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arXiv:1304.4258 · Physical Review B

Competing supersolids of Bose-Bose mixtures in a triangular lattice

Fabien Trousselet, Pamela Rueda‐Fonseca, Arnaud Ralko

Published Feb 5, 2014• 6 citations
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Abstract

We study the ground-state properties of a frustrated two-species mixture of hard-core bosons on a triangular lattice, as a function of tunable amplitudes for tunneling and interactions. By combining three different methods, a self-consistent cluster mean-field, exact diagonalization, and effective theories, we unravel a very rich and complex phase diagram. More specifically, we discuss the existence of three original mixture supersolids: (i) a commensurate with frozen densities and supersolidity in spin degrees of freedom, in a regime of strong interspecies interactions; and (ii) when this interaction is weaker, two mutually competing incommensurate supersolids. Finally, we show how these phases can be stabilized by a quantum fluctuation enhancement of peculiar insulating parent states.

DOI
10.1103/physrevb.89.085104

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We study the ground-state properties of a frustrated two-species mixture of hard-core bosons on a triangular lattice, as a function of tunable amplitudes for tunneling and interactions. By combining three different methods, a self-consistent cluster mean-field, exact diagonalization, and effective theories, we unravel a very rich and complex phase diagram. More specifically, we discuss the existence of three original mixture supersolids: (i) a commensurate with frozen densities and supersolidity in spin degrees of freedom, in a regime of strong interspecies interactions; and (ii) when this interaction is weaker, two mutually competing incommensurate supersolids. Finally, we show how these phases can be stabilized by a quantum fluctuation enhancement of peculiar insulating parent states.
We study ground-state properties in a hard-core Bose-Hubbard model on a layered triangular lattice. Combining cluster mean-field theory with the density matrix renormalization group method, we discuss the effect of the interlayer coupling on the supersolid states realized in a single layered model. By examining the distributions for the particle density and superfluid order parameter, the rich phase diagram of the system is obtained. We find that the supersolid states are widely stabilized at a commensurate filling, in contrast to the case of the single layered model. The nature of the supersolid states is also addressed.
Using worm-type quantum Monte Carlo simulations, we investigate bosonic mixtures on a triangular lattice of two species of bosons, which interact via nearest-neighbor intraspecies (VVV) and on-site interspecies (UUU) repulsions. For the case of symmetric hopping amplitude (tA/V=tB/V{t}_{A}/V={t}_{B}/VtA​/V=tB​/V) and U/V=1U/V=1U/V=1, we determine a rich ground-state phase diagram that contains double-solid, double-superfluid, supersolid (SS), solid-superfluid (solid-SF), and counterflow supersolid (CSS) states. The SS, solid-SF, and CSS states exhibit spontaneous symmetry breaking among the three sublattices of the triangular lattice and between the two species, which leads to a nonzero crystalline density wave order in each species. We, furthermore, show that the CSS and the SS states are present for ${t}_{A}/V\ensuremath{\ne}{t}_{B}/V$, and the latter even survives up to the ${t}_{A}/V\ensuremath{\rightarrow}\ensuremath{\infty}$ or ${t}_{B}/V\ensuremath{\rightarrow}\ensuremath{\infty}$ limit. The effects induced by the variation of U/VU/VU/V and by the imbalance of particle numbers of the two species are also explored.
We study the soft-core extended Bose-Hubbard model in a two-dimensional triangular lattice by using the quantum Monte Carlo methods. The ground-state phase diagram of the system exhibits a very fruitful structure and is much intriguing. Aside from the Mott insulating state, four kinds of solid states with respect to the commensurate filling factors $\ensuremath{\rho}=1∕3,2∕3$ and $\ensuremath{\rho}=1$ are identified. In incommensurate fillings, superfluid, supersolid, as well as phase-separation states are detected. As in the case of the hard-core bosons, a supersolid phase exists in $1∕3<\ensuremath{\rho}<2∕3$ while it is unstable toward the phase separation in $\ensuremath{\rho}<1∕3$. However, this instability is refrained in $2∕3<\ensuremath{\rho}<1$ due to the softening of the bosons, and then a supersolid phase survives.
We investigate the interplay between commensurate lock-in and incommensurate supersolid phases of the hard-core bosons at half-filling with anisotropic nearest-neighbor hopping and repulsive interactions on triangular lattice. We use numerical quantum and variational Monte Carlo as well as analytical Schwinger boson mean-field analysis to establish the ground states and phase diagram. It is shown that, for finite-size systems, there exist a series of jumps between different supersolid phases as the anisotropy parameter is changed. The density ordering wave vectors are locked to commensurate values and jump between adjacent supersolids. In the thermodynamic limit, however, the magnitude of these jumps vanishes leading to a continuous set of novel incommensurate supersolid phases.
We present a scenario where a supersolid is induced in one of the components of a mixture of two species bosonic atoms where there are no long-range interactions. We study a system of normal and hard-core boson mixture with only the former possessing long-range interactions. We consider three cases: the first where the total density is commensurate and the other two where it is incommensurate to the lattice. By suitable choices of the densities of normal and hard-core bosons and the interaction strengths between them, we predict that the charge density wave and the supersolid orders can be induced in the hard-core species as a result of the competing interatomic interactions.
We have systematically studied the hard-core Bose-Hubbard model with correlated hopping on a triangular lattice using the density-matrix renormalization group method. A rich ground-state phase diagram is determined. In this phase diagram there is a supersolid phase and a pair superfluid phase due to the interplay between the ordinary frustrated boson hopping and an unusual correlated hopping. In particular, we find that the quantum phase transition between the supersolid phase and the pair superfluid phase is continuous.