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 be enhanced at the cost of a strong reduction of the superfluidity, which shows that the two order parameters cannot be in a simple superposition. We also observe an unusual impurity pinning effect in the solid ordered phase, which results in two distinct states separated by a first-order transition.
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 …
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 ground state properties of a frustrated two-species mixture of hard-core bosons on a triangular lattice, as a function of tunable amplitudes for tunnelling and interactions. By combining three different methods, a self-consistent cluster mean-field, exact diagonalizations 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 in…
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)…
Hard-core bosons on a triangular lattice with nearest neighbor repulsion are a prototypical example of a system with supersolid behavior on a lattice. We show that in this model the physical origin of the supersolid phase can be understood quantitatively and analytically by constructing quasiparticle excitations of defects that are moving on an ordered background. The location of the solid to supersolid phase transition line is predicted from the effective model for both positive and negative (frustrated) hopping parameters. For positive hopping parameters the calculations agree very accuratel…
Dynamical signatures of Hardcore-Boson Supersolid on the Triangular Lattice
Nanjing University of Science and Technology（南京理工大学）；Beihang University（北京航空航天大学）；RIKEN Center for Emergent Matter Science (CEMS)（理化学研究所凝聚物质科学中心）；Beijing Normal University（北京师范大学）；University of California, Davis（加州大学戴维斯分校）
We numerically demonstrate that a supersolid phase exists in a frustrated hard-core boson system on a triangular lattice over a wide range of interaction strength. In the infinite repulsion (Ising) limit, we establish a mapping to the same problem with unfrustrated hopping, which connects the supersolid to the known results in that case. The weak superfluidity can be destroyed or strongly enhanced by a next nearest neighbor hopping term, which provides valuable information for experimental realization of a supersolid phase on optical lattice.
We have systematically studied the hard-core Bose-Hubbard model with correlated hopping on a triangular lattice using 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.
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 investigate the extended hard-core Bose-Hubbard model on the triangular lattice as a function of spatial anisotropy with respect to both tunneling 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 demonstr…
Dissipationless dynamics of spin supersolid states in a spin-1/2 triangular antiferromagnet with impurities
RIKEN Center for Emergent Matter Science (CEMS)（理化学研究所物质结构理论研究中心）；School of Physics, Beihang University（北京航空航天大学物理学院）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；Peng Huanwu Collaborative Center for Research and Education, Beihang University（北京航空航天大学彭桓武研究中心）；RIKEN Center for Computational Science (R-CCS)（理化学研究所计算科学中心）；RIKEN Center for Quantum Computing (RQC)（理化学研究所量子计算中心）；RIKEN Pioneering Research Institute (PRI)（理化学所先锋研究本部）；Advanced Science Research Center, Japan Atomic Energy Agency（日本原子力研究机构先进科学研究中心）
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.
We study the spin-1/2 XXZ model on the triangular lattice with a nearest neighbor antiferromagnetic Ising coupling $J_z>0$ and unfrustrated ($J_\perp<0$) or frustrated ($J_\perp>0$) kinetic terms in 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 $J_\perp$. For $J_\perp<0$, we find a $\sqrt{3}\times\sqrt{3}$ supersolid for $J_z/|J_\perp| \gtrsim 4.7$, in excellent agreement with quantum Monte Carlo data. For $J_\perp >0$, a distinct $\s…
