Journal of the Physical Society of Japan

Quantum Monte Carlo Study of Hard-Core Bosons on the Shastry–Sutherland Lattice

Jing-Yu Gan

Published Mar 10, 2011• 2 citations

Abstract

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.

DOI: 10.1143/jpsj.80.034604

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Journal of the Physical Society of Japan

Quantum Monte Carlo Study of Hard-Core Bosons on the Shastry–Sutherland Lattice

Jing-Yu Gan

Published Mar 10, 2011• 2 citations

Publisher

Abstract

DOI: 10.1143/jpsj.80.034604

Related papers

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Physical Review AFeb 14, 20178 citations

t

, are studied. We find that for small values of anisotropy ratio ${t}^{\ensuremath{'}}/t$, a solid state emerges at $\ensuremath{\rho}=1/2$ and a supersolid is unstable toward phase separation; for large values of anisotropy ratio ${t}^{\ensuremath{'}}/t$, solid states emerge at $\ensuremath{\rho}=1/3$, 2/3, and a supersolid phase is stable in the region $\ensuremath{\rho}<2/3$; for intermediate values of anisotropy ratio ${t}^{\ensuremath{'}}/t$, three kinds of solid states at fillings $\ensuremath{\rho}=1/3$, 1/2, and $\ensuremath{\rho}=2/3$ coexist and no stable supersolid phase is observed. At half filling, we find that with increasing frustration ${t}^{\ensuremath{'}}/t$, the $\ensuremath{\rho}=1/2$ solid transitions indirectly into the supersolid via an intervening superfluid.

y

direction on the two-dimensional

xy

plane. To perform efficient simulations of long-range interacting systems, we use the worm algorithm with an

O(N)

Monte Carlo method. We obtain the ground-state phase diagram that includes a superfluid phase and a striped solid phase at half-filling as two main phases. In addition to these two main phases, we find a small region where there are multiple plateaus in the particle density for small hopping amplitudes. In this region, the number of plateaus increases as the system size increases. This indicates the appearance of numerous competing ground states due to frustrated interactions. In our simulations, we find no evidence of a supersolid phase.

z=0.15

, which is smaller than results obtained on smaller lattices. This indicates that

z

approaches zero in the thermodynamic limit, and thus the transition is also first order even at the Heisenberg point.

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 (

{t}_{1}

), anisotropic next-nearest-neighbor hopping (${t}_{2}^{\ensuremath{'}}$), and nearest-neighbor repulsion (

{V}_{1}

). 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.