Persistent supersolid phase of hard-core bosons on the triangular lattice

Giant magnetocaloric effect in spin supersolid candidate Na2BaCo(PO4)2

Supersolid, an exotic quantum state of matter that consists of particles forming an incompressible solid structure while simultaneously showing superfluidity of zero viscosity1, is one of the long-standing pursuits in fundamental research2,3. Although the initial report of 4He supersolid turned out to be an artefact4, this intriguing quantum matter has inspired enthusiastic investigations into ultracold quantum gases5-8. Nevertheless, the realization of supersolidity in condensed matter remains elusive. Here we find evidence for a quantum magnetic analogue of supersolid-the spin supersolid-in the recently synthesized triangular-lattice antiferromagnet Na2BaCo(PO4)2 (ref. 9). Notably, a giant magnetocaloric effect related to the spin supersolidity is observed in the demagnetization cooling process, manifesting itself as two prominent valley-like regimes, with the lowest temperature attaining below 100 mK. Not only is there an experimentally determined series of critical fields but the demagnetization cooling profile also shows excellent agreement with the theoretical simulations with an easy-axis Heisenberg model. Neutron diffractions also successfully locate the proposed spin supersolid phases by revealing the coexistence of three-sublattice spin solid order and interlayer incommensurability indicative of the spin superfluidity. Thus, our results reveal a strong entropic effect of the spin supersolid phase in a frustrated quantum magnet and open up a viable and promising avenue for applications in sub-kelvin refrigeration, especially in the context of persistent concerns about helium shortages10,11.

Spin supersolid phase in coupled alternating spin chains

We study the ground state phase diagram of a two dimensional mixed-spin system of coupled alternating spin-1 and 1/2 chains with a stripe supersolid phase. Utilizing different analytical and numerical approaches such as mean field approximation, cluster mean field theory and linear spin wave theory, we demonstrate that our system displays a rich ground state phase diagram including novel stripe supersolid, solids with different fillings and super-counterfluid phases, in addition to a stripe solid with half filling, superfluid and Mott insulating phases. In order to find a minimal mixed-spin model for stripe supersolidity, in the second part of the paper we consider two kinds of mixed-spin system of coupled alternating spin-1 and 1/2 chains with (i) anisotropic nearest neighbor interactions, (ii) anisotropic hoppings and study their ground state phase diagrams. We demonstrate that, for the systems with uniform hoppings, the repulsive intra-chains interactions are necessary for stripe supersolidity. In this case the minimal two dimensional mixed-spin model is a system of spin-1 and spin-1/2 XXZ chains, interacting via Ising Hamiltonian. In the case of anisotropic hoppings, a system of coupled Ising chains is the minimal model.

Sign-Problem-Free Monte Carlo Simulation of Certain Frustrated Quantum Magnets

We introduce a quantum Monte Carlo (QMC) method for efficient sign-problem-free simulations of a broad class of frustrated S=1/2 antiferromagnets using the basis of spin eigenstates of clusters to avoid the severe sign problem faced by other QMC methods. We demonstrate the utility of the method in several cases with competing exchange interactions and flag important limitations as well as possible extensions of the method.

Quantum Domain Walls Induce Incommensurate Supersolid Phase on the Anisotropic Triangular Lattice

We investigate the extended hard-core Bose-Hubbard model on the triangular lattice as a function of spatial anisotropy with respect to both hopping and nearest-neighbor interaction strength. At half-filling the system can be tuned from decoupled one-dimensional chains to a two-dimensional solid phase with alternating density order by adjusting the anisotropic coupling. At intermediate anisotropy, however, frustration effects dominate and an incommensurate supersolid phase emerges, which is characterized by incommensurate density order as well as an anisotropic superfluid density. We demonstrate that this intermediate phase results from the proliferation of topological defects in the form of quantum bosonic domain walls. Accordingly, the structure factor has peaks at wave vectors, which are linearly related to the number of domain walls in a finite system in agreement with extensive quantum Monte Carlo simulations. We discuss possible connections with the supersolid behavior in the high-temperature superconducting striped phase.

