Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1206.2694 · Physical Review B

Quantum phases of hardcore bosons with long-range interactions on a square lattice

Daisuke Yamamoto, Akiko Masaki, Ippei Danshita

Published Aug 27, 2012• 66 citations
arXivHTMLPDF

Abstract

We study the ground-state phase diagrams of hardcore bosons with long-range interactions on a square lattice using the linear spin-wave theory and a cluster mean-field method. Specifically, we consider the two types of long-range interaction: One consists only of the nearest- and next-nearest-neighbor interactions, and the other is the dipole-dipole interaction that decays with the interparticle distance $r$ as $\ensuremath{\sim}$${r}^{\ensuremath{-}3}$. It is known from previous analyses by quantum Monte Carlo methods that a checkerboard supersolid (CSS) is absent in the ground-state phase diagram of the former case while it is present in the latter. In the former, we find that quantum fluctuations around mean-field solutions are enhanced by the direct competition between the checkerboard and striped solid orders and that they destabilize the CSS phase. On the other hand, the emergence of the CSS phase in the latter case can be attributed to the absence of such a competition with other solid orders. We also show that the cluster mean-field method allows for the determination of phase boundaries in a precise quantitative manner when scaling with respect to the cluster size is taken into account. It is found that the phase transition between the superfluid and the solid (or CSS) is of the first order in the vicinity of the particle-hole symmetric line.

DOI
10.1103/physrevb.86.054516

Related papers

Quantum phases of hardcore bosons with repulsive dipolar density-density interactions on two-dimensional lattices

Jan Alexander Koziol, Giovanna Morigi, Kai Phillip Schmidt

We analyse the ground-state quantum phase diagram of hardcore Bosons interacting with repulsive dipolar potentials. The bosons dynamics is described by the extended-Bose-Hubbard Hamiltonian on a two-dimensional lattice. The ground state results from the interplay between the lattice geometry and the long-range interactions, which we account for by means of a classical spin mean-field approach limited by the size of the considered unit cells. This extended classical spin mean-field theory accounts for the long-range density-density interaction without truncation. We consider three different lattice geometries: square, honeycomb, and triangular. In the limit of zero hopping the ground state is always a devil’s staircase of solid (gapped) phases. Such crystalline phases with broken translational symmetry are robust with respect to finite hopping amplitudes. At intermediate hopping amplitudes, these gapped phases melt, giving rise to various lattice supersolid phases, which can have exotic features with multiple sublattice densities. At sufficiently large hoppings the ground state is a superfluid. The stability of phases predicted by our approach is gauged by comparison to the known quantum phase diagrams of the Bose-Hubbard model with nearest-neighbour interactions as well as quantum Monte Carlo simulations for the dipolar case on the square and triangular lattice. Our results are of immediate relevance for experimental realisations of self-organised crystalline ordering patterns in analogue quantum simulators, e.g., with ultracold dipolar atoms in an optical lattice.

arXiv:2311.10632•SciPost Physics•Oct 10, 2024•8 citations

Study of long-range orders of hard-core bosons coupled to cooperative normal modes in two-dimensional lattices

Amrita Ghosh, Sreenija Yarlagadda

Understanding the microscopic mechanism of coexisting long-range orders (such as lattice supersolidity) in strongly correlated systems is a subject of immense interest. We study the possible manifestations of long-range orders, including lattice-supersolid phases with differently broken symmetry, in a two-dimensional square lattice system of hard-core bosons (HCBs) coupled to archetypal cooperative/coherent normal-mode distortions such as those in perovskites. At strong HCB-phonon coupling, using a duality transformation to map the strong-coupling problem to a weak-coupling one, we obtain an effective Hamiltonian involving nearest-neighbor, next-nearest-neighbor, and next-to-next-nearest-neighbor hoppings and repulsions. Using stochastic series expansion quantum Monte Carlo, we construct the phase diagram of the system. As coupling strength is increased, we find that the system undergoes a first-order quantum phase transition from a superfluid to a checkerboard solid at half-filling and from a superfluid to a diagonal striped solid [with crystalline ordering wave vector $\stackrel{P\vec}{Q}=(2\ensuremath{\pi}/3,2\ensuremath{\pi}/3)$ or $(2\ensuremath{\pi}/3,4\ensuremath{\pi}/3)]$ at one-third filling without showing any evidence of supersolidity. On tuning the system away from these commensurate fillings, checkerboard supersolid is generated near half-filling whereas a rare diagonal striped supersolid is realized near one-third filling. Interestingly, there is an asymmetry in the extent of supersolidity about one-third filling. Within our framework, we also provide an explanation for the observed checkerboard and stripe formations in ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{NiO}}_{4}$ at $x=1/2$ and $x=1/3$.

arXiv:1610.01447•Physical review. B./Physical review. B•Sep 6, 2017•6 citations

Competing quantum phases of hard-core bosons with tilted dipole-dipole interaction