Using large-scale quantum Monte Carlo simulations we study bosons hopping on a triangular lattice with nearest (V) and next-nearest (V') neighbor repulsive interactions. In the limit where V=0 but V' is large, we find an example of an unusual period-three striped supersolid state that is stable at 1/2-filling. We discuss the relationship of this state to others on the rich ground-state phase diagram, which include a previously-discovered nearest-neighbor supersolid, a uniform superfluid, as well as several Mott insulating phases. We study several superfluid- and supersolid-to-Mott phase transi…
We investigate the interplay between commensurate lock-in and incommensurate supersolid phases of the hardcore 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 wavevectors are locked to commensurate valu…
We study the softcore 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. Except the Mott insulating state, four kinds of solid states with respect to the commensurate filling factors $ρ=1/3,2/3$ and $ρ=1$ are identified. Two of them (CDW II and CDW III) are newly predicted. In incommensurate fillings, superfluid, spuersolid as well as phase separation states are detected . As in the case for the hardcore bosons, a supersolid phase exists in $1/3<ρ<2/3$ whi…
A microscopic design rule for spin supersolids in triangular-lattice magnets
Advanced Science Research Center, Japan Atomic Energy Agency（日本原子力机构先进科学研究中心）；RIKEN Center for Emergent Matter Science (CEMS)（理化学研究所 emergent matter science 中心）
We analyze the hard-core Bose-Hubbard model with both the three-body and nearest neighbor repulsions on the triangular lattice. The phase diagram is achieved by means of the semi-classical approximation and the quantum Monte Carlo simulation. For a system with only the three-body interactions, both the supersolid phase and one third solid disappear while the two thirds solid stably exists. As the thermal behavior of the bosons with nearest neighbor repulsion, the solid and the superfluid undergo the 3-state Potts and the Kosterlitz-Thouless type phase transitions, respectively. In a system wit…
We study the magnetic phase diagram and hysteresis behavior of weakly coupled spin dimers on a triangular lattice using the cluster mean-field method with cluster-size scaling. We find that the magnetization curve has plateaus at 1/3 and 2/3 of the total magnetization, in which local singlet and triplet states form a superlattice pattern. Moreover, if increasing (decreasing) the magnetic field from the 1/3 (2/3) plateau, the Bose-Einstein condensation (BEC) of triplons occurs on the superlattice background, leading to the transition into magnon supersolid phase. We also find that the first-ord…
The majority of magnetic materials possess some degree of magnetic anisotropy, either at the level of a single ion, or in the exchange interactions between different magnetic ions. Where these exchange interactions are also frustrated, the competition between them and anisotropy can stabilize a wide variety of new phases in applied magnetic field. Motivated by the hexagonal delafossite 2H-AgNiO 2, we study the Heisenberg antiferromagnet on a layered triangular lattice with competing first- and second-neighbour interactions and single-ion easy-axis anisotropy. Using a combination of classical M…
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…
The effect of nonmagnetic impurities on the phase diagram of the classical Heisenberg antiferromagnet on a triangular lattice is investigated. We present analytical arguments confirmed by numerical calculations that at zero temperature vacancies stabilize a conical state providing an example of "order by quenched disorder" effect. Competition between thermal fluctuations and the site disorder leads to a complicated H-T phase diagram, which is deduced from the classical Monte Carlo simulations for a representative vacancy concentration. For the XY triangular-lattice antiferromagnet with in-plan…
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…
Several material families show competition between superconductivity and other orders. When such competition is driven by doping, it invariably involves spatial inhomogeneities which can seed competing orders. We study impurity-induced charge order in the attractive Hubbard model, a prototypical model for competition between superconductivity and charge density wave order. We show that a single impurity induces a charge-ordered texture over a length scale set by the energy cost of the competing phase. Our results are consistent with a strong-coupling field theory proposed earlier in which supe…
