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

Physical review. B, Condensed matter

Ground-state phase diagram of an interacting Bose model with near-neighbor repulsion

Parhat Niyaz, Richard T. Scalettar, Ching Yin Fong, G. G. Batrouni

Published Oct 1, 1991• 53 citations
Publisher

Abstract

We study the ground-state phase diagram of a one-dimensional lattice model of interacting bosons at commensurate filling. When the ratio of interaction strengths to bandwidth is small, the bosons condense into a superfluid phase. For large on-site repulsion, there is a phase transition to a localized Mott phase where the gap \ensuremath{\Delta} is nonzero and the Fourier transform at zero momentum of the density-density correlation function S(q=0) diverges. For large intersite repulsion, S(q=\ensuremath{\pi}) diverges first. By examining the superfluid density ${\mathrm{\ensuremath{\rho}}}_{\mathit{s}}$, in addition to the gap and S(q), we obtain a complete characterization of the phase diagram.

DOI
10.1103/physrevb.44.7143

Related papers

Phase diagram and momentum distribution of an interacting Bose gas in a bichromatic lattice

Xiaolong Deng, R. Citro, Anna Minguzzi +1 more

We determine the phase diagram and the momentum distribution for a one-dimensional Bose gas with repulsive short-range interactions in the presence of a two-color lattice potential, with an incommensurate ratio among the respective wavelengths, by using a combined numerical (density matrix renormalization group) and analytical (bosonization) analysis. The system displays a delocalized (superfluid) phase at small values of the intensity of the secondary lattice ${\mathit{V}}_{2}$ and a localized (Bose-glasslike) phase at larger intensity ${\mathit{V}}_{2}$. We analyze the localization transition as a function of the height ${\mathit{V}}_{2}$ beyond the known limits of free and hard-core bosons. We find that weak repulsive interactions disfavor the localized phase, i.e., they increase the critical value of ${\mathit{V}}_{2}$ at which localization occurs. In the case of integer filling of the primary lattice, the phase diagram at fixed density displays, in addition to a transition from a superfluid to a Bose glass phase, a transition to a Mott-insulating state for not too large ${\mathit{V}}_{2}$ and large repulsion. We also analyze the emergence of a Bose-glass phase by looking at the evolution of the Mott-insulator lobes when increasing ${\mathit{V}}_{2}$. The Mott lobes shrink and disappear above a critical value of ${\mathit{V}}_{2}$. Finally, we characterize the superfluid phase by the momentum distribution, and show that it displays a power-law decay at small momenta typical of Luttinger liquids, with an exponent depending on the combined effect of the interactions and of the secondary lattice. In addition, we observe two side peaks that are due to the diffraction of the Bose gas by the second lattice. This latter feature could be observed in current experiments as characteristics of pseudo-random Bose systems.

arXiv:0803.3128•Physical Review A•Jul 21, 2008•70 citations

Phase diagram of interacting bosons on the honeycomb lattice

Stefan Weßel

We study the ground-state properties of repulsively interacting bosons on the honeycomb lattice using large-scale quantum Monte Carlo simulations. In the hard-core limit, the half-filled system develops long-ranged diagonal order for sufficiently strong nearest-neighbor repulsion. This staggered solid melts at a first-order quantum phase transition into the superfluid phase, without the presence of any intermediate supersolid phase. Within the superfluid phase, both the superfluid density and the compressibility exhibit local minima near the particle (hole) density of one quarter, while the density and the condensate fraction show inflection points in this region. Relaxing the hard-core constraint, supersolid phases emerge for soft-core bosons. The suppression of the superfluid density is found to persist for sufficiently large, finite on-site repulsion.

arXiv:cond-mat/0701337•Physical Review B•May 2, 2007•53 citations

One-dimensional Bose-Hubbard model with nearest-neighbor interaction

Till D. Kühner, Steven R. White, H. Monien

We study the one-dimensional Bose-Hubbard model using the density-matrix renormalization group. For the cases of on-site interactions and additional nearest-neighbor interactions the phase boundaries of the Mott insulators and charge-density wave phases are determined. We find a direct phase transition between the charge-density wave phase and the superfluid phase, and no supersolid or normal phases. In the presence of nearest-neighbor interaction the charge density wave phase is completely surrounded by a region in which the effective interactions in the superfluid phase are repulsive. In this region a single impurity causes the system to be insulating. An even bigger region of the superfluid phase is driven into a Bose-glass phase by any finite quenched disorder. We determine the boundaries of both regions in the phase diagram. The ac conductivity of the superfluid phase in the attractive and the repulsive region is calculated, and a big superfluid stiffness is found in the attractive as well as the repulsive region.