Huan-Kuang Wu, Wei-Lin Tu

Different quantum phases of a hard-core boson induced by dipole-dipole interaction with varying angles of polarization are discussed in this work. We consider the two most influential leading terms with anisotropy due to the tilted polarization of the on-site boson in the square lattice. To ensure the concreteness of this truncation, we compare our phase diagrams, obtained numerically from the cluster mean-field theory (CMFT) and infinite projected entangled-pair state (iPEPS), with that of the long-range interacting model from quantum Monte Carlo. Next, we focus on the case where the azimuthal angle is fixed to $\ensuremath{\phi}=\ensuremath{\pi}/4$. Using the mean-field analysis where the quantum spin operators are replaced by $c$ numbers, we aim to search for the underlying phases, especially the supersolid. Our results show a competing scenario mainly between two ordered phases with different sizes of unit cell, where a first-order transition takes place in between them. With the help of the CMFT and variational iPEPS, the phase boundaries predicted by the mean-field theory are determined more precisely. Our discoveries elucidate the possible underlying supersolid phases which might be seen in the ultracold experiments with strongly dipolar atoms. Moreover, our results indicate that an effective triangular optical lattice can be realized by fine tuning the polarization of dipoles in a square lattice.

arXiv:2006.09861•Physical Review A•Nov 9, 2020•22 citations

Interacting hard-core bosons with anisotropic hopping: Checkerboard supersolid, order by disorder, and first-order phase transitions

Huo Xiao, Yong-Yong Cui, Dali Wang +1 more

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.

Physical Review A•Feb 14, 2017•8 citations

Two-species hard-core bosons on the triangular lattice: A quantum Monte Carlo study

Jian-Ping Lv, Qing‐Hu Chen, Youjin Deng

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 ($V$) and on-site 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, 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 $U/V$ and by the imbalance of particle numbers of the two species are also explored.

arXiv:1311.1604•Physical Review A•Jan 30, 2014•18 citations

Inhomogeneous hard-core bosonic mixture with checkerboard supersolid phase: Quantum and thermal phase diagram

Fatemeh Heydarinasab, Jahanfar Abouie

We introduce an inhomogeneous bosonic mixture composed of two kinds of hard-core and semi-hard-core bosons with different nilpotency conditions and demonstrate that in contrast with the standard hard-core Bose-Hubbard model, our bosonic mixture with nearest- and next-nearest-neighbor interactions on a square lattice develops the checkerboard supersolid phase characterized by the simultaneous superfluid and checkerboard solid orders. Our bosonic mixture is created from a two-orbital Bose-Hubbard model including two kinds of bosons: a single-orbital boson and a two-orbital boson. By mapping the bosonic mixture to an anisotropic inhomogeneous spin model in the presence of a magnetic field, we study the ground-state phase diagram of the model by means of cluster mean field theory and linear spin-wave theory and show that various phases such as solid, superfluid, supersolid, and Mott insulator appear in the phase diagram of the mixture. Competition between the interactions and magnetic field causes the mixture to undergo different kinds of first- and second-order phase transitions. By studying the behavior of the spin-wave excitations, we find the reasons of all first- and second-order phase transitions. We also obtain the temperature phase diagram of the system using cluster mean field theory. We show that the checkerboard supersolid phase persists at finite temperature comparable with the interaction energies of bosons.

