We present a variational wavefunction which explains the behaviour of the supersolid state formed by hard-core bosons on the triangular lattice. The wavefunction is a linear superposition of {\em only and all} configurations minimising the repulsion between the bosons (which it thus implements as a hard constraint). Its properties can be evaluated exactly--in particular, the variational minimisation of the energy yields (i) the surprising and initially controversial spontaneous density deviation from half-filling (ii) a quantitatively accurate estimate of the corresponding density wave (solid) order parameter.
We study hard-core bosons with unfrustrated hopping ($t$) and nearest neighbour repulsion ($U$) on the triangular lattice. At half-filling, the system undergoes a zero temperature ($T$) quantum phase transition from a superfluid phase at small $U$ to a supersolid at $U_c \approx 4.45$ in units of $2t$. This supersolid phase breaks the lattice translation symmetry in a characteristic $\sqrt{3} \times \sqrt{3}$ pattern, and is remarkably stable--indeed, a smooth extrapolation of our results indicates that the supersolid phase persists for arbitrarily large $U/t$.
We study a model of hard-core bosons with frustrated nearest-neighbor hopping ($t$) and repulsion ($V$) on the triangular lattice. We argue for a supersolid ground state in the large repulsion ($V\gg|t|$) limit where a dimer representation applies, by constructing a unitary mapping to the well understood unfrustrated hopping case. This generalized 'Marshall sign rule' allows us to establish the precise nature of the supersolid order by utilizing a recently proposed dimer variational wavefunction, whose correlations can be efficiently calculated using the Grassman approach. By continuity, a sup…
We study the extended Jaynes-Cummings-Hubbard model on triangular cavity lattices and zigzag ladders. By using density-matrix renormalization group methods, we observe various types of solids with different density patterns and find evidence for light supersolids, which exist in extended regions of the phase diagram of the zigzag ladder. Furthermore, we observe strong pair correlations in the supersolid phase due to the interplay between the atoms in the cavities and atom-photon interaction. By means of cluster mean-field simulations and a scaling of the cluster size extending our analysis to …
Prototypical models and their material incarnations are cornerstones to the understanding of quantum magnetism. Here we show theoretically that the recently synthesized magnetic compound Na$_2$BaCo(PO$_4$)$_2$ (NBCP) is a rare, nearly ideal material realization of the $S=1/2$ triangular-lattice antiferromagnet with significant easy-axis spin exchange anisotropy. By combining the automatic parameter searching and tensor-network simulations, we establish a microscopic model description of this material with realistic model parameters, which can not only fit well the experimental thermodynamic da…
We study the effect of impurities in a supersolid phase in comparison to the behavior in the solid and superfluid phases. A supersolid phase has been established for interacting hardcore bosons on a triangular lattice which may be realizable by ultracold atomic gases. Static vacancies are considered in this model which always lower the magnitude of the order parameter in the solid or superfluid phases. In the supersolid phase, however, the impurities directly affect both order parameters simultaneously and thereby reveal an interesting interplay between them. In particular the solid order may …
We study a system of heteronuclear molecules on a triangular lattice and analyze the potential of this system for the experimental realization of a supersolid phase. The ground state phase diagram contains superfluid, solid and supersolid phases. At finite temperatures and strong interactions there is an additional emulsion region, in contrast to similar models with short-range interactions. We derive the maximal critical temperature $T_c$ and the corresponding entropy $S/N = 0.04(1)$ for supersolidity and find feasible experimental conditions for its realization.
