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:1808.01993 · Physical review. B./Physical review. B

Quantum XX model with competing short- and long-range interactions: Phases and phase transitions in and out of equilibrium

Ferenc Iglói, Benjamin Blaß, Gergő Roósz, Heiko Rieger

Published Nov 15, 2018• 32 citations
arXivHTMLPDF

Abstract

We consider the quantum XX model in the presence of competing nearest-neighbor and global-range interactions, which is equivalent to a Bose-Hubbard model with cavity mediated global-range interactions in the hard-core boson limit. Using fermionic techniques the problem is solved exactly in one dimension in the thermodynamic limit. The ground state phase diagram consists of two ordered phases: ferromagnetic (F) and antiferromagnetic (AF), as well as an XY phase having quasi-long-range order. We have also studied quantum relaxation after sudden quenches. Quenching from the AF phase to the XY region remanent AF order is observed below a dynamical transition line. In the opposite quench, from the XY region to the AF phase beyond a static metastability line AF order arises on top of remanent XY quasi-long-range order, which corresponds to dynamically generated supersolid state in the equivalent Bose-Hubbard model with hard-core bosons.

DOI
10.1103/physrevb.98.184415

Related papers

Quantum Relaxation and Metastability of Lattice Bosons with Cavity-Induced Long-Range Interactions

Benjamin Blaß, Heiko Rieger, Gergő Roósz +1 more

The coupling of cold atoms to the radiation field within a high-finesse optical resonator, an optical cavity, induces long-range interactions which can compete with an underlying optical lattice. The interplay between short- and long-range interactions gives rise to new phases of matter including supersolidity (SS) and density waves (DW), and interesting quantum dynamics. Here it is shown that for hard-core bosons in one dimension the ground state phase diagram and the quantum relaxation after sudden quenches can be calculated exactly in the thermodynamic limit. Remanent DW order is observed for quenches from a DW ground state into the superfluid (SF) phase below a dynamical transition line. After sufficiently strong SF to DW quenches beyond a static metastability line DW order emerges on top of remanent SF order, giving rise to a dynamically generated SS state. Our method to handle infinite- and short-range interactions in the infinite system size limit opens a way to solve exactly other Hamiltonians with infinite- and short-range interactions as well.

arXiv:1711.10961•Physical Review Letters•Aug 28, 2018•34 citations

The Effect of Disorder on the Phase Diagrams of Hard-Core Lattice Bosons With Cavity-Mediated Long-Range and Nearest-Neighbor Interactions

Chao Zhang, Heiko Rieger

We use quantum Monte Carlo simulations with the worm algorithm to study the phase diagram of a two-dimensional Bose-Hubbard model with cavity-mediated long-range interactions and uncorrelated disorder in the hard-core limit. Our study shows the system is in a supersolid phase at weak disorder and a disordered solid phase at stronger disorder. Due to long-range interactions, a large region of metastable states exists in both clean and disordered systems. By comparing the phase diagrams for both clean and disordered systems, we find that disorder suppresses metastable states and superfluidity. We compare these results with the phase diagram of the extended Bose-Hubbard model with nearest-neighbor interactions. Here, the supersolid phase does not exist even at weak disorder. We identify two kinds of glassy phases: a Bose glass phase and a disordered solid phase. The glassy phases intervene between the density-wave and superfluid phases as the Griffiths phase of the Bose-Hubbard model. The disordered solid phase intervenes between the density-wave and Bose glass phases since both have a finite structure factor.

arXiv:1910.03981•Frontiers in Physics•Jan 24, 2020•8 citations

Quantum disordered ground state for hard-core bosons on the frustrated square lattice

Ansgar Kalz, A. Honecker, Sebastian Fuchs +1 more

We investigate the phase diagram of hard-core bosons on a square lattice with competing interactions. The hard-core bosons can also be represented by spin-$1/2$ operators and the model can therefore be mapped onto an anisotropic ${J}_{1}$-${J}_{2}$ Heisenberg model. We find the N\'eel state and a collinear antiferromagnetic state as classical ordered phases to be suppressed by the introduction of ferromagnetic exchange terms in the $x$-$y$ plane that result in a ferromagnetic phase for large interactions. For an intermediate regime, the emergence of new quantum states like valence bond crystals or supersolids is predicted for similar models. We do not observe any signal for long-range order in terms of conventional order or dimer correlations in our model and find an exponential decay in the spin correlations. Hence, all evidence is pointing toward a quantum-disordered ground state for a small region in the phase diagram.

