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

Mott insulator--to--superfluid phase transition for arbitrary dimensionality and filling in the Bose-Hubbard model

Dennis Hinrichs, Matthias Langemeyer, Niklas Teichmann, Martin Holthaus

Published Mar 21, 2009• 0 citations
OpenAlex

Abstract

We study the transition from a Mott insulator to a superfluid in the Bose-Hubbard model at zero temperature for the experimental relevant dimensionalities one, two and three, and in the mean-field limit of high dimensionalities. Converting Kato's perturbation series into an efficient numerical algorithm capable of reaching high orders, we obtain accurate critical parameters for any filling factor.

Related papers

Bose-Hubbard phase diagram with arbitrary integer filling

Niklas Teichmann, Dennis Hinrichs, Martin Holthaus +1 more

We study the transition from a Mott insulator to a superfluid in both the two- and the three-dimensional Bose-Hubbard model at zero temperature, employing the method of the effective potential. Converting Kato's perturbation series into an algorithm capable of reaching high orders, we obtain accurate critical parameters for any integer filling factor. Our technique allows us to monitor both the approach to the mean-field limit by considering spatial dimensionalities $d>3$ and to the quantum rotor limit of high filling, which refers to an array of Josephson junctions.

arXiv:0810.0643•Physical Review B•Mar 6, 2009•65 citations

Process-chain approach and its application to bosonic lattice systems

Dennis Hinrichs, Niklas Teichmann, Martin Holthaus

We study the transition from a Mott insulator to a superfluid in the Bose-Hubbard model at zero temperature for different lattice types. Converting Kato's perturbation series into an efficient numerical algorithm capable of reaching high orders, we obtain accurate critical parameters for any filling factor g and dimensionality d. Furthermore we clarify the g- and the d-dependence of the critical value and devise a method for extracting the critical value from the correlation function.

•Mar 12, 2010•0 citations

Superfluid-to-Mott-insulator transition in the one-dimensional Bose-Hubbard model for arbitrary integer filling factors

Ippei Danshita, Anatoli Polkovnikov

We study the quantum phase transition between the superfluid and the Mott insulator in the one-dimensional (1D) Bose-Hubbard model. Using the time-evolving block-decimation method, we numerically calculate the tunneling splitting of two macroscopically distinct states with different winding numbers. From the scaling of the tunneling splitting with respect to the system size, we determine the critical point of the superfluid-to-Mott-insulator transition for arbitrary integer filling factors. We find that the critical values versus the filling factor in 1D, 2D, and 3D are well approximated by a simple analytical function. We also discuss the condition for determining the transition point from a perspective of the instanton method.

arXiv:1110.4308•Physical Review A•Dec 28, 2011•40 citations

Phase diagram and thermodynamics of the three-dimensional Bose-Hubbard model

Barbara Capogrosso-Sansone, Nikolay V. Prokof'ev, Boris V. Svistunov

We report results of quantum Monte Carlo simulations of the Bose-Hubbard model in three dimensions. Critical parameters for the superfluid-to-Mott-insulator transition are determined with significantly higher accuracy than has been done in the past. In particular, the position of the critical point at filling factor $n=1$ is found to be at ${(U∕t)}_{\mathrm{c}}=29.34(2)$, and the insulating gap $\ensuremath{\Delta}$ is measured with accuracy of a few percent of the hopping amplitude $t$. We obtain the effective mass of particle and hole excitations in the insulating state---with explicit demonstration of the emerging particle-hole symmetry and relativistic dispersion law at the transition tip---along with the sound velocity in the strongly correlated superfluid phase. These parameters are the necessary ingredients to perform analytic estimates of the low temperature $(T⪡\ensuremath{\Delta})$ thermodynamics in macroscopic samples. We present accurate thermodynamic curves, including these for specific heat and entropy, for typical insulating $(U∕t=40)$ and superfluid $(t∕U=0.0385)$ phases. Our data can serve as a basis for accurate experimental thermometry, and a guide for appropriate initial conditions if one attempts to use interacting bosons in quantum information processing.

arXiv:cond-mat/0701178•Physical Review B•Apr 16, 2007•296 citations

Mott-insulator phase of the one-dimensional Bose-Hubbard model: A high-order perturbative study

Bogdan Damski, Jakub Zakrzewski

The one-dimensional Bose-Hubbard model at a unit filling factor is studied by means of a very high-order symbolic perturbative expansion. Analytical expressions are derived for the ground-state quantities such as energy per site, variance of on-site occupation, and correlation functions: $⟨{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}_{j}^{\ifmmode\dagger\else\textdagger\fi{}}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}_{j+r}⟩$ and $⟨{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{n}}_{j}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{n}}_{j+r}⟩$. These findings are compared to numerics and good agreement is found in the Mott insulator phase. Our results provide analytical approximations to important observables in the Mott phase, and are also of direct relevance to future experiments with ultracold atomic gases placed in optical lattices. We also discuss the symmetry of the Bose-Hubbard model associated with the sign change of the tunneling coupling.

arXiv:cond-mat/0603030•Physical Review A•Oct 11, 2006•38 citations

Phases and transitions in the spin-1 Bose-Hubbard model: Systematics of a mean-field theory

