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

Journal of Physics A Mathematical and Theoretical

Attaining the maximum Bose–Einstein condensation in a finite-size hard-core boson model

Elías Ríos, David M Schneider, P. Capuzzi, Diego R. Alcoba, Ofelia B. Oña, Alicia Torre, Luis Laín

Published Nov 23, 2023• 0 citations
Publisher

Abstract

Abstract We propose a model for hard-core bosons in a lattice which allows to achieve the optimal occupation number predicted by Tennie et al (2017 Phys. Rev. B 96 064502) for a finite number of sites. The model is based on an extension of the Hamiltonian of the so-called Hubbard star, whose quantum properties are studied by means of quantum information descriptors such as the von Neumann entropy and the mutual information. These metrics are analyzed as a function of the one- and two-particle reduced density matrices, allowing to explore the relationship between condensation and entanglement by means of a control parameter that, under a given limit, connects our findings with previous results. All developments comprised in this article have been derived by analytical methods.

DOI
10.1088/1751-8121/ad0f4b

Related papers

Universal upper bounds on the Bose-Einstein condensate and the Hubbard star

Felix Tennie, Vlatko Vedral, Christian Schilling

For $N$ hard-core bosons on an arbitrary lattice with $d$ sites and independent of additional interaction terms we prove that the hard-core constraint itself already enforces a universal upper bound on the Bose-Einstein condensate given by ${N}_{\text{max}}=(N/d)(d\ensuremath{-}N+1)$. This bound can only be attained for one-particle states $|\ensuremath{\varphi}\ensuremath{\rangle}$ with equal amplitudes with respect to the hard-core basis (sites) and when the corresponding $N$-particle state $|\mathrm{\ensuremath{\Psi}}\ensuremath{\rangle}$ is maximally delocalized. This result is generalized to the maximum condensate possible within a given sublattice. We observe that such maximal local condensation is only possible if the mode entanglement between the sublattice and its complement is minimal. We also show that the maximizing state $|\mathrm{\ensuremath{\Psi}}\ensuremath{\rangle}$ is related to the ground state of a bosonic ``Hubbard star'' showing Bose-Einstein condensation.

arXiv:1707.07004•Physical review. B./Physical review. B•Aug 2, 2017•14 citations

The two-state Bose-Hubbard model in the hard-core boson limit: Non-ergodicity and the Bose-Einstein condensation

Stasyuk, Stasyuk

The Bose-Einstein condensation in the hard-core boson limit (HCB) of the Bose-Hubbard model with two local states and the particle hopping in the excited band only is investigated.For the purpose of considering the nonergodicity, a single-particle spectral density is calculated in the random phase approximation by means of the temperature boson Green functions.The non-ergodic contribution to the momentum distribution function of particles (connected with the static density fluctuations) increases significantly and becomes comparable with the ergodic contribution in the superfluid phase near the tricritical point.

arXiv:1210.1424•Condensed Matter Physics•Sep 19, 2012•4 citations

Scaling of the von Neumann entropy across a finite-temperature phase transition

V. Popkov, Mario Salerno

The spectrum of the reduced density matrix and the temperature dependence of the von Neumann entropy (VNE) are analytically obtained for a system of hard-core bosons on a complete graph which exhibits a phase transition to a Bose-Einstein condensate at T = T c . It is demonstrated that the VNE undergoes a crossover from purely logarithmic at T =0 to purely linear in block size n behaviour for T ⩾ T c . For intermediate temperatures, VNE is a sum of two contributions which are interpreted as the classical (Gibbs) and the quantum (due to entanglement) parts of the von Neumann entropy.

arXiv:0804.1061•Europhysics Letters (EPL)•Oct 28, 2008•7 citations

Properties of the single-site reduced density matrix in the Bose-Bose resonance model in the ground state and in quantum quenches

Florian Dorfner, Fabian Heidrich‐Meisner

We study properties of the single-site reduced density matrix in the Bose-Bose resonance model as a function of system parameters. This model describes a single-component Bose gas with a resonant coupling to a diatomic molecular state, here defined on a lattice. A main goal is to demonstrate that the eigenstates of the single-site reduced density matrix have structures that are characteristic for the various quantum phases of this system. Since the Hamiltonian conserves only the global particle number but not the number of bosons and molecules individually, these eigenstates, referred to as optimal modes, can be nontrivial linear combinations of bare eigenstates of the molecular and boson particle number. We numerically analyze the optimal modes and their weights, the latter giving the importance of the corresponding state, in the ground state of the Bose-Bose resonance model. We find that the single-site von Neumann entropy is sensitive to the location of the phase boundaries. We explain the structure of the optimal modes and their weight spectra using perturbation theory and via a comparison to results for the single-component Bose-Hubbard model. We further study the dynamical evolution of the optimal modes and of the single-site entanglement entropy in two quantum quenches that cross phase boundaries of the model and show that these quantities are thermal in the steady state. For our numerical calculations, we use the density-matrix renormalization group method for ground-state calculations and time evolution in a Krylov subspace for the quench dynamics as well as exact diagonalization.