arXiv:cond-mat/9906019•Physical review. B, Condensed matter•May 1, 2000•401 citations

Dynamic properties of the one-dimensional Bose-Hubbard model

Satoshi Ejima, Holger Fehske, Florian Gebhard

We use the density-matrix renormalization group method to investigate ground-state and dynamic properties of the one-dimensional Bose-Hubbard model, the effective model of ultracold bosonic atoms in an optical lattice. For fixed maximum site occupancy n b = 5, we calculate the phase boundaries between the Mott insulator and the "superfluid" phase for the lowest two Mott lobes. We extract the Tomonaga-Luttinger parameter from the density-density correlation function and determine accurately the critical interaction strength for the Mott transition. For both phases, we study the momentum distribution function in the homogeneous system, and the particle distribution and quasi-momentum distribution functions in a parabolic trap. With our zero-temperature method we determine the photoemission spectra in the Mott insulator and in the "superfluid" phase of the one-dimensional Bose-Hubbard model. In the insulator, the Mott gap separates the quasi-particle and quasi-hole dispersions. In the "superfluid" phase the spectral weight is concentrated around zero momentum.

arXiv:1102.2028•Europhysics Letters (EPL)•Feb 1, 2011•105 citations

Boson localization and the superfluid-insulator transition

Matthew P. A. Fisher, Peter B. Weichman, G. Grinstein +1 more

The phase diagrams and phase transitions of bosons with short-ranged repulsive interactions moving in periodic and/or random external potentials at zero temperature are investigated with emphasis on the superfluid-insulator transition induced by varying a parameter such as the density. Bosons in periodic potentials (e.g., on a lattice) at T=0 exhibit two types of phases: a superfluid phase and Mott insulating phases characterized by integer (or commensurate) boson densities, by the existence of a gap for particle-hole excitations, and by zero compressibility. Generically, the superfluid onset transition in d dimensions from a Mott insulator to superfluidity is ``ideal,'' or mean field in character, but at special multicritical points with particle-hole symmetry it is in the universality class of the (d+1)-dimensional XY model. In the presence of disorder, a third, ``Bose glass'' phase exists. This phase is insulating because of the localization effects of the randomness and analogous to the Fermi glass phase of interacting fermions in a strongly disordered potential.The Bose glass phase is characterized by a finite compressibility, no gap, but an infinite superfluid susceptibility. In the presence of disorder the transition to superfluidity is argued to occur only from the Bose glass phase, and never directly from the Mott insulator. This zero-temperature superfluid-insulator transition is studied via generalizations of the Josephson scaling relation for the superfluid density at the ordinary \ensuremath{\lambda} transition, highlighting the crucial role of quantum fluctuations. The transition is found to have a dynamic critical exponent z exactly equal to d and correlation length and order-parameter correlation exponents \ensuremath{\nu} and \ensuremath{\eta} which satisfy the bounds \ensuremath{\nu}\ensuremath{\ge}2/d and \ensuremath{\eta}\ensuremath{\le}2-d, respectively. It is argued that the superfluid-insulator transition in the presence of disorder may have an upper critical dimension ${d}_{c}$ which is infinite, but a perturbative renormalization-group calculation wherein the critical exponents have mean-field values for weak disorder above d=4 is also discussed. Many of these conclusions are verified by explicit calculations on a model of one-dimensional bosons in the presence of both random and periodic potentials. The general results are applied to experiments on $^{4}\mathrm{He}$ absorbed in porous media such as Vycor. Some measurable properties of the superfluid onset are predicted exactly [e.g., the exponent x relating the \ensuremath{\lambda} transition temperature to the zero-temperature superfluid density is found to be d/2(d-1)], while stringent bounds are placed on others. Analysis of preliminary data is consistent with these predictions.

