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

Study of long-range orders due to cooperative breathing mode in two dimensions

Amrita Ghosh, Sudhakar Yarlagadda

Published Oct 5, 2016• 0 citations
OpenAlex

Abstract

We study hard-core-bosons (HCBs) on a square lattice with a perovskite-type structure. The HCBs interact with the in-plane (xy) oxygen atoms via cooperative breathing mode. On the other hand, non-cooperative HCB-phonon interaction exists for the out-of-plane oxygen atoms in the z-direction. Using a non-perturbative treatment, we derive an effective Hamiltonian which involves nearest-neighbor, next-nearest-neighbor and next-to-next-nearest-neighbor hoppings and repulsions. Using a quantum Monte Carlo simulation involving stochastic-series-expansion method, we construct the phase diagram of the system. At half-filling, the system exhibits a checkerboard solid characterized by ordering wavevector $\vec{Q}=(\pi,\pi)$. Slightly away from half-filling, we get a region of checkerboard supersolid, the width of which decreases with increasing HCB-phonon interaction strength. On the other hand at $\frac{1}{3}$-filling, the system manifests the existence of a novel striped solid with a peak in the structure factor at wavevector $\vec{Q}=(2\pi/3,2\pi/3)$ or $(2\pi/3,4\pi/3)$. On both sides of this charge-density-wave, we get a striped supersolid with an asymmetry in the extent.

Related papers

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

Coexistence of long-range orders in a Bose-Holstein model

Satyaki Kar, Sudhakar Yarlagadda

Exploring supersolidity in naturally occurring and artificially designed systems has been and will continue to be an area of immense interest. Here, we study how superfluid and charge-density-wave (CDW) states cooperate or compete in a minimal model for hard-core-bosons (HCBs) coupled locally to optical phonons: a two-dimensional Bose-Holstein model. Our study is restricted to the parameter regimes of strong HCB-phonon coupling and non-adiabaticity. We use Quantum Monte Carlo simulation (involving stochastic-series-expansion technique) to study phase transitions and to investigate whether we have homogeneous or phase-separated coexistence. The effective Hamiltonian involves, besides a nearest-neighbor hopping and a nearest-neighbor repulsion, sizeable double-hopping terms (obtained from second-order perturbation). At densities not far from half-filling, in the parameter regime where the double-hopping terms are non-negligible (negligible) compared to the nearest-neighbor hopping, we get checkerboard-supersolidity (phase separation) with CDW being characterized by ordering wavevector $\vec{Q}=(π,π)$.

arXiv:1501.04528•Jan 19, 2015•0 citations

Supersolid in a one-dimensional model of hard-core bosons

Tapan Mishra, Ramesh V. Pai, Subroto Mukerjee

We study a system of hard-core boson on a one-dimensional lattice with frustrated next-nearest-neighbor hopping and nearest-neighbor interaction. At half filling, for equal magnitude of nearest- and next-nearest-neighbor hopping, the ground state of this system exhibits a first-order phase transition from a bond-ordered solid to a charge-density-wave solid as a function of the nearest-neighbor interaction. Moving away from half filling we investigate the system at incommensurate densities, where we find a supersolid phase which has concurrent off-diagonal long-range order and density-wave order which is unusual in a system of hard-core bosons in one dimension. Using the finite-size density-matrix renormalization group method, we obtain the complete phase diagram for this model.

arXiv:1309.4412•Physical Review A•Jan 21, 2014•26 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

Vacancy supersolid of hard-core bosons on the square lattice

Long Dang, Massimo Boninsegni, Lode Pollet

The ground state of hard-core bosons on the square lattice with nearest and next-nearest-neighbor repulsion is studied by quantum Monte Carlo simulations. A supersolid phase with vacancy condensation and ``star'' diagonal ordering is found for filling $\ensuremath{\rho}<0.25$. At filling $\ensuremath{\rho}>0.25$, a supersolid phase exists between the star and the stripe crystal at $\ensuremath{\rho}=0.5$. No supersolid phase occurs for $\ensuremath{\rho}>0.25$ if the ground state at half-filling is either a checkerboard crystal or a superfluid. No commensurate supersolid phase is observed.

arXiv:0803.1116•Physical Review B•Oct 29, 2008•46 citations

Quantum phases of hard-core bosons on two-dimensional lattices with anisotropic dipole-dipole interaction

Takahiro Ohgoe, Takafumi Suzuki, Naoki Kawashima

By using an unbiased quantum Monte Carlo method, we investigate the hard-core Bose-Hubbard model on a square lattice with the anisotropic dipole-dipole interaction. To study the effect of the anisotropy, dipole moments are assumed to be polarized in the $y$ direction on the two-dimensional $xy$ plane. To perform efficient simulations of long-range interacting systems, we use the worm algorithm with an $O(N)$ Monte Carlo method. We obtain the ground-state phase diagram that includes a superfluid phase and a striped solid phase at half-filling as two main phases. In addition to these two main phases, we find a small region where there are multiple plateaus in the particle density for small hopping amplitudes. In this region, the number of plateaus increases as the system size increases. This indicates the appearance of numerous competing ground states due to frustrated interactions. In our simulations, we find no evidence of a supersolid phase.