arXiv:1603.03592•Physical Review A•Jun 20, 2016•9 citations

Exact solution of the Bose-Hubbard model on the Bethe lattice

Guilhem Semerjian, Marco Tarzia, Francesco Zamponi

The exact solution of a quantum Bethe lattice model in the thermodynamic limit amounts to solve a functional self-consistent equation. In this paper we obtain this equation for the Bose-Hubbard model on the Bethe lattice, under two equivalent forms. The first one, based on a coherent-state path integral, leads in the large connectivity limit to the mean-field treatment of Fisher et al. [Phys. Rev. B 40, 546 (1989)] at the leading order, and to the bosonic dynamical mean field theory as a first correction, as recently derived by Byczuk and Vollhardt [Phys. Rev. B 77, 235106 (2008)]. We obtain an alternative form of the equation using the occupation number representation, which can be easily solved with an arbitrary numerical precision, for any finite connectivity. We thus compute the transition line between the superfluid and Mott insulator phases of the model, along with thermodynamic observables and the space and imaginary-time dependence of correlation functions. The finite connectivity of the Bethe lattice induces a richer physical content with respect to its infinitely connected counterpart: a notion of distance between sites of the lattice is preserved, and the bosons are still weakly mobile in the Mott insulator phase. The Bethe lattice construction can be viewed as an approximation to the finite-dimensional version of the model. We show indeed a quantitatively reasonable agreement between our predictions and the results of Quantum Monte Carlo simulations in two and three dimensions.

arXiv:0904.3075•Physical Review B•Jul 31, 2009•42 citations

Eigenstate entanglement entropy in Bose-Hubbard models

G. Medoš, L. Vidmar

While the eigenstate entanglement entropy has been extensively studied for fermionic systems, much less is known about bosonic systems. Here, we study the entanglement entropy of mid-spectrum eigenstates of Bose-Hubbard models, focusing on weakly disordered models with and without particle-number conservation, and contrasting them with the translationally-invariant model. We analyze the volume-law and O(1) contributions to the entanglement entropy via the averages over mid-spectrum eigenstates and the corresponding distributions. We derive the volume-law coefficient of the entanglement entropy by generalizing the mean-field approach from [Phys. Rev. Lett. 119, 220603 (2017)] to many-body systems with a tunable local bosonic cutoff, which agrees with previous analytical and numerical results from [Phys. Rev. B 110, 235154 (2024)]. We show that the volume-law contribution to the entanglement entropy does not change upon breaking translational invariance via on-site disorder. We then numerically study the role of the subleading O(1) contribution to the entanglement entropy. We find that, in the particle-number conserving case, it exhibits a nontrivial dependence on the particle-number density and the local bosonic cutoff, while without particle-number conservation, results suggest the emergence of a universal O(1) contribution beyond the random pure state predictions.