Melting of Three-Sublattice Order in Easy-Axis Antiferromagnets on Triangular and Kagome Lattices

When the constituent spins have an energetic preference to lie along an easy axis, triangular and kagome lattice antiferromagnets often develop long-range order that distinguishes the three sublattices of the underlying triangular Bravais lattice. In zero magnetic field, this three-sublattice order melts either in a two-step manner, i.e., via an intermediate phase with power-law three-sublattice order controlled by a temperature-dependent exponent η(T)∈(1/9,1/4), or via a transition in the three-state Potts universality class. Here, I predict that the uniform susceptibility to a small easy-axis field B diverges as χ(B)∼|B|^{-[(4-18η)/(4-9η)]} in a large part of the intermediate power-law ordered phase [corresponding to η(T)∈(1/9,2/9)], providing an easy-to-measure thermodynamic signature of two-step melting. I also show that these two melting scenarios can be generically connected via an intervening multicritical point and obtain numerical estimates of multicritical exponents.

Phase diagram of the triangular extended Hubbard model

We study the extended Hubbard model on the triangular lattice as a function of filling and interaction strength. The complex interplay of kinetic frustration and strong interactions on the triangular lattice leads to exotic phases where long-range charge order, antiferromagnetic order, and metallic conductivity can coexist. Variational Monte Carlo simulations show that three kinds of ordered metallic states are stable as a function of nearest neighbor interaction and filling. The coexistence of conductivity and order is explained by a separation into two functional classes of particles: part of them contributes to the stable order, while the other part forms a partially filled band on the remaining substructure. The relation to charge ordering in charge transfer salts is discussed.

Combined topological and Landau order from strong correlations in Chern bands

We present a class of states with both topological and conventional Landau order that arise out of strongly interacting spinless fermions in fractionally filled and topologically nontrivial bands with Chern number C=±1. These quantum states show the features of fractional Chern insulators, such as fractional Hall conductivity and interchange of ground-state levels upon insertion of a magnetic flux. In addition, they exhibit charge order and a related additional trivial ground-state degeneracy. Band mixing and geometric frustration of the charge pattern place these lattice states markedly beyond a single-band description.

Quantum phase diagram of the triangular-lattice XXZ model in a magnetic field

The triangular lattice of S=1/2 spins with XXZ anisotropy is a ubiquitous model for various frustrated systems in different contexts. We determine the quantum phase diagram of the model in the plane of the anisotropy parameter and the magnetic field by means of a large-size cluster mean-field method with a scaling scheme. We find that quantum fluctuations break up the nontrivial continuous degeneracy into two first-order phase transitions. In between the two transition boundaries, the degeneracy-lifting results in the emergence of a new coplanar phase not predicted in the classical counterpart of the model. We suggest that the quantum phase transition to the nonclassical coplanar state can be observed in triangular-lattice antiferromagnets with large easy-plane anisotropy or in the corresponding optical-lattice systems.

Engineering novel optical lattices

Optical lattices have developed into a widely used and highly recognized tool to study many-body quantum physics with special relevance for solid state type systems. One of the most prominent reasons for this success is the high degree of tunability in the experimental setups. While at the beginning quasi-static, cubic geometries were mainly explored, the focus of the field has now shifted toward new lattice topologies and the dynamical control of lattice structures. In this review we intend to give an overview of the progress recently achieved in this field on the experimental side. In addition, we discuss theoretical proposals exploiting specifically these novel lattice geometries.

Columnar antiferromagnetic order and spin supersolid phase on the extended Shastry-Sutherland lattice

We use large scale quantum Monte Carlo simulations to study an extended version of the canonical Shastry-Sutherland model--including additional interactions and exchange anisotropy--over a wide range of interaction parameters and an applied magnetic field. The model is appropriate for describing the low energy properties of some members of the rare earth tetraborides. Working in the limit of large Ising-like exchange anisotropy, we demonstrate the stabilization of columnar antiferromagnetic order in the ground state at zero field and an extended magnetization plateau at 1/2 the saturation magnetization in the presence of an applied longitudinal magnetic field--qualitatively similar to experimentally observed low-temperature phases in ErB(4). Our results show that for an optimal range of exchange parameters, a spin supersolid ground state is realized over a finite range of an applied field between the columnar antiferromagnetic phase and the magnetization plateau. The full momentum dependence of the longitudinal and transverse components of the static structure factor is calculated in the spin supersolid phase to demonstrate the simultaneous existence of diagonal and off-diagonal long-range order. Our results provide crucial guidance in designing further experiments to search for the interesting spin supersolid phase in ErB(4).