arXiv:1101.5115•Physical Review B•May 31, 2011•12 citations

Phase diagrams of the disordered Bose-Hubbard model with cavity-mediated long-range and nearest-neighbor interactions

Chao Zhang, Heiko Rieger

Abstract Recent experiments with ultracold atoms in an optical lattice have realized cavity-mediated long-range interaction and observed the emergence of a supersolid phase and a density wave phase in addition to Mott insulator and superfluid phases. Here we consider theoretically the effect of uncorrelated disorder on the phase diagram of this system and study the two-dimensional Bose-Hubbard model with cavity-mediated long-range interactions and uncorrelated diagonal disorder. We also study the phase diagram of the extended Bose-Hubbard model with nearest-neighbor interactions in the presence of uncorrelated diagonal disorder. The extended Bose-Hubbard model with nearest-neighbor interactions has been realized in the experiment using dipolar interaction recently. With the help of quantum Monte Carlo simulations using the worm algorithm, we determine the phase diagram of those two models. We compare the phase diagrams of cavity-mediated long-range interactions with nearest-neighbor interactions. We show that two kinds of Bose glass phases exist: one with and one without density wave order. We also find that weak disorder enhances the supersolid phase. Graphical abstract

arXiv:1908.11165•The European Physical Journal B•Feb 1, 2020•8 citations

Phase diagrams of Bose-Hubbard model and antiferromagnetic spin-1/2 models on a honeycomb lattice

Takashi Nakafuji, Ikuo Ichinose

Motivated by the recent experimental realization of the Haldane model by ultracold fermions in an optical lattice, we investigate phase diagrams of the hard-core Bose-Hubbard model on a honeycomb lattice. This model is closely related with a spin-1/2 antiferromagnetic (AF) quantum spin model. Nearest-neighbor (NN) hopping amplitude is positive and it prefers an AF configuration of phases of Bose-Einstein condensates. On the other hand, an amplitude of the next-NN hopping depends on an angle variable as in the Haldane model. Phase diagrams are obtained by means of an extended path-integral Monte Carlo simulation. Besides the AF state, a ${120}^{\ensuremath{\circ}}$-order state, there appear other phases including a Bose metal in which no long-range orders exist.

arXiv:1705.06012•Physical Review A•Jul 26, 2017•11 citations

Phase transitions in a Bose-Hubbard model with cavity-mediated global-range interactions

Nishant Dogra, Ferdinand Brennecke, Sebastian D. Huber +1 more

We study a system with competing short- and global-range interactions in the framework of the Bose-Hubbard model. Using a mean-field approximation we obtain the phase diagram of the system and observe four different phases: a superfluid, a supersolid, a Mott insulator, and a charge-density wave, where the transitions between the various phases can be either of first or second order. We qualitatively support these results using Monte Carlo simulations. An analysis of the low-energy excitations shows that the second-order phase transition from the charge-density wave to the supersolid is associated with the softening of particle- and holelike excitations which give rise to a gapless mode and an amplitude Higgs mode in the supersolid phase. This amplitude Higgs mode is further transformed into a roton mode which softens at the supersolid to superfluid phase transition.

