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arXiv:1904.12649 · Physical Review A

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

Kuldeep Suthar, Hrushikesh Sable, Rukmani Bai, Soumik Bandyopadhyay, Sukla Pal, D. Angom

Published Jul 20, 2020• 32 citations
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Abstract

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.

DOI
10.1103/physreva.102.013320

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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 zkBT\ensuremath⩾Vz{k}_{B}T\ensuremath{\geqslant}VzkB​T\ensuremath⩾V, thermal energy comparable to or higher than the long-range interaction energy, the supersolidity of the system is destroyed.
We use the Gutzwiller ansatz and analyze the phase diagram of the extended Bose-Hubbard Hamiltonian with on-site (UUU) and nearest-neighbor (VVV) repulsions. For ddd-dimensional hypercubic lattices, when 2dV<U2\mathit{dV}<U2dV<U, it is well known that the ground state alternates between the charge-density-wave (CDW) and Mott insulators, and the supersolid (SS) phase occupies small regions around the CDW insulators. However, when 2dV>U2\mathit{dV}>U2dV>U, in this Rapid Communication, we show that the ground state has only CDW insulators, and more importantly, the SS phase occupies a much larger region in the phase diagram, existing up to very large hopping values which could be orders of magnitude higher than that of the well-known case. In particular, the SS-superfluid phase boundary increases linearly as a function of hopping when $2\mathit{dV}\ensuremath{\gtrsim}1.5U$, for which the prospects of observing the SS phase with dipolar Bose gases loaded into optical lattices is much higher.
We report our findings on the quantum phase transitions in cold bosonic atoms in a one-dimensional optical lattice using the finite-size density-matrix renormalization-group method in the framework of the extended Bose-Hubbard model. We consider wide ranges of values for the filling factors and the nearest-neighbor interactions. At commensurate fillings, we obtain two different types of charge-density wave phases and a Mott insulator phase. However, departure from commensurate fillings yields the exotic supersolid phase where both the crystalline and the superfluid orders coexist. In addition, we obtain the signatures for the solitary waves and the superfluid phase.
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.
By using the inhomogeneous mean-field theory, the phase diagram of the two-dimensional soft-core extended Bose-Hubbard model with both on-site and nearest-neighbor interactions in the presence of spatial disorder is determined. Rich phases, including Mott-insulator, checkerboard solid, supersolid, superfluid and disordered solid are obtained. Interestingly, due to the presence of disorder, a new disordered solid phase is found between the incompressible lobes, and it is demonstrated that the supersolid phase can survive in two-dimensional soft-core bosons. Furthermore, the system undergoes the phase transition from a disordered solid into a solid order or supersolid landscape when the disorder strength is increased. For weak nearest-neighbor repulsion, the increase of the disorder strength induces both checkerboard solid and supersolid phases shrinking to smaller hopping regions. However, for strong nearest-neighbor repulsion, the disorder stabilizes the supersolid phase and makes it occupying a remarkably broad region in the phase diagram. The analytical expressions for the phase boundaries between the incompressible and compressible phases are also obtained, which are in qualitative agreement with our numerical results.
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 ground-state phase diagram of the soft-core Bose-Hubbard model with the nearest-neighbor repulsion on a square lattice by using an unbiased quantum Monte Carlo method. In contrast to a previous study [P. Sengupta et al., Phys. Rev. Lett. 94, 207202 (2005)], we present the ground-state phase diagrams up to high hopping amplitudes. As a result, in addition to the known supersolid above half-filling, we find a supersolid phase below and at half-filling for high hopping amplitudes. In addition, for a strong nearest-neighbor repulsion, we show that the supersolid phase occupies a remarkably broad region in the phase diagram. These results are in agreement with the results of the Gutzwiller mean-field approximation [M. Iskin, Phys. Rev. A 83, 051606(R) (2011); T. Kimura, Phys. Rev. A 84, 063630 (2011)]. However, it turns out that the regions of the supersolid phases are significantly smaller than the mean-field results.