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arXiv:1011.1068 · Physical Review B

Thermal phase transitions of supersolids in the extended Bose-Hubbard model

Kwai-Kong Ng

Published Nov 3, 2010• 14 citations
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Abstract

We investigate numerically the finite-temperature phase diagrams of the extended Bose-Hubbard model in a two-dimensional square lattice. In particular, we focus on the melting of supersolid phases of two different crystal orderings, stripe and star orders, arising from the competition of the nearest- and next-nearest-neighbor interactions in the vicinity of quarter filling. The two crystal orders are the result of broken translational symmetry in either one or in both $x$ and $y$ directions. The broken gauge symmetry of the supersolids are found to be restored via a Kosterlitz-Thouless transition while the broken translational symmetries are restored via a single second-order phase transition, instead of two second-order transitions in the Ising universality class. On the other hand, the phase transitions between the star and stripe orders are first order in nature.

DOI
10.1103/physrevb.82.184505

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We investigate numerically the finite-temperature phase diagrams of the extended Bose-Hubbard model in a two-dimensional square lattice. In particular, we focus on the melting of supersolid phases of two different crystal orderings, stripe and star orders, arising from the competition of the nearest- and next-nearest-neighbor interactions in the vicinity of quarter filling. The two crystal orders are the result of broken translational symmetry in either one or in both xxx and yyy directions. The broken gauge symmetry of the supersolids are found to be restored via a Kosterlitz-Thouless transition while the broken translational symmetries are restored via a single second-order phase transition, instead of two second-order transitions in the Ising universality class. On the other hand, the phase transitions between the star and stripe orders are first order in nature.
We study the ground-state phase diagram of the hard-core extended boson Hubbard model on the square lattice with both nearest- and next-nearest-neighbor hoppings and repulsions, using Gutzwiller mean-field theory and quantum Monte Carlo simulations. We observe the formation of supersolid states with checkerboard, striped, and quarter-filled crystal structures when the system is doped away from commensurate fillings. In the striped supersolid phase, a strong anisotropy in the superfluid density is obtained from the simulations; however, the transverse component remains finite, indicating a true two-dimensional superflow. We find that upon doping, the striped supersolid transitions directly into the supersolid with quarter-filled crystal structure, via a first-order stripe melting transition.
We present a comprehensive numerical study on the ground state phase diagram of the two-dimensional hard core bosonic extended Hubbard model with nearest (V1)({V}_{1})(V1​) and next nearest neighbor (V2)({V}_{2})(V2​) repulsions. In addition to the quantum solid and superfluid phases, we report the existence of a striped supersolid and three-quarter (quarter)-filled supersolid at commensurate density $\ensuremath{\rho}=0.75$ (0.25) due to the interplay of V1{V}_{1}V1​ and V2{V}_{2}V2​ interactions. The nature of the three-quarter-filled supersolid and the associated quantum solid will be discussed. The observed quantum phase transition between the two supersolids of different symmetries is found to be first order.
We numerically study the ground state phase diagram of the two-dimensional hard-core Bose-Hubbard model with nearest-(V(1)) and next-nearest-neighbour (V(2)) repulsions. In particular, we focus on the quarter-filled phases where one supersolid and two solid phases are observed. Using both canonical and grand canonical quantum Monte Carlo (QMC) methods and a mean-field calculation, we provide evidence for the existence of a commensurate supersolid. Despite the two possible diagonal long-range orderings for the solid phase, only one kind of supersolid phase is found to be energetically stable. The competition between the two solid phases manifests itself as a first-order phase transition around 2V(2) ∼ V(1). The change of order parameters as a function of the chemical potential is also presented.
We study the phase transitions of interacting bosons at zero temperature between superfluid (SF) and supersolid (SS) states. The latter are characterized by simultaneous off-diagonal long-range order and broken translational symmetry. The critical phenomena is described by a long-wavelength effective action, derived on symmetry grounds and verified by explicit calculation. We consider two types of supersolid ordering: checkerboard (X) and collinear (C), which are the simplest cases arising in two dimensions on a square lattice. We find that the SF-CSS transition is in the three-dimensional XY universality class. The SF-XSS transition exhibits nontrivial critical behavior, and appears, within a d=3-\ensuremath{\epsilon} expansion, to be driven generically first order by fluctuations. However, within a one-loop calculation directly in d=2 a strong-coupling fixed point with striking ``non-Bose-liquid'' behavior is found. At special isolated multicritical points of particle-hole symmetry, the system falls into the three-dimensional Ising universality class.
We use two quantum Monte Carlo algorithms to map out the phase diagram of the two-dimensional hardcore boson Hubbard model with near (V1){(V}_{1})(V1​) and next near (V2){(V}_{2})(V2​) neighbor repulsion. At half filling we find three phases: superfluid (SF), checkerboard solid, and striped solid depending on the relative values of V1,V2,{V}_{1}{,V}_{2},V1​,V2​, and the kinetic energy. Doping away from half filling, the checkerboard solid undergoes phase separation: The superfluid and solid phases coexist but not as a single thermodynamic phase. As a function of doping, the transition from the checkerboard solid is therefore first order. In contrast, doping the striped solid away from half filling instead produces a striped supersolid phase: coexistence of density order with superfluidity as a single phase. One surprising result is that the entire line of transitions between the SF and checkerboard solid phases at half filling appears to exhibit dynamical O(3)O(3)O(3) symmetry restoration. The transitions appear to be in the same universality class as the special Heisenberg point even though this symmetry is explicitly broken by the V2{V}_{2}V2​ interaction.
We study the finite temperature properties of the extended Bose-Hubbard model on a cubic lattice. This model exhibits the so-called supersolid state. To start with, we investigate the ground-state phase diagram and find the supersolid state in the region of underdoped (less than the half-filled) density in contrast to the cases of one- and two-dimensional systems where the superfluid state and the solid state show the phase separation. Next, we investigate ordering processes at finite temperatures by quantum Monte Carlo simulations and find successive superfluid and solid phase transitions. There, we find that the two order parameters compete with each other. We establish a finite temperature phase diagram, which contains the superfluid, the solid, the supersolid, and the disordered phases. We develop a mean-field theory to analyze the ordering processes and compare the result with that obtained by simulations and discuss the mechanism of the competition of these two orders. We also study how the supersolid region shrinks as the on-site repulsion becomes strong.