Unbinding of giant vortices in states of competing order

We consider a two-dimensional system with two order parameters, one with O(2) symmetry and one with O(M), near a point in parameter space where they couple to become a single O(2+M) order. While the O(2) sector supports vortex excitations, these vortices must somehow disappear as the high symmetry point is approached. We develop a variational argument which shows that the size of the vortex cores diverges as 1/√Δ and the Berezinskii-Kosterlitz-Thouless transition temperature of the O(2) order vanishes as 1/ln(1/Δ), where Δ denotes the distance from the high-symmetry point. Our physical picture is confirmed by a renormalization group analysis which gives further logarithmic corrections, and demonstrates full symmetry restoration within the cores.

Exotic gapless mott insulators of bosons on multileg ladders

We present evidence for an exotic gapless insulating phase of hard-core bosons on multileg ladders with a density commensurate with the number of legs. In particular, we study in detail a model of bosons moving with direct hopping and frustrating ring exchange on a 3-leg ladder at ν=1/3 filling. For sufficiently large ring exchange, the system is insulating along the ladder but has two gapless modes and power law transverse density correlations at incommensurate wave vectors. We propose a determinantal wave function for this phase and find excellent comparison between variational Monte Carlo and density matrix renormalization group calculations on the model Hamiltonian, thus providing strong evidence for the existence of this exotic phase. Finally, we discuss extensions of our results to other N-leg systems and to N-layer two-dimensional structures.

Supersolid phases in a realistic three-dimensional spin model

Supersolid phases, in which a superfluid component coexists with conventional crystalline long range order, have recently attracted a great deal of attention in the context of both solid helium and quantum spin systems. Motivated by recent experiments on 2H-AgNiO2, we study the magnetic phase diagram of a realistic three-dimensional spin model with single-ion anisotropy and competing interactions on a layered triangular lattice, using classical Monte Carlo simulation techniques, complemented by spin-wave calculations. For parameters relevant to experiment, we find a cascade of different phases as a function of magnetic field, including three phases which are supersolids in the sense of Liu and Fisher. One of these phases is continuously connected with the collinear ground state of AgNiO2, and is accessible at relatively low values of magnetic field. The nature of this transition, and its possible observation, are discussed.

Quarter-filled supersolid and solid phases in the extended Bose-Hubbard model

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.

Supersolid phase with cold polar molecules on a triangular lattice

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 with 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.

Quantum phases of cold polar molecules in 2D optical lattices

We study the quantum phases of hard-core bosonic polar molecules on a two-dimensional square lattice interacting via repulsive dipole-dipole interactions. In the limit of small tunneling, we find evidence for a devil's staircase, where Mott solids appear at rational fillings of the lattice. For finite tunneling, we establish the existence of extended regions of parameters where the ground state is a supersolid, obtained by doping the solids either with particles or vacancies. We discuss the effects of finite temperature and finite-size confining potentials as relevant to experiments.

Quantum melting of valence-bond crystal insulators and novel supersolid phase at commensurate density

Bosonic and fermionic Hubbard models on the checkerboard lattice are studied numerically for infinite on-site repulsion. At particle density n=1/4 and strong nearest-neighbor repulsion, insulating Valence-Bond crystals (VBC) of resonating particle pairs are stabilized. Their melting into superfluid or metallic phases under increasing hopping is investigated at T=0 K. We identify a novel and unconventional commensurate VBC supersolid region, precursor to the melting of the bosonic crystal. Hardcore bosons (spins) are compared to fermions (electrons), as well as positive to negative (frustrating) hoppings.