Physical review. B, Condensed matter•Jul 1, 1989•3,511 citations

Superfluid and Mott-insulator phases of one-dimensional Bose-Fermi mixtures

Aleksander Zujev, A. Baldwin, Richard T. Scalettar +3 more

We study the ground state phases of Bose-Fermi mixtures in one-dimensional optical lattices with quantum Monte Carlo simulations using the canonical worm algorithm. Depending on the filling of bosons and fermions, and the on-site intra- and interspecies interaction, different kinds of incompressible and superfluid phases appear. On the compressible side, correlations between bosons and fermions can lead to a distinctive behavior of the bosonic superfluid density and the fermionic stiffness, as well as of the equal-time Green functions, which allow one to identify regions where the two species exhibit anticorrelated flow. We present here complete phase diagrams for these systems at different fillings and as a function of the interaction parameters.

arXiv:0711.4635•Physical Review A•Sep 26, 2008•30 citations
We study the ground-state phase diagram of a one-dimensional lattice model of interacting bosons at commensurate filling. When the ratio of interaction strengths to bandwidth is small, the bosons condense into a superfluid phase. For large on-site repulsion, there is a phase transition to a localized Mott phase where the gap \ensuremath{\Delta} is nonzero and the Fourier transform at zero momentum of the density-density correlation function S(q=0) diverges. For large intersite repulsion, S(q=\ensuremath{\pi}) diverges first. By examining the superfluid density \ensuremathρs{\mathrm{\ensuremath{\rho}}}_{\mathit{s}}\ensuremathρs​, in addition to the gap and S(q), we obtain a complete characterization of the phase diagram.
We determine the phase diagram and the momentum distribution for a one-dimensional Bose gas with repulsive short-range interactions in the presence of a two-color lattice potential, with an incommensurate ratio among the respective wavelengths, by using a combined numerical (density matrix renormalization group) and analytical (bosonization) analysis. The system displays a delocalized (superfluid) phase at small values of the intensity of the secondary lattice V2{\mathit{V}}_{2}V2​ and a localized (Bose-glasslike) phase at larger intensity V2{\mathit{V}}_{2}V2​. We analyze the localization transition as a function of the height V2{\mathit{V}}_{2}V2​ beyond the known limits of free and hard-core bosons. We find that weak repulsive interactions disfavor the localized phase, i.e., they increase the critical value of V2{\mathit{V}}_{2}V2​ at which localization occurs. In the case of integer filling of the primary lattice, the phase diagram at fixed density displays, in addition to a transition from a superfluid to a Bose glass phase, a transition to a Mott-insulating state for not too large V2{\mathit{V}}_{2}V2​ and large repulsion. We also analyze the emergence of a Bose-glass phase by looking at the evolution of the Mott-insulator lobes when increasing V2{\mathit{V}}_{2}V2​. The Mott lobes shrink and disappear above a critical value of V2{\mathit{V}}_{2}V2​. Finally, we characterize the superfluid phase by the momentum distribution, and show that it displays a power-law decay at small momenta typical of Luttinger liquids, with an exponent depending on the combined effect of the interactions and of the secondary lattice. In addition, we observe two side peaks that are due to the diffraction of the Bose gas by the second lattice. This latter feature could be observed in current experiments as characteristics of pseudo-random Bose systems.
We study the ground-state properties of repulsively interacting bosons on the honeycomb lattice using large-scale quantum Monte Carlo simulations. In the hard-core limit, the half-filled system develops long-ranged diagonal order for sufficiently strong nearest-neighbor repulsion. This staggered solid melts at a first-order quantum phase transition into the superfluid phase, without the presence of any intermediate supersolid phase. Within the superfluid phase, both the superfluid density and the compressibility exhibit local minima near the particle (hole) density of one quarter, while the density and the condensate fraction show inflection points in this region. Relaxing the hard-core constraint, supersolid phases emerge for soft-core bosons. The suppression of the superfluid density is found to persist for sufficiently large, finite on-site repulsion.
We study the one-dimensional Bose-Hubbard model using the density-matrix renormalization group. For the cases of on-site interactions and additional nearest-neighbor interactions the phase boundaries of the Mott insulators and charge-density wave phases are determined. We find a direct phase transition between the charge-density wave phase and the superfluid phase, and no supersolid or normal phases. In the presence of nearest-neighbor interaction the charge density wave phase is completely surrounded by a region in which the effective interactions in the superfluid phase are repulsive. In this region a single impurity causes the system to be insulating. An even bigger region of the superfluid phase is driven into a Bose-glass phase by any finite quenched disorder. We determine the boundaries of both regions in the phase diagram. The ac conductivity of the superfluid phase in the attractive and the repulsive region is calculated, and a big superfluid stiffness is found in the attractive as well as the repulsive region.