arXiv:1110.2109•Physical Review A•Dec 26, 2012•19 citations
We study hard-core-bosons (HCBs) on a square lattice with a perovskite-type structure. The HCBs interact with the in-plane (xy) oxygen atoms via cooperative breathing mode. On the other hand, non-cooperative HCB-phonon interaction exists for the out-of-plane oxygen atoms in the z-direction. Using a non-perturbative treatment, we derive an effective Hamiltonian which involves nearest-neighbor, next-nearest-neighbor and next-to-next-nearest-neighbor hoppings and repulsions. Using a quantum Monte Carlo simulation involving stochastic-series-expansion method, we construct the phase diagram of the system. At half-filling, the system exhibits a checkerboard solid characterized by ordering wavevector Q⃗=(π,π)\vec{Q}=(\pi,\pi)Q​=(π,π). Slightly away from half-filling, we get a region of checkerboard supersolid, the width of which decreases with increasing HCB-phonon interaction strength. On the other hand at 13\frac{1}{3}31​-filling, the system manifests the existence of a novel striped solid with a peak in the structure factor at wavevector Q⃗=(2π/3,2π/3)\vec{Q}=(2\pi/3,2\pi/3)Q​=(2π/3,2π/3) or (2π/3,4π/3)(2\pi/3,4\pi/3)(2π/3,4π/3). On both sides of this charge-density-wave, we get a striped supersolid with an asymmetry in the extent.
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.
Exploring supersolidity in naturally occurring and artificially designed systems has been and will continue to be an area of immense interest. Here, we study how superfluid and charge-density-wave (CDW) states cooperate or compete in a minimal model for hard-core-bosons (HCBs) coupled locally to optical phonons: a two-dimensional Bose-Holstein model. Our study is restricted to the parameter regimes of strong HCB-phonon coupling and non-adiabaticity. We use Quantum Monte Carlo simulation (involving stochastic-series-expansion technique) to study phase transitions and to investigate whether we have homogeneous or phase-separated coexistence. The effective Hamiltonian involves, besides a nearest-neighbor hopping and a nearest-neighbor repulsion, sizeable double-hopping terms (obtained from second-order perturbation). At densities not far from half-filling, in the parameter regime where the double-hopping terms are non-negligible (negligible) compared to the nearest-neighbor hopping, we get checkerboard-supersolidity (phase separation) with CDW being characterized by ordering wavevector Q⃗=(π,π)\vec{Q}=(π,π)Q​=(π,π).
We study a system of hard-core boson on a one-dimensional lattice with frustrated next-nearest-neighbor hopping and nearest-neighbor interaction. At half filling, for equal magnitude of nearest- and next-nearest-neighbor hopping, the ground state of this system exhibits a first-order phase transition from a bond-ordered solid to a charge-density-wave solid as a function of the nearest-neighbor interaction. Moving away from half filling we investigate the system at incommensurate densities, where we find a supersolid phase which has concurrent off-diagonal long-range order and density-wave order which is unusual in a system of hard-core bosons in one dimension. Using the finite-size density-matrix renormalization group method, we obtain the complete phase diagram for this model.
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.
The ground state of hard-core bosons on the square lattice with nearest and next-nearest-neighbor repulsion is studied by quantum Monte Carlo simulations. A supersolid phase with vacancy condensation and ``star'' diagonal ordering is found for filling $\ensuremath{\rho}<0.25$. At filling $\ensuremath{\rho}>0.25$, a supersolid phase exists between the star and the stripe crystal at $\ensuremath{\rho}=0.5$. No supersolid phase occurs for $\ensuremath{\rho}>0.25$ if the ground state at half-filling is either a checkerboard crystal or a superfluid. No commensurate supersolid phase is observed.
By using an unbiased quantum Monte Carlo method, we investigate the hard-core Bose-Hubbard model on a square lattice with the anisotropic dipole-dipole interaction. To study the effect of the anisotropy, dipole moments are assumed to be polarized in the yyy direction on the two-dimensional xyxyxy plane. To perform efficient simulations of long-range interacting systems, we use the worm algorithm with an O(N)O(N)O(N) Monte Carlo method. We obtain the ground-state phase diagram that includes a superfluid phase and a striped solid phase at half-filling as two main phases. In addition to these two main phases, we find a small region where there are multiple plateaus in the particle density for small hopping amplitudes. In this region, the number of plateaus increases as the system size increases. This indicates the appearance of numerous competing ground states due to frustrated interactions. In our simulations, we find no evidence of a supersolid phase.