Supersolidity in the triangular lattice spin-1/2 XXZ model: a variational perspective

We study the spin-1/2 XXZ model on the triangular lattice with a nearest neighbor antiferromagnetic Ising coupling J(z) > 0 and unfrustrated (J(perpendicular) < 0) or frustrated (J(perpendicular) >0) kinetic terms in a zero magnetic field. Incorporating long-range Jastrow correlations over a mean-field spin state, we obtain the variational phase diagram of this model on large lattices for arbitrary J(z) and either sign of J(perpendicular). For J(perpendicular) < 0, we find a square root(3) x square root(3) supersolid for J(z)/J(perpendicular)| approximately > 4.7, in excellent agreement with quantum Monte Carlo data. For J(perpendicular) > 0, a distinct square root(3) x square root(3) supersolid is found to emerge for J(z)/J(perpendicular) > or = 1. Both supersolids exhibit a spontaneous density deviation from half-filling. At J(z)/J(perpendicular) = infinity, the crystalline order parameters of these two supersolids are nearly identical, consistent with exact results.

Supersolid phases of a doped valence-bond quantum antiferromagnet: evidence for a coexisting superconducting order parameter

Motivated by numerical evidence of the valence-bond ground state of the two-dimensional Heisenberg pyrochlore lattice, we argue using a t-J model that it evolves under doping into novel phases characterized by superconductivity coexisting with the underlying valence-bond solid order. A fermionic mean-field theory supplemented by exact diagonalization results provide strong arguments in favor of the stability of such supersolid phases. The resemblance with modulated superconducting patterns in high-Tc cuprates as well as possible relevance to frustrated noncuprate superconductors such as spinels and pyrochlores is discussed.

Cascade of magnetic-field-induced quantum phase transitions in a spin-1/2 triangular-lattice antiferromagnet

We report magnetocaloric and magnetic-torque evidence that in Cs2CuBr4--a geometrically frustrated Heisenberg S=1/2 triangular-lattice antiferromagnet--quantum fluctuations stabilize a series of spin states at simple increasing fractions of the saturation magnetization Ms. Only the first of these states--at M=1/3Ms--has been theoretically predicted. We discuss how the higher fraction quantum states might arise and propose model spin arrangements. We argue that the first-order nature of the transitions into those states is due to strong lowering of the energies by quantum fluctuations, with implications for the general character of quantum phase transitions in geometrically frustrated systems.

Monte Carlo study of degenerate ground states and residual entropy in a frustrated honeycomb lattice Ising model

We study a classical fully frustrated honeycomb lattice Ising model using Markov-chain Monte Carlo methods and exact calculations. The Hamiltonian realizes a degenerate ground-state manifold of equal-energy states, where each hexagonal plaquette of the lattice has one and only one unsatisfied bond, with an extensive residual entropy that grows as the number of spins N. Traditional single-spin-flip Monte Carlo methods fail to sample all possible spin configurations in this ground state efficiently, due to their separation by large energy barriers. We develop a nonlocal "chain-flip" algorithm that solves this problem, and demonstrate its effectiveness on the Ising Hamiltonian with and without perturbative interactions. The two perturbations considered are a slightly weakened bond and an external magnetic field h. For some cases, the chain-flip move is necessary for the simulation to find an ordered ground state. In the case of the magnetic field, two magnetized ground states with nonextensive entropy are found, and two special values of h exist where the residual entropy again becomes extensive, scaling proportionally to N ln phi, where phi is the golden ratio.

Extended supersolid phase of frustrated hard-core bosons on a triangular lattice

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>>|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 wave function, whose correlations can be efficiently calculated using the Grassmann approach. By continuity, a supersolid is predicted over the wide parameter range, V>-2t>0. This also establishes a simple phase diagram for the triangular lattice spin 1/2 XXZ antiferromagnet.

Dimensional tuning of electronic states under strong and frustrated interactions

We study a model of strongly interacting spinless fermions on an anisotropic triangular lattice. At half-filling and the limit of strong repulsive nearest-neighbor interactions, the fermions align in stripes and form an insulating state. When a particle is doped, it either follows a one-dimensional free motion along the stripes or fractionalizes perpendicular to the stripes. The two propagations yield a dimensional tuning of the electronic state. We study the stability of this phase and derive an effective model to describe the low-energy excitations. Spectral functions are presented which can be used to experimentally detect signatures of the charge excitations.

Variational wave-function study of the triangular lattice supersolid

We present a variational wave function which explains the behavior of the supersolid state formed by hard-core bosons on the triangular lattice. The wave function is a linear superposition of only and all configurations minimizing the repulsion between the bosons (which it thus implements as a hard constraint). Its properties can be evaluated exactly--in particular, the variational minimization 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.