Ramesh V. Pai, K. Sheshadri, Rahul Anil Pandit

We generalize the mean-field theory for the spinless Bose-Hubbard model to account for the different types of superfluid phases that can arise in the spin-1 case. In particular, our mean-field theory can distinguish polar and ferromagnetic superfluids, Mott insulator, that arise at integer fillings at zero temperature, and normal Bose liquids into which the Mott insulators evolve at finite temperatures. We find, in contrast to the spinless case, that several of the superfluid-Mott insulator transitions are of first order at finite temperatures. Our systematic study yields rich phase diagrams that include first-order and second-order transitions and a variety of tricritical points. We discuss the possibility of realizing such phase diagrams in experimental systems.

arXiv:0705.2080•Physical Review B•Jan 8, 2008•67 citations
We study the transition from a Mott insulator to a superfluid in the Bose-Hubbard model at zero temperature for the experimental relevant dimensionalities one, two and three, and in the mean-field limit of high dimensionalities. Converting Kato's perturbation series into an efficient numerical algorithm capable of reaching high orders, we obtain accurate critical parameters for any filling factor.
We study the transition from a Mott insulator to a superfluid in both the two- and the three-dimensional Bose-Hubbard model at zero temperature, employing the method of the effective potential. Converting Kato's perturbation series into an algorithm capable of reaching high orders, we obtain accurate critical parameters for any integer filling factor. Our technique allows us to monitor both the approach to the mean-field limit by considering spatial dimensionalities d>3d>3d>3 and to the quantum rotor limit of high filling, which refers to an array of Josephson junctions.
We study the transition from a Mott insulator to a superfluid in the Bose-Hubbard model at zero temperature for different lattice types. Converting Kato's perturbation series into an efficient numerical algorithm capable of reaching high orders, we obtain accurate critical parameters for any filling factor g and dimensionality d. Furthermore we clarify the g- and the d-dependence of the critical value and devise a method for extracting the critical value from the correlation function.
We study the quantum phase transition between the superfluid and the Mott insulator in the one-dimensional (1D) Bose-Hubbard model. Using the time-evolving block-decimation method, we numerically calculate the tunneling splitting of two macroscopically distinct states with different winding numbers. From the scaling of the tunneling splitting with respect to the system size, we determine the critical point of the superfluid-to-Mott-insulator transition for arbitrary integer filling factors. We find that the critical values versus the filling factor in 1D, 2D, and 3D are well approximated by a simple analytical function. We also discuss the condition for determining the transition point from a perspective of the instanton method.
We report results of quantum Monte Carlo simulations of the Bose-Hubbard model in three dimensions. Critical parameters for the superfluid-to-Mott-insulator transition are determined with significantly higher accuracy than has been done in the past. In particular, the position of the critical point at filling factor n=1n=1n=1 is found to be at (U∕t)c=29.34(2){(U∕t)}_{\mathrm{c}}=29.34(2)(U∕t)c​=29.34(2), and the insulating gap $\ensuremath{\Delta}$ is measured with accuracy of a few percent of the hopping amplitude ttt. We obtain the effective mass of particle and hole excitations in the insulating state---with explicit demonstration of the emerging particle-hole symmetry and relativistic dispersion law at the transition tip---along with the sound velocity in the strongly correlated superfluid phase. These parameters are the necessary ingredients to perform analytic estimates of the low temperature $(T⪡\ensuremath{\Delta})$ thermodynamics in macroscopic samples. We present accurate thermodynamic curves, including these for specific heat and entropy, for typical insulating (U∕t=40)(U∕t=40)(U∕t=40) and superfluid (t∕U=0.0385)(t∕U=0.0385)(t∕U=0.0385) phases. Our data can serve as a basis for accurate experimental thermometry, and a guide for appropriate initial conditions if one attempts to use interacting bosons in quantum information processing.
The one-dimensional Bose-Hubbard model at a unit filling factor is studied by means of a very high-order symbolic perturbative expansion. Analytical expressions are derived for the ground-state quantities such as energy per site, variance of on-site occupation, and correlation functions: $⟨{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}_{j}^{\ifmmode\dagger\else\textdagger\fi{}}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}_{j+r}⟩$ and $⟨{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{n}}_{j}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{n}}_{j+r}⟩$. These findings are compared to numerics and good agreement is found in the Mott insulator phase. Our results provide analytical approximations to important observables in the Mott phase, and are also of direct relevance to future experiments with ultracold atomic gases placed in optical lattices. We also discuss the symmetry of the Bose-Hubbard model associated with the sign change of the tunneling coupling.
We generalize the mean-field theory for the spinless Bose-Hubbard model to account for the different types of superfluid phases that can arise in the spin-1 case. In particular, our mean-field theory can distinguish polar and ferromagnetic superfluids, Mott insulator, that arise at integer fillings at zero temperature, and normal Bose liquids into which the Mott insulators evolve at finite temperatures. We find, in contrast to the spinless case, that several of the superfluid-Mott insulator transitions are of first order at finite temperatures. Our systematic study yields rich phase diagrams that include first-order and second-order transitions and a variety of tricritical points. We discuss the possibility of realizing such phase diagrams in experimental systems.