We establish the nature of the supersolid phase observed for hardcore bosons on the triangular lattice near half-integer filling factor, and study the phase diagram of the system at finite temperature. We find that the solid order is always of the (2m,-m',-m') with m changing discontinuously from positive to negative values at half-filling, contrary to predictions of other phases, based on an analogy with the properties of Ising spins in transverse magnetic field. At finite temperature we find two intersecting second-order transition lines, one in the 3-state Potts universality class and the o…
We systematically study an extended Bose-Hubbard model with atom hopping and atom-pair hopping in the presence of a three-body constraint on the triangular lattice. By means of large-scale Quantum Monte Carlo simulations, the ground-state phase diagram are studied. We find a continuous transition between the atomic superfluid phase and the pair superfluid when the ratio of the atomic hopping and the atom-pair hopping is adapted. We then focus on the interplay among the atom-pair hopping, the on-site repulsion and the nearest-neighbor repulsion. With on-site repulsion present, we observe first …
Herein, we study the extended Jaynes-Cummings-Hubbard model mainly by the large-scale worm quantum Monte-Carlo method to check whether or not a light supersolid phase exists in various geometries, such as the one-dimensional chain, square lattices and triangular lattices. To achieve our purpose, the ground state phase diagrams are investigated. For the one-dimensional chain and square lattices, a first-order transition occurs between the superfluid phase and the solid phase and therefore there is no stable supersolid phase existing in these geometries. Interestingly, soliton/beats of the local…
Motivated by the realization of Bose-Einstein condensates (BEC) in non-cubic lattices, in this work we study the phases and collective excitation of bosons with nearest neighbor interaction in a triangular lattice at finite temperature, using mean field (MF) and cluster mean field (CMF) theory. We compute the finite temperature phase diagram both for hardcore and softcore bosons, as well analyze the effect of correlation arising due to lattice frustration and interaction systematically using CMF method. A semi-analytic estimate of the transition temperatures between different phases are derive…
Using worm-type quantum Monte Carlo simulations, we investigate bosonic mixtures on the triangular lattice of two species of bosons, which interact via nearest-neighbour intraspecies ($V$) and onsite interspecies ($U$) repulsions. For the case of symmetric hopping amplitude ($t_A/V=t_B/V$) and $U/V=1$, we determine a rich ground-state phase diagram that contains double solid, double superfluid (2SF), 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 trian…
By the photoassociation method, the trimer superfluid phase disappears in the one dimensional state-dependent optical lattice if the ratio of the three-body interaction $W$ to the trimer tunneling $J$is kept at $W/J=12$ [Phys Rev A. {\bf 90}, 033622(2014)]. To search for a trimer superfluid and trimer supersolid, we load the cold atom into two-dimensional lattices, whose coordinate number $z$ and kinetic energy $-zJ$ are respectively larger and lower than those of a one dimensional lattice. Herein, we study the Bose-Hubbard model, which has an additional trimer tunneling term, a three-body int…
Negative signs in many-body wavefunctions play an important role in quantum mechanics. The ground-state wavefunction of double semion model on a two-dimensional hexagonal lattice contains an intrinsic sign which cannot be removed by any local transformation. Here we proposed a generic double semion wavefunction in tensor network representation, and the wavefunction norm is mapped to the partition function of a triangular lattice Ashkin-Teller model with imaginary magnetic fields and imaginary three-spin triangular face interactions. To solve this non-Hermitian model with parity-time (PT) symme…
We investigate the zero temperature quantum phases of a Bose-Bose mixture on a triangular lattice using Bosonic Dynamical Mean Field Theory (BDMFT). We consider the case of total filling one where geometric frustration arises for asymmetric hopping. We map out a rich ground state phase diagram including xy-ferromagnetic, spin-density wave, superfluid, and supersolid phases. In particular, we identify a stripe spin-density wave phase for highly asymmetric hopping. On top of the spin-density wave, we find that the system generically shows weak charge (particle) density wave order.
We study the spin-$1$ model in a triangular lattice in presence of a uniaxial anisotropy field using a Cluster Mean-Field approach (CMF). The interplay between antiferromagnetic exchange, lattice geometry and anisotropy forces Gutzwiller mean-field approaches to fail in a certain region of the phase diagram. There, the CMF yields two supersolid (SS) phases compatible with those present in the spin-$1/2$ XXZ model onto which the spin-$1$ system maps. Between these two SS phases, the three-sublattice order is broken and the results of the CMF depend heavily on the geometry and size of the cluste…
We study the mechanism of loop condensation in the quantum dimer model on the triangular lattice. The triangular lattice quantum dimer model displays a topologically ordered quantum liquid phase in addition to conventionally ordered phases with broken symmetry. In the context of systems with extended loop-like degrees of freedom, the formation of such topological order can be described in terms of loop condensation. Using Monte Carlo calculations with local and directed-loop updates, we compute geometric properties of the transition graph loop distributions of several triangular lattice quantu…
The search for spontaneous pattern formation in equilibrium phases with genuine quantum properties is a leading direction of current research. In this work we investigate the effect of quantum fluctuations - zero point motion and exchange interactions - on the phases of an ensemble of bosonic particles with isotropic hard-soft corona interactions. We perform extensive path-integral Monte Carlo simulations to determine their ground state properties. A rich phase diagram, parametrized by the density of particles and the interaction strength of the soft-corona potential, reveals supersolid stripe…