cond-mat.stat-mechCross-listedarXiv:2604.09180•Apr 13, 2026•0 citations
Abstract We propose a model for hard-core bosons in a lattice which allows to achieve the optimal occupation number predicted by Tennie et al (2017 Phys. Rev. B 96 064502) for a finite number of sites. The model is based on an extension of the Hamiltonian of the so-called Hubbard star, whose quantum properties are studied by means of quantum information descriptors such as the von Neumann entropy and the mutual information. These metrics are analyzed as a function of the one- and two-particle reduced density matrices, allowing to explore the relationship between condensation and entanglement by means of a control parameter that, under a given limit, connects our findings with previous results. All developments comprised in this article have been derived by analytical methods.
For NNN hard-core bosons on an arbitrary lattice with ddd sites and independent of additional interaction terms we prove that the hard-core constraint itself already enforces a universal upper bound on the Bose-Einstein condensate given by ${N}_{\text{max}}=(N/d)(d\ensuremath{-}N+1)$. This bound can only be attained for one-particle states $|\ensuremath{\varphi}\ensuremath{\rangle}$ with equal amplitudes with respect to the hard-core basis (sites) and when the corresponding NNN-particle state $|\mathrm{\ensuremath{\Psi}}\ensuremath{\rangle}$ is maximally delocalized. This result is generalized to the maximum condensate possible within a given sublattice. We observe that such maximal local condensation is only possible if the mode entanglement between the sublattice and its complement is minimal. We also show that the maximizing state $|\mathrm{\ensuremath{\Psi}}\ensuremath{\rangle}$ is related to the ground state of a bosonic ``Hubbard star'' showing Bose-Einstein condensation.
The Bose-Einstein condensation in the hard-core boson limit (HCB) of the Bose-Hubbard model with two local states and the particle hopping in the excited band only is investigated.For the purpose of considering the nonergodicity, a single-particle spectral density is calculated in the random phase approximation by means of the temperature boson Green functions.The non-ergodic contribution to the momentum distribution function of particles (connected with the static density fluctuations) increases significantly and becomes comparable with the ergodic contribution in the superfluid phase near the tricritical point.
The spectrum of the reduced density matrix and the temperature dependence of the von Neumann entropy (VNE) are analytically obtained for a system of hard-core bosons on a complete graph which exhibits a phase transition to a Bose-Einstein condensate at T = T c . It is demonstrated that the VNE undergoes a crossover from purely logarithmic at T =0 to purely linear in block size n behaviour for T ⩾ T c . For intermediate temperatures, VNE is a sum of two contributions which are interpreted as the classical (Gibbs) and the quantum (due to entanglement) parts of the von Neumann entropy.
We study properties of the single-site reduced density matrix in the Bose-Bose resonance model as a function of system parameters. This model describes a single-component Bose gas with a resonant coupling to a diatomic molecular state, here defined on a lattice. A main goal is to demonstrate that the eigenstates of the single-site reduced density matrix have structures that are characteristic for the various quantum phases of this system. Since the Hamiltonian conserves only the global particle number but not the number of bosons and molecules individually, these eigenstates, referred to as optimal modes, can be nontrivial linear combinations of bare eigenstates of the molecular and boson particle number. We numerically analyze the optimal modes and their weights, the latter giving the importance of the corresponding state, in the ground state of the Bose-Bose resonance model. We find that the single-site von Neumann entropy is sensitive to the location of the phase boundaries. We explain the structure of the optimal modes and their weight spectra using perturbation theory and via a comparison to results for the single-component Bose-Hubbard model. We further study the dynamical evolution of the optimal modes and of the single-site entanglement entropy in two quantum quenches that cross phase boundaries of the model and show that these quantities are thermal in the steady state. For our numerical calculations, we use the density-matrix renormalization group method for ground-state calculations and time evolution in a Krylov subspace for the quench dynamics as well as exact diagonalization.
The exact solution of a quantum Bethe lattice model in the thermodynamic limit amounts to solve a functional self-consistent equation. In this paper we obtain this equation for the Bose-Hubbard model on the Bethe lattice, under two equivalent forms. The first one, based on a coherent-state path integral, leads in the large connectivity limit to the mean-field treatment of Fisher et al. [Phys. Rev. B 40, 546 (1989)] at the leading order, and to the bosonic dynamical mean field theory as a first correction, as recently derived by Byczuk and Vollhardt [Phys. Rev. B 77, 235106 (2008)]. We obtain an alternative form of the equation using the occupation number representation, which can be easily solved with an arbitrary numerical precision, for any finite connectivity. We thus compute the transition line between the superfluid and Mott insulator phases of the model, along with thermodynamic observables and the space and imaginary-time dependence of correlation functions. The finite connectivity of the Bethe lattice induces a richer physical content with respect to its infinitely connected counterpart: a notion of distance between sites of the lattice is preserved, and the bosons are still weakly mobile in the Mott insulator phase. The Bethe lattice construction can be viewed as an approximation to the finite-dimensional version of the model. We show indeed a quantitatively reasonable agreement between our predictions and the results of Quantum Monte Carlo simulations in two and three dimensions.
While the eigenstate entanglement entropy has been extensively studied for fermionic systems, much less is known about bosonic systems. Here, we study the entanglement entropy of mid-spectrum eigenstates of Bose-Hubbard models, focusing on weakly disordered models with and without particle-number conservation, and contrasting them with the translationally-invariant model. We analyze the volume-law and O(1) contributions to the entanglement entropy via the averages over mid-spectrum eigenstates and the corresponding distributions. We derive the volume-law coefficient of the entanglement entropy by generalizing the mean-field approach from [Phys. Rev. Lett. 119, 220603 (2017)] to many-body systems with a tunable local bosonic cutoff, which agrees with previous analytical and numerical results from [Phys. Rev. B 110, 235154 (2024)]. We show that the volume-law contribution to the entanglement entropy does not change upon breaking translational invariance via on-site disorder. We then numerically study the role of the subleading O(1) contribution to the entanglement entropy. We find that, in the particle-number conserving case, it exhibits a nontrivial dependence on the particle-number density and the local bosonic cutoff, while without particle-number conservation, results suggest the emergence of a universal O(1) contribution beyond the random pure state predictions.