arXiv:1604.00865•Physical Review A•Aug 29, 2016•99 citations
We consider the quantum XX model in the presence of competing nearest-neighbor and global-range interactions, which is equivalent to a Bose-Hubbard model with cavity mediated global-range interactions in the hard-core boson limit. Using fermionic techniques the problem is solved exactly in one dimension in the thermodynamic limit. The ground state phase diagram consists of two ordered phases: ferromagnetic (F) and antiferromagnetic (AF), as well as an XY phase having quasi-long-range order. We have also studied quantum relaxation after sudden quenches. Quenching from the AF phase to the XY region remanent AF order is observed below a dynamical transition line. In the opposite quench, from the XY region to the AF phase beyond a static metastability line AF order arises on top of remanent XY quasi-long-range order, which corresponds to dynamically generated supersolid state in the equivalent Bose-Hubbard model with hard-core bosons.
The coupling of cold atoms to the radiation field within a high-finesse optical resonator, an optical cavity, induces long-range interactions which can compete with an underlying optical lattice. The interplay between short- and long-range interactions gives rise to new phases of matter including supersolidity (SS) and density waves (DW), and interesting quantum dynamics. Here it is shown that for hard-core bosons in one dimension the ground state phase diagram and the quantum relaxation after sudden quenches can be calculated exactly in the thermodynamic limit. Remanent DW order is observed for quenches from a DW ground state into the superfluid (SF) phase below a dynamical transition line. After sufficiently strong SF to DW quenches beyond a static metastability line DW order emerges on top of remanent SF order, giving rise to a dynamically generated SS state. Our method to handle infinite- and short-range interactions in the infinite system size limit opens a way to solve exactly other Hamiltonians with infinite- and short-range interactions as well.
We use quantum Monte Carlo simulations with the worm algorithm to study the phase diagram of a two-dimensional Bose-Hubbard model with cavity-mediated long-range interactions and uncorrelated disorder in the hard-core limit. Our study shows the system is in a supersolid phase at weak disorder and a disordered solid phase at stronger disorder. Due to long-range interactions, a large region of metastable states exists in both clean and disordered systems. By comparing the phase diagrams for both clean and disordered systems, we find that disorder suppresses metastable states and superfluidity. We compare these results with the phase diagram of the extended Bose-Hubbard model with nearest-neighbor interactions. Here, the supersolid phase does not exist even at weak disorder. We identify two kinds of glassy phases: a Bose glass phase and a disordered solid phase. The glassy phases intervene between the density-wave and superfluid phases as the Griffiths phase of the Bose-Hubbard model. The disordered solid phase intervenes between the density-wave and Bose glass phases since both have a finite structure factor.
We investigate the phase diagram of hard-core bosons on a square lattice with competing interactions. The hard-core bosons can also be represented by spin-1/21/21/2 operators and the model can therefore be mapped onto an anisotropic J1{J}_{1}J1​-J2{J}_{2}J2​ Heisenberg model. We find the N\'eel state and a collinear antiferromagnetic state as classical ordered phases to be suppressed by the introduction of ferromagnetic exchange terms in the xxx-yyy plane that result in a ferromagnetic phase for large interactions. For an intermediate regime, the emergence of new quantum states like valence bond crystals or supersolids is predicted for similar models. We do not observe any signal for long-range order in terms of conventional order or dimer correlations in our model and find an exponential decay in the spin correlations. Hence, all evidence is pointing toward a quantum-disordered ground state for a small region in the phase diagram.
Abstract Recent experiments with ultracold atoms in an optical lattice have realized cavity-mediated long-range interaction and observed the emergence of a supersolid phase and a density wave phase in addition to Mott insulator and superfluid phases. Here we consider theoretically the effect of uncorrelated disorder on the phase diagram of this system and study the two-dimensional Bose-Hubbard model with cavity-mediated long-range interactions and uncorrelated diagonal disorder. We also study the phase diagram of the extended Bose-Hubbard model with nearest-neighbor interactions in the presence of uncorrelated diagonal disorder. The extended Bose-Hubbard model with nearest-neighbor interactions has been realized in the experiment using dipolar interaction recently. With the help of quantum Monte Carlo simulations using the worm algorithm, we determine the phase diagram of those two models. We compare the phase diagrams of cavity-mediated long-range interactions with nearest-neighbor interactions. We show that two kinds of Bose glass phases exist: one with and one without density wave order. We also find that weak disorder enhances the supersolid phase. Graphical abstract
Motivated by the recent experimental realization of the Haldane model by ultracold fermions in an optical lattice, we investigate phase diagrams of the hard-core Bose-Hubbard model on a honeycomb lattice. This model is closely related with a spin-1/2 antiferromagnetic (AF) quantum spin model. Nearest-neighbor (NN) hopping amplitude is positive and it prefers an AF configuration of phases of Bose-Einstein condensates. On the other hand, an amplitude of the next-NN hopping depends on an angle variable as in the Haldane model. Phase diagrams are obtained by means of an extended path-integral Monte Carlo simulation. Besides the AF state, a ${120}^{\ensuremath{\circ}}$-order state, there appear other phases including a Bose metal in which no long-range orders exist.
We study a system with competing short- and global-range interactions in the framework of the Bose-Hubbard model. Using a mean-field approximation we obtain the phase diagram of the system and observe four different phases: a superfluid, a supersolid, a Mott insulator, and a charge-density wave, where the transitions between the various phases can be either of first or second order. We qualitatively support these results using Monte Carlo simulations. An analysis of the low-energy excitations shows that the second-order phase transition from the charge-density wave to the supersolid is associated with the softening of particle- and holelike excitations which give rise to a gapless mode and an amplitude Higgs mode in the supersolid phase. This amplitude Higgs mode is further transformed into a roton mode which softens at the supersolid to superfluid phase transition.