Supersolid bose-fermi mixtures in optical lattices

We study a mixture of strongly interacting bosons and spinless fermions with on-site repulsion in a three-dimensional optical lattice. For this purpose we develop and apply a generalized dynamical mean-field theory, which is exact in infinite dimensions and reliably describes the full range from weak to strong coupling. We restrict ourselves to half filling. For weak Bose-Fermi repulsion a supersolid forms, in which bosonic superfluidity coexists with charge-density wave order. For stronger interspecies repulsion the bosons become localized while the charge-density wave order persists. The system is unstable against phase separation for weak repulsion among the bosons.

Supersolid phase induced by correlated hopping in spin-1/2 frustrated quantum magnets

We show that correlated hopping of triplets, which is often the dominant source of kinetic energy in dimer-based frustrated quantum magnets, produces a remarkably strong tendency to form supersolid phases in a magnetic field. These phases are characterized by simultaneous modulation and ordering of the longitudinal and transverse magnetization, respectively. Using quantum Monte Carlo and a semiclassical approach for an effective hard-core boson model with nearest-neighbor repulsion on a square lattice, we prove, in particular, that a supersolid phase can exist even if the repulsion is not strong enough to stabilize an insulating phase at half-filling. Experimental implications for frustrated quantum antiferromagnets in a magnetic field at zero and finite temperature are discussed.

Spin supersolid in an anisotropic spin-one Heisenberg chain

We consider an S=1 Heisenberg chain with strong exchange (Delta=J(z)/J(perpendicular)) and single-ion uniaxial anisotropy (D) in a magnetic field (B) along the symmetry axis. The low-energy spectrum is described by an effective S=1/2 XXZ model that acts on two different low-energy sectors for a finite range of fields. The vacuum of each sector exhibits Ising-like antiferromagnetic ordering coexisting with the finite spin stiffness obtained from the exact solution of the XXZ model. In this way, we demonstrate the existence of a spin supersolid phase. We also compute the full Delta-B quantum phase diagram using a quantum Monte Carlo method.

Crystalline phase of strongly interacting fermi mixtures

We show that the system of weakly bound molecules of heavy and light fermionic atoms is characterized by a long-range intermolecular repulsion and can undergo a gas-crystal quantum transition if the mass ratio exceeds a critical value. For the critical mass ratio above 100 obtained in our calculations, this crystalline order can be observed as a superlattice in an optical lattice for heavy atoms with a small filling factor. We also find that this novel system is sufficiently stable with respect to molecular relaxation into deep bound states and to the process of trimer formation.

Fermionic stabilization and density-wave ground state of a polar condensate

We examine the stability of a trapped dipolar condensate mixed with a single-component fermion gas at T=0. Whereas pure dipolar condensates with a small s-wave interaction are unstable even at small dipole-dipole interaction strength, we find that the admixture of fermions can significantly stabilize them, depending on the strength of the boson-fermion interaction. Within the stable regime we find a region where a ground state is characterized by a density wave along the soft trap direction.

Quantum and thermal transitions out of the supersolid phase of a 2D quantum antiferromagnet

We investigate the thermodynamic properties of a field-induced supersolid phase in a 2D quantum antiferromagnet model. Using quantum Monte Carlo simulations, a very rich phase diagram is mapped out in the temperature-magnetic-field plane, with an extended supersolid region where a diagonal (solid) order coexists with a finite XY spin stiffness (superfluid). The various quantum and thermal transitions out of the supersolid state are characterized. Experimental consequences in the context of field-induced magnetization plateau materials are briefly discussed.

Novel quantum phases of dipolar bose gases in optical lattices

We investigate the quantum phases of polarized dipolar bosons loaded into a two-dimensional square and three-dimensional cubic optical lattices. We show that the long-range and anisotropic nature of the dipole-dipole interaction induces a rich variety of quantum phases, including the supersolid and striped supersolid phases in two-dimensional lattices, and the layered supersolid phase in three-dimensional lattices.

Field-induced supersolid phase in spin-one Heisenberg models

We use numerical methods to demonstrate that the phase diagram of S=1 Heisenberg models with uniaxial anisotropy contains an extended supersolid phase. We show that this Hamiltonian is a particular case of a more general and ubiquitous model that describes the low-energy spectrum of some isotropic and frustrated spin-dimer systems. This result is crucial for finding a spin supersolid state in real magnets.