Dipolar and quadrupolar spin supersolid states in a spin-1 triangular antiferromagnet
RIKEN Center for Emergent Matter Science (CEMS)（理化学研究所物质结构研究センター）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；RIKEN Center for Computational Science (R-CCS)（理化学研究所计算科学研究中心）；RIKEN Center for Quantum Computing (RQC)（理化学研究所量子计算研究中心）；RIKEN Pioneering Research Institute (PRI)（理化学研究所开创性研究所）；Advanced Science Research Center, Japan Atomic Energy Agency（日本原子力机构先进科学研究中心）
Flux Magnetism in a Strongly Interacting Dipolar Lattice Supersolid under Tunable Gauge Fields
Technische Universität Berlin（柏林工业大学）；Consiglio Nazionale delle Ricerche - Istituto Nazionale di Ottica（意大利国家研究委员会光学研究所）；European Laboratory for Nonlinear Spectroscopy (LENS), Università di Firenze（佛罗伦萨大学非线性光谱欧洲实验室）；University of Florence（佛罗伦萨大学）；ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology（巴塞罗那科技研究所光子科学研究所）；ICREA（加泰罗尼亚高级研究院）；Politecnico di Torino（都灵理工大学）
By using the dual vortex method (DVM), we develop systematically a simple and effective scheme to use the vortex degree of freedoms on dual lattices to characterize the symmetry breaking patterns of the boson insulating states in the direct lattices. Then we apply our scheme to study quantum phases and phase transitions in an extended boson Hubbard model slightly away from $ 1/3 $ ($ 2/3 $) filling on frustrated lattices such as triangular and kagome lattice. In a triangular lattice at $ 1/3 $, we find a X-CDW, a stripe CDW phase which was found perviously by a density operator formalism (DOF)…
Super-Solid phase in a U(2) symmetric S = 1 Magnet on the Triangular Lattice
Renmin University of China（中国人民大学）；Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所凝聚态物理国家实验室）；University of Chinese Academy of Sciences（中国科学院大学）
We study the properties of t-t'-V model of hard-core bosons on the triangular lattice that can be realized in optical lattices. By mapping to the spin-1/2 XXZ model in a field, we determine the phase diagram of the t-V model where the supersolid characterized by the ordering pattern (x,x,-2x') ("ferrimagnetic" or SS A) is a ground state for chemical potential μ>3V. By turning on either temperature or t' at half-filling μ=3V, we find a first order transition from SS A to the elusive supersolid characterized by the (x,-x,0) ordering pattern ("antiferromagnetic" or SS C). In addition, we find a l…
We use a quantum lattice gas model to describe essential aspects of the motion of 4He atoms and of 3He impurities in solid 4He. This study suggests that 3He impurities bind to defects and promote 4He atoms to interstitial sites which can turn the bosonic quantum disordered crystal into a metastable supersolid. It is suggested that defects and interstitial atoms are produced during the solid 4He nucleation process where the role of 3He impurities (in addition to the cooling rate) is known to be important even at very small (1 ppm) impurity concentration. It is also proposed that such defects ca…
Angular Modulations in Magnetic Torque Induced by Phase Transitions in the Triangular Supersolid $2H$-AgNiO$_2$
University of Oxford（牛津大学）；Harvard John A. Paulson School of Engineering and Applied Sciences（哈佛大学约翰·A·保尔森工程与应用科学学院）；Florida State University（佛罗里达州立大学）；Max-Planck-Institut fur Festkörperforschung（马克斯·普朗克固体研究所）
We study topography of the spin-polarized bound states of magnetic impurities embedded in triangular lattice of a superconducting host. Such states have been observed experimentally in 2H-NbSe$_{2}$ crystal [G. C. M'enard et al., Nat.Phys. 11, 1013 (2015)] and revealed the oscillating particle-hole asymmetry extending to tens of nanometers. Using the Bogoliubov-de Gennes approach we explore the Yu-Shiba-Rusinov states in presence of spin-orbit interaction. We also study the bound states of double impurities for several relative positions in a triangular lattice.