We use the density-matrix renormalization group method to investigate ground-state and dynamic properties of the one-dimensional Bose-Hubbard model, the effective model of ultracold bosonic atoms in an optical lattice. For fixed maximum site occupancy n b = 5, we calculate the phase boundaries between the Mott insulator and the "superfluid" phase for the lowest two Mott lobes. We extract the Tomonaga-Luttinger parameter from the density-density correlation function and determine accurately the critical interaction strength for the Mott transition. For both phases, we study the momentum distribution function in the homogeneous system, and the particle distribution and quasi-momentum distribution functions in a parabolic trap. With our zero-temperature method we determine the photoemission spectra in the Mott insulator and in the "superfluid" phase of the one-dimensional Bose-Hubbard model. In the insulator, the Mott gap separates the quasi-particle and quasi-hole dispersions. In the "superfluid" phase the spectral weight is concentrated around zero momentum.
The phase diagrams and phase transitions of bosons with short-ranged repulsive interactions moving in periodic and/or random external potentials at zero temperature are investigated with emphasis on the superfluid-insulator transition induced by varying a parameter such as the density. Bosons in periodic potentials (e.g., on a lattice) at T=0 exhibit two types of phases: a superfluid phase and Mott insulating phases characterized by integer (or commensurate) boson densities, by the existence of a gap for particle-hole excitations, and by zero compressibility. Generically, the superfluid onset transition in d dimensions from a Mott insulator to superfluidity is ``ideal,'' or mean field in character, but at special multicritical points with particle-hole symmetry it is in the universality class of the (d+1)-dimensional XY model. In the presence of disorder, a third, ``Bose glass'' phase exists. This phase is insulating because of the localization effects of the randomness and analogous to the Fermi glass phase of interacting fermions in a strongly disordered potential.The Bose glass phase is characterized by a finite compressibility, no gap, but an infinite superfluid susceptibility. In the presence of disorder the transition to superfluidity is argued to occur only from the Bose glass phase, and never directly from the Mott insulator. This zero-temperature superfluid-insulator transition is studied via generalizations of the Josephson scaling relation for the superfluid density at the ordinary \ensuremath{\lambda} transition, highlighting the crucial role of quantum fluctuations. The transition is found to have a dynamic critical exponent z exactly equal to d and correlation length and order-parameter correlation exponents \ensuremath{\nu} and \ensuremath{\eta} which satisfy the bounds \ensuremath{\nu}\ensuremath{\ge}2/d and \ensuremath{\eta}\ensuremath{\le}2-d, respectively. It is argued that the superfluid-insulator transition in the presence of disorder may have an upper critical dimension dc{d}_{c}dc​ which is infinite, but a perturbative renormalization-group calculation wherein the critical exponents have mean-field values for weak disorder above d=4 is also discussed. Many of these conclusions are verified by explicit calculations on a model of one-dimensional bosons in the presence of both random and periodic potentials. The general results are applied to experiments on 4He^{4}\mathrm{He}4He absorbed in porous media such as Vycor. Some measurable properties of the superfluid onset are predicted exactly [e.g., the exponent x relating the \ensuremath{\lambda} transition temperature to the zero-temperature superfluid density is found to be d/2(d-1)], while stringent bounds are placed on others. Analysis of preliminary data is consistent with these predictions.
We study the ground state phases of Bose-Fermi mixtures in one-dimensional optical lattices with quantum Monte Carlo simulations using the canonical worm algorithm. Depending on the filling of bosons and fermions, and the on-site intra- and interspecies interaction, different kinds of incompressible and superfluid phases appear. On the compressible side, correlations between bosons and fermions can lead to a distinctive behavior of the bosonic superfluid density and the fermionic stiffness, as well as of the equal-time Green functions, which allow one to identify regions where the two species exhibit anticorrelated flow. We present here complete phase diagrams for these systems at different fillings and as a function of the interaction parameters.