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arXiv:1902.10091 · Physical review. B./Physical review. B

Mixed-order transition and tricritical point associated with checkerboard supersolidity in the two-dimensional t2−V1 model

Amrita Ghosh, Satyaki Kar, Sudhakar Yarlagadda

Published Jan 28, 2020• 2 citations
arXivHTMLPDF

Abstract

We use quantum Monte Carlo method employing stochastic-series-expansion technique to study the ground state properties of the ${t}_{2}\ensuremath{-}{V}_{1}$ model of hard-core bosons on a square lattice. We find that, away from half fillings, the minimal combination of nearest-neighbor repulsion ${V}_{1}$ and next-nearest-neighbor hopping ${t}_{2}$ may give rise to checkerboard supersolidity. The nature of the quantum phase transition, where the superfluid changes to a checkerboard supersolid, depends on the relative strength of ${V}_{1}/{t}_{2}$ and the average site occupancy. Interestingly, at the half filling, the model displays the extreme Thouless effect. As the filling is varied away from half filling, the model exhibits initially a mixed-order transition, next a tricritical point, and finally a second-order transition.

DOI
10.1103/physrevb.101.035147

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We use quantum Monte Carlo method employing stochastic-series-expansion technique to study the ground state properties of the t2\ensuremath−V1{t}_{2}\ensuremath{-}{V}_{1}t2​\ensuremath−V1​ model of hard-core bosons on a square lattice. We find that, away from half fillings, the minimal combination of nearest-neighbor repulsion V1{V}_{1}V1​ and next-nearest-neighbor hopping t2{t}_{2}t2​ may give rise to checkerboard supersolidity. The nature of the quantum phase transition, where the superfluid changes to a checkerboard supersolid, depends on the relative strength of V1/t2{V}_{1}/{t}_{2}V1​/t2​ and the average site occupancy. Interestingly, at the half filling, the model displays the extreme Thouless effect. As the filling is varied away from half filling, the model exhibits initially a mixed-order transition, next a tricritical point, and finally a second-order transition.
Using extensive quantum Monte Carlo simulations, we study a minimum model of interacting hard-core bosons on a square lattice with hoppings of different lengths, featuring nearest-neighbor hopping (t1{t}_{1}t1​), anisotropic next-nearest-neighbor hopping (${t}_{2}^{\ensuremath{'}}$), and nearest-neighbor repulsion (V1{V}_{1}V1​). The paradigmatic checkerboard supersolid (CSS) phase emerges as ${t}_{2}^{\ensuremath{'}}$ turns on, with the solid order being characterized by ordering vector $\mathbf{q}=(\ensuremath{\pi},\ensuremath{\pi})$. This serves as a rare example of the CSS phase which is obtained by doping a checkerboard solid and harbors spontaneously broken gauge and translational symmetries. A first-order supersolid-to-superfluid transition is observed. Moreover, we find a solid order-by-thermal disorder behavior together with a superfluid-to-solid transition upon increasing temperature. The underlying picture of the order-by-disorder phenomenon is figured out within the framework of the entropy effect.
The ground state of hard-core bosons on the square lattice with nearest and next-nearest-neighbor repulsion is studied by quantum Monte Carlo simulations. A supersolid phase with vacancy condensation and ``star'' diagonal ordering is found for filling $\ensuremath{\rho}<0.25$. At filling $\ensuremath{\rho}>0.25$, a supersolid phase exists between the star and the stripe crystal at $\ensuremath{\rho}=0.5$. No supersolid phase occurs for $\ensuremath{\rho}>0.25$ if the ground state at half-filling is either a checkerboard crystal or a superfluid. No commensurate supersolid phase is observed.
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.
Understanding the microscopic mechanism of coexisting long-range orders (such as lattice supersolidity) in strongly correlated systems is a subject of immense interest. We study the possible manifestations of long-range orders, including lattice-supersolid phases with differently broken symmetry, in a two-dimensional square lattice system of hard-core bosons (HCBs) coupled to archetypal cooperative/coherent normal-mode distortions such as those in perovskites. At strong HCB-phonon coupling, using a duality transformation to map the strong-coupling problem to a weak-coupling one, we obtain an effective Hamiltonian involving nearest-neighbor, next-nearest-neighbor, and next-to-next-nearest-neighbor hoppings and repulsions. Using stochastic series expansion quantum Monte Carlo, we construct the phase diagram of the system. As coupling strength is increased, we find that the system undergoes a first-order quantum phase transition from a superfluid to a checkerboard solid at half-filling and from a superfluid to a diagonal striped solid [with crystalline ordering wave vector $\stackrel{P\vec}{Q}=(2\ensuremath{\pi}/3,2\ensuremath{\pi}/3)$ or $(2\ensuremath{\pi}/3,4\ensuremath{\pi}/3)]$ at one-third filling without showing any evidence of supersolidity. On tuning the system away from these commensurate fillings, checkerboard supersolid is generated near half-filling whereas a rare diagonal striped supersolid is realized near one-third filling. Interestingly, there is an asymmetry in the extent of supersolidity about one-third filling. Within our framework, we also provide an explanation for the observed checkerboard and stripe formations in ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{NiO}}_{4}$ at x=1/2x=1/2x=1/2 and x=1/3x=1/3x=1/3.
We study the ground state properties of the extended hard-core Bose–Hubbard model in a two-dimensional Shastry–Sutherland lattice by quantum Monte Carlo simulations. The effects of the geometric frustration, described by the ratio t ′ / t between hopping integrals along the nearest-neighbor links and the diagonal links, are studied. We find that for small values of frustration amplitude t ′ / t , a checkerboard solid state emerges at ρ= 1/2; for large values of frustration amplitude t ′ / t , a solid state emerges at ρ= 1/2 with one boson per dimer (dimers on diagonal links); for intermediate values of frustration amplitude t ′ / t , besides the ρ= 1/2 solid state, the ρ= 1/3,2/3 solid states emerge. No stable supersolid state is observed in our calculations. At half filling, we find solid-superfluid-solid phase transition as the frustration amplitude t ′ / t is increased.