feasibility of observing such phases in experiments.
We investigate the effects of artificial magnetic fields on the ground-state of the two-dimensional Bose-Hubbard model. Using an asymmetric Bose-Hubbard model, we demonstrate that anisotropic hopping amplitude localizes bosons and enlarges the insulating and supersolid regions. We show these increases in the presence of artificial gauge fields up to the symmetric point of the field. Moreover, our calculations exhibit real-space modulations of the superfluid and supersolid phases. The bosonic current exhibits vortices in these phases, whose configurations depend on the commensuration between the magnetic field and the lattice. Although the magnetic field explicitly breaks the translational symmetry of the square lattice, this symmetry is restored in the Mott insulator phase. The local densities shows a checkerboard pattern in the density-wave and supersolid phases, regardless of the magnetic field strength. We investigate thermal fluctuations and demonstrate the robustness of insulating and supersolid phases up to temperatures comparable to the interaction energy, which supports the feasibility of observing such phases in experiments.
We examine the zero- and finite-temperature phase diagrams of soft-core bosons of the extended Bose-Hubbard model on a square optical lattice. To study various quantum phases and their transitions we employ single-site and cluster Gutzwiller mean-field theory. We have observed that the Mott insulator phase vanishes above a critical value of nearest-neighbor interaction and the supersolid phase occupies a larger region in the phase diagram. We show that the presence of an artificial gauge field enlarges the domain of the supersolid phase. The finite temperature destroys the crystalline structure of the supersolid phase and thereby favors the normal fluid--to--superfluid phase transition. The presence of an envelope harmonic potential demonstrates the coexistence of different phases, and at $z{k}_{B}T\ensuremath{\geqslant}V$, thermal energy comparable to or higher than the long-range interaction energy, the supersolidity of the system is destroyed.
We study the effects of an artificial gauge field on the ground-state phases of the Bose-Hubbard model on a checkerboard superlattice in two dimensions, including the superfluid phase and the Mott and alternating Mott insulators. First, we discuss the single-particle Hofstadter problem, and show that the presence of a checkerboard superlattice gives rise to a magnetic flux-independent energy gap in the excitation spectrum. Then, we consider the many-particle problem, and derive an analytical mean-field expression for the superfluid-Mott and superfluid--alternating-Mott insulator phase transition boundaries. Finally, since the phase diagram of the Bose-Hubbard model on a checkerboard superlattice is in many ways similar to that of the extended Bose-Hubbard model, we comment on the effects of magnetic field on the latter model, and derive an analytical mean-field expression for the superfluid-insulator phase transition boundaries as well.
We study the effect of an artificial gauge field on the zero-temperature phase diagram of an extended Bose-Hubbard model that describes ultracold atoms in optical lattices with long-range interactions by using strong-coupling perturbation theory. We determine analytically the effect of the artificial gauge field on the density-wave--supersolid (DW-SS) and the Mott-insulator--superfluid (MI-SF) transition boundary. The momentum distribution at these two transition boundaries is also calculated in this approach. It is shown that such a momentum distribution, which can be observed in time-of-flight measurements, reveals the symmetry of the gauge potential through the formation of a magnetic Brillouin zone and clearly distinguishes between the DW-SS and MI-SF boundary. We also point out that, in a symmetric gauge, the momentum distribution structure at these transition boundaries bears distinctive signatures of vortices in supersolid and superfluid phases.
Motivated by experiments on Josephson junction arrays, and cold atoms in an optical lattice in a synthetic magnetic field, we study the ``fully frustrated'' Bose-Hubbard model with half a magnetic flux quantum per plaquette. We obtain the phase diagram of this model on a two-leg ladder at integer filling via the density matrix renormalization group approach, complemented by Monte Carlo simulations on an effective classical XYXYXY model. The ground state at intermediate correlations is consistently shown to be a chiral Mott insulator (CMI) with a gap to all excitations and staggered loop currents which spontaneously break time-reversal symmetry. We characterize the CMI state as a vortex supersolid or an indirect exciton condensate, and discuss various experimental implications.
Abstract Ground-state phases of the ultracold bosons in 2D optical lattices subject to artificial magnetic flux are studied by the inhomogeneous Gutzwiller variational method. Results show that the density of a vortex increases linearly with the magnetic flux per plaquette. For a smaller magnetic flux, no supersolid (SS) states are present. The superfluid (SF) states are vortex liquids of either particle-type or hole-type, depending on whether the average filling is greater or less than the integer number. For a larger magnetic flux, regular density-wave states, which also exhibit superfluidity of either particle-type or hole-type, appear at the boundary between the Mott insulator and the SF. Moreover, the uniform SF phases differ to the conventional SF by carrying convection super-current and coreless vorticity. The convection super-current or vorticity in the SS phases assemble in pairs or stripes, as well as checkerboards, according to the flux strength per unit cell.