arXiv:1711.03020•Physical review. B./Physical review. B•Sep 5, 2017•12 citations
We study the ground-state phase diagrams of hardcore bosons with long-range interactions on a square lattice using the linear spin-wave theory and a cluster mean-field method. Specifically, we consider the two types of long-range interaction: One consists only of the nearest- and next-nearest-neighbor interactions, and the other is the dipole-dipole interaction that decays with the interparticle distance rrr as \ensuremath{\sim}$${r}^{\ensuremath{-}3}. It is known from previous analyses by quantum Monte Carlo methods that a checkerboard supersolid (CSS) is absent in the ground-state phase diagram of the former case while it is present in the latter. In the former, we find that quantum fluctuations around mean-field solutions are enhanced by the direct competition between the checkerboard and striped solid orders and that they destabilize the CSS phase. On the other hand, the emergence of the CSS phase in the latter case can be attributed to the absence of such a competition with other solid orders. We also show that the cluster mean-field method allows for the determination of phase boundaries in a precise quantitative manner when scaling with respect to the cluster size is taken into account. It is found that the phase transition between the superfluid and the solid (or CSS) is of the first order in the vicinity of the particle-hole symmetric line.
We analyse the ground-state quantum phase diagram of hardcore Bosons interacting with repulsive dipolar potentials. The bosons dynamics is described by the extended-Bose-Hubbard Hamiltonian on a two-dimensional lattice. The ground state results from the interplay between the lattice geometry and the long-range interactions, which we account for by means of a classical spin mean-field approach limited by the size of the considered unit cells. This extended classical spin mean-field theory accounts for the long-range density-density interaction without truncation. We consider three different lattice geometries: square, honeycomb, and triangular. In the limit of zero hopping the ground state is always a devil’s staircase of solid (gapped) phases. Such crystalline phases with broken translational symmetry are robust with respect to finite hopping amplitudes. At intermediate hopping amplitudes, these gapped phases melt, giving rise to various lattice supersolid phases, which can have exotic features with multiple sublattice densities. At sufficiently large hoppings the ground state is a superfluid. The stability of phases predicted by our approach is gauged by comparison to the known quantum phase diagrams of the Bose-Hubbard model with nearest-neighbour interactions as well as quantum Monte Carlo simulations for the dipolar case on the square and triangular lattice. Our results are of immediate relevance for experimental realisations of self-organised crystalline ordering patterns in analogue quantum simulators, e.g., with ultracold dipolar atoms in an optical lattice.
Understanding the microscopic mechanism of coexisting long-range orders (such as lattice supersolidity) in strongly correlated systems is a subject of immense interest. We study the possible manifestations of long-range orders, including lattice-supersolid phases with differently broken symmetry, in a two-dimensional square lattice system of hard-core bosons (HCBs) coupled to archetypal cooperative/coherent normal-mode distortions such as those in perovskites. At strong HCB-phonon coupling, using a duality transformation to map the strong-coupling problem to a weak-coupling one, we obtain an effective Hamiltonian involving nearest-neighbor, next-nearest-neighbor, and next-to-next-nearest-neighbor hoppings and repulsions. Using stochastic series expansion quantum Monte Carlo, we construct the phase diagram of the system. As coupling strength is increased, we find that the system undergoes a first-order quantum phase transition from a superfluid to a checkerboard solid at half-filling and from a superfluid to a diagonal striped solid [with crystalline ordering wave vector $\stackrel{P\vec}{Q}=(2\ensuremath{\pi}/3,2\ensuremath{\pi}/3)$ or $(2\ensuremath{\pi}/3,4\ensuremath{\pi}/3)]$ at one-third filling without showing any evidence of supersolidity. On tuning the system away from these commensurate fillings, checkerboard supersolid is generated near half-filling whereas a rare diagonal striped supersolid is realized near one-third filling. Interestingly, there is an asymmetry in the extent of supersolidity about one-third filling. Within our framework, we also provide an explanation for the observed checkerboard and stripe formations in ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{NiO}}_{4}$ at x=1/2x=1/2x=1/2 and x=1/3x=1/3x=1/3.
Different quantum phases of a hard-core boson induced by dipole-dipole interaction with varying angles of polarization are discussed in this work. We consider the two most influential leading terms with anisotropy due to the tilted polarization of the on-site boson in the square lattice. To ensure the concreteness of this truncation, we compare our phase diagrams, obtained numerically from the cluster mean-field theory (CMFT) and infinite projected entangled-pair state (iPEPS), with that of the long-range interacting model from quantum Monte Carlo. Next, we focus on the case where the azimuthal angle is fixed to $\ensuremath{\phi}=\ensuremath{\pi}/4$. Using the mean-field analysis where the quantum spin operators are replaced by ccc numbers, we aim to search for the underlying phases, especially the supersolid. Our results show a competing scenario mainly between two ordered phases with different sizes of unit cell, where a first-order transition takes place in between them. With the help of the CMFT and variational iPEPS, the phase boundaries predicted by the mean-field theory are determined more precisely. Our discoveries elucidate the possible underlying supersolid phases which might be seen in the ultracold experiments with strongly dipolar atoms. Moreover, our results indicate that an effective triangular optical lattice can be realized by fine tuning the polarization of dipoles in a square lattice.
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 (t1{t}_{1}t1​), anisotropic next-nearest-neighbor hopping (${t}_{2}^{\ensuremath{'}}$), and nearest-neighbor repulsion (V1{V}_{1}V1​). 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.
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 introduce an inhomogeneous bosonic mixture composed of two kinds of hard-core and semi-hard-core bosons with different nilpotency conditions and demonstrate that in contrast with the standard hard-core Bose-Hubbard model, our bosonic mixture with nearest- and next-nearest-neighbor interactions on a square lattice develops the checkerboard supersolid phase characterized by the simultaneous superfluid and checkerboard solid orders. Our bosonic mixture is created from a two-orbital Bose-Hubbard model including two kinds of bosons: a single-orbital boson and a two-orbital boson. By mapping the bosonic mixture to an anisotropic inhomogeneous spin model in the presence of a magnetic field, we study the ground-state phase diagram of the model by means of cluster mean field theory and linear spin-wave theory and show that various phases such as solid, superfluid, supersolid, and Mott insulator appear in the phase diagram of the mixture. Competition between the interactions and magnetic field causes the mixture to undergo different kinds of first- and second-order phase transitions. By studying the behavior of the spin-wave excitations, we find the reasons of all first- and second-order phase transitions. We also obtain the temperature phase diagram of the system using cluster mean field theory. We show that the checkerboard supersolid phase persists at finite temperature comparable with the interaction energies of bosons.