Modification of directed-loop algorithm for continuous space simulation of bosonic systems

We modify the directed-loop algorithm (DLA) to solve the problem that typically arises from large on-site interaction. The large on-site interaction is inevitable when one tries to simulate a Bose gas system in continuum by discretizing the space with small lattice spacings. While the efficiency of a straightforward application of DLA decreases as the mesh becomes finer, the performance of the new method does not depend on it except for the trivial factor due to the increase in the number of lattice points.

Hard-core bosons on the kagome lattice: valence-bond solids and their quantum melting

Using large scale quantum Monte Carlo simulations and dual vortex theory, we analyze the ground state phase diagram of hard-core bosons on the kagome lattice with nearest-neighbor repulsion. In contrast with the case of a triangular lattice, no supersolid emerges for strong interactions. While a uniform superfluid prevails at half filling, two novel solid phases emerge at densities rho=1/3 and rho=2/3. These solids exhibit an only partial ordering of the bosonic density, allowing for local resonances on a subset of hexagons of the kagome lattice. We provide evidence for a weakly first-order phase transition at the quantum melting point between these solid phases and the superfluid.

Supersolid phase in spin dimer XXZ systems under a magnetic field

Using the quantum Monte Carlo method, we study, under external magnetic fields, the ground state phase diagram of the two-dimensional spin S=1/2 dimer model with an anisotropic intraplane antiferromagnetic coupling. With the anisotropy 4 greater/approximately Delta greater/approximately 3, a supersolid phase characterized by a nonuniform Bose condensate density that breaks translational symmetry is found. The rich phase diagram also contains a checkerboard solid, an antiferromagnet in the z axis, and a superfluid phase formed by S(z)= +1 spin triplets which has a finite staggered magnetization in the in-plane direction. As we show, the model can be realized as a consequence of including the next nearest neighbor coupling among dimers and our results suggest that spin dimer systems may be an ideal model system to study the supersolid phase.

Spin nematics and magnetization plateau transition in anisotropic kagome magnets

We study S=1 kagome antiferromagnets with an isotropic Heisenberg exchange J and strong easy-axis single-ion anisotropy D. For D>>J, the low-energy physics can be described by an effective S=1/2 XXZ model with antiferromagnetic Jz approximately J and ferromagnetic J perpendicular approximately J2/D. Exploiting this connection, we argue that nontrivial ordering into a "spin-nematic" occurs whenever D dominates over J, and discuss its experimental signatures. We also study a magnetic field induced transition to a magnetization plateau state at magnetization 1/3 which breaks lattice translation symmetry due to ordering of the Sz and occupies a lobe in the B/Jz-Jz/J perpendicular phase diagram.

Excitations in correlated superfluids near a continuous transition into a supersolid

We study a superfluid on a lattice close to a transition into a supersolid phase and show that a uniform superflow in the homogeneous superfluid can drive the roton gap to zero. This leads to supersolid order around the vortex core in the superfluid, with the size of the modulated pattern around the core being related to the bulk superfluid density and roton gap. We also study the electronic tunneling density of states for a uniform superconductor near a phase transition into a supersolid phase. Implications are considered for strongly correlated superconductors.

Supersolid phase of hard-core bosons on a triangular lattice

We study properties of the supersolid phase observed for hard-core bosons on the triangular lattice near half-integer filling factor, and 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, in contrast with phases observed for Ising spins in a transverse magnetic field. At finite temperature we find two intersecting second-order transition lines: one in the 3-state Potts universality class and the other of the Kosterlitz-Thouless type.

Supersolid order from disorder: hard-core bosons on the triangular lattice

We study the interplay of Mott localization, geometric frustration, and superfluidity for hard-core bosons with nearest-neighbor repulsion on the triangular lattice. For this model at half filling, we demonstrate that superfluidity survives for arbitrarily large repulsion, and that diagonal solid order emerges in the strongly correlated regime from an order-by-disorder mechanism. This is thus an unusual example of a stable supersolid phase of hard-core lattice bosons at a commensurate filling.