We report on a phenomenological study of superfluid to Mott insulator transitions of bosons on the triangular lattice, focusing primarily on the interplay between Mott localization and geometrical charge frustration at 1/2-filling. A general dual vortex field theory is developed for arbitrary rational filling factors f, based on the appropriate projective symmetry group. At the simple non-frustrated density f=1/3, we uncover an example of a deconfined quantum critical point very similar to that found on the half-filled square lattice. Turning to f=1/2, the behavior is quite different. Here, we…
The Heisenberg model on a face center cubic (fcc) lattice is a typical three-dimensional frustrated spin system expected to have magnetization plateaus and supersolid phases. There are model compounds $A_2$CoTeO$_6$ ($A$ = Ca, Sr, Pb) for the fcc lattice but with lattice distortions. Motivated by the presence of the compounds, we investigate the ground state of the spin-1/2 antiferromagnetic Heisenberg model on a tetragonally distorted fcc lattice in the magnetic field using a large-size cluster mean-field method for the sake of finding new supersolid phases. We find five supersolid phases in …
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…
We study ground state properties and excitation spectra for hard-core Bosons on square and triangular lattices, at half filling, using series expansion methods. Nearest-neighbor repulsion between the Bosons leads to the development of short-range density order at the antiferromagnetic wavevector, and simultaneously a roton minima in the density excitation spectra. On the square-lattice, the model maps on to the well studied XXZ model, and the roton gap collapses to zero precisely at the Heisenberg symmetry point, leading to the well known spectra for the Heisenberg antiferromagnet. On the tria…
Transverse order and longitudinal fluctuations in a near-Ising spin supersolid
ETH Zürich（苏黎世联邦理工学院）；Université Grenoble Alpes, CEA, IRIG, MEM, MDN（格勒诺布尔阿尔卑斯大学）；J-PARC Center, Japan Atomic Energy Agency（日本原子力机构J-ARC中心）；Dresden High Magnetic Field Laboratory (HLD-EMFL) and Würzburg-Dresden Cluster of Excellence ctd.qmat, Helmholtz-Zentrum Dresden-Rossendorf（德累斯顿强磁场实验室和维尔茨堡-德累斯特卓越集群ctd.qmat，亥姆霍兹德累斯顿-罗斯多夫中心）；PSI Center for Neutron and Muon Sciences（保罗谢尔研究所中子与μ子科学中心）；Neutron Scattering Division, Oak Ridge National Laboratory（橡树岭国家实验室中子散射部）
We introduce a new numerical method for the solution of self-consistent equations in the cluster mean-field theory. The method uses the density matrix renormalization group method to solve the associated cluster problem. We obtain an accurate critical value of the supersolid-superfluid transitions in the hard-core bosonic Hubbard model on a triangular lattice, which is comparable with the recent quantum Monte Carlo results. This algorithm is applicable to more general classes of models with a larger number of degrees of freedom.
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-AgNiO$_2$, 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 pha…
We theoretically investigate the Heisenberg antiferromagnet on a triangular lattice doped with nonmagnetic impurities. Two nontrivial effects resulting from collective impurity behavior are predicted. The first one is related to presence of uncompensated magnetic moments localized near vacancies as revealed by the low-temperature Curie tail in the magnetic susceptibility. These moments exhibit an anomalous growth with the impurity concentration, which we attribute to the clustering mechanism. In an external magnetic field, impurities lead to an even more peculiar phenomenon lifting the classic…
We study effects of nonmagnetic impurities in a spin-1/2 frustrated triangular antiferromagnet with the aim of understanding the observed broadening of $^{13}$C NMR lines in the organic spin liquid material $κ$-(ET)$_2$Cu$_2$(CN)$_3$. For high temperatures down to $J/3$, we calculate local susceptibility near a nonmagnetic impurity and near a grain boundary for the nearest neighbor Heisenberg model in high temperature series expansion. We find that the local susceptibility decays to the uniform one in few lattice spacings, and for a low density of impurities we would not be able to explain the…
We study effects of nonmagnetic impurities in a Spin Bose-Metal (SBM) phase discovered in a two-leg triangular strip spin-1/2 model with ring exchanges (D. N. Shenget al, arXiv:0902.4210). This phase is a quasi-1D descendant of a 2D spin liquid with spinon Fermi sea, and the present study aims at interpolating between the 1D and 2D cases. Different types of defects can be treated as local energy perturbations, which we find are always relevant. As a result, a nonmagnetic impurity generically cuts the system into two decoupled parts. We calculate bond energy and local spin susceptibility near t…
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…
In this paper, we study phase diagram of a system of two-component hard-core bosons with nearest-neighbor (NN) pseudo-spin antiferromagnetic (AF) interactions in a stacked triangular lattice. Hamiltonian of the system contains three parameters one of which is the hopping amplitude $t$ between NN sites, and the other two are the NN pseudo-spin exchange interaction $J$ and the one that measures anisotropy of pseudo-spin interactions. We investigate the system by means of the Monte-Carlo simulations and clarify the low-temperature phase diagram. In particular, we are interested in how the competi…
