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:1212.2219 · Physical Review A

Scaling of the gap, fidelity susceptibility, and Bloch oscillations across the superfluid-to-Mott-insulator transition in the one-dimensional Bose-Hubbard model

Juan Carrasquilla, Salvatore R. Manmana, Marcos Rigol

Published Apr 8, 2013• 83 citations
arXivHTMLPDF

Abstract

We investigate the interaction-induced superfluid-to-Mott-insulator transition in the one-dimensional Bose-Hubbard model (BHM) for fillings $n=1$, $n=2$, and $n=3$ by studying the single-particle gap, the fidelity susceptibility, and the amplitude of Bloch oscillations via density-matrix renormalization-group methods. We apply a generic scaling procedure for the gap, which allows us to determine the critical points with very high accuracy. We also study how the fidelity susceptibility behaves across the phase transition. Furthermore, we show that in the BHM, and in a system of spinless fermions, the amplitude of Bloch oscillations after a tilt of the lattice vanishes at the critical points. This indicates that Bloch oscillations can serve as a tool to detect the transition point in ongoing experiments with ultracold gases.

DOI
10.1103/physreva.87.043606

Related papers

delity susceptibility, and Bloch oscillations across the superuid to Mott insulator transition in the one-dimensional Bose-Hubbard model

Juan Carrasquilla, Salvatore R. Manmana, Marcos Rigol

delity susceptibility, and the amplitude of Bloch oscillations via densitymatrix renormalization-group methods. We apply a generic scaling procedure for the gap, which allows us to determine the critical points with very high accuracy. We also study how the delity susceptibility behaves across the phase transition. Furthermore, we show that in the BHM, and in a system of spinless fermions, the amplitude of Bloch oscillations after a tilt of the lattice vanishes at the critical points. This indicates that Bloch oscillations can serve as a tool to detect the transition point in ongoing experiments with ultracold gases.

•Jan 1, 2013•0 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

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

Thermodynamics of a Bose gas near the superfluid–Mott-insulator transition

Adam Rançon, N. Dupuis

We study the thermodynamics near the generic (density-driven) superfluid--Mott-insulator transition in the three-dimensional Bose-Hubbard model using the nonperturbative renormalization-group approach. At low energy, the physics is controlled by the Gaussian fixed point and becomes universal. Thermodynamic quantities can then be expressed in terms of the universal scaling functions of the dilute Bose gas universality class while the microscopic physics enters only via two nonuniversal parameters, namely, the effective mass ${m}^{*}$ and the ``scattering length'' ${a}^{*}$ of the elementary excitations at the quantum critical point between the superfluid and Mott-insulating phases. A notable exception is the condensate density in the superfluid phase which is proportional to the quasiparticle weight ${Z}_{\mathrm{qp}}$ of the elementary excitations. The universal regime is defined by ${m}^{*}{a}^{*}{}^{2}T\ensuremath{\ll}1$ and ${m}^{*}{a}^{*}{}^{2}|\ensuremath{\delta}\ensuremath{\mu}|\ensuremath{\ll}1$ or, equivalently, $|\overline{n}\ensuremath{-}{\overline{n}}_{c}|{a}^{*}{}^{3}\ensuremath{\ll}1$, where $\ensuremath{\delta}\ensuremath{\mu}=\ensuremath{\mu}\ensuremath{-}{\ensuremath{\mu}}_{c}$ is the chemical potential shift from the quantum critical point $(\ensuremath{\mu}={\ensuremath{\mu}}_{c},\phantom{\rule{0.28em}{0ex}}T=0)$ and $\overline{n}\ensuremath{-}{\overline{n}}_{c}$ the doping with respect to the commensurate density ${\overline{n}}_{c}$ of the $T=0$ Mott insulator. We compute ${Z}_{\mathrm{qp}}$, ${m}^{*}$, and ${a}^{*}$ and find that they vary strongly with both the ratio $t/U$ between hopping amplitude and onsite repulsion and the value of the (commensurate) density ${\overline{n}}_{c}$. Finally, we discuss the experimental observation of universality and the measurement of ${Z}_{\mathrm{qp}}$, ${m}^{*}$, and ${a}^{*}$ in a cold-atomic gas in an optical lattice.

arXiv:1207.2053•Physical Review A•Oct 24, 2012•23 citations

Quantum phase transition of the Bose-Hubbard model with anisotropic hopping on a cubic lattice

Tao Wang, Xue‐Feng Zhang

In a quantum many-body system, dimensionality plays a critical role in determining the type of quantum phase transition. To study the quantum system during dimensional crossover, we studied the Bose-Hubbard model on a cubic lattice with anisotropic hopping by using the high-order symbolic strong-coupling expansion method. The analytic series expanded boundaries between the Mott insulator and the superfluid phase up to eighth order are calculated. The critical exponents are extracted by the Pad\'e resummation method, which clearly shows dimensional crossover behavior. Meanwhile, the critical points at commensurate filling can also be obtained, and they match well with the prediction of renormalization group theory. Finally, the scaling of the gap energy and the whole phase diagram are given, and they can be taken as the benchmark for experiment and numerical simulations in future study.

arXiv:2002.10602•Physical review. B./Physical review. B•Jul 30, 2020•1 citation
We investigate the interaction-induced superfluid-to-Mott-insulator transition in the one-dimensional Bose-Hubbard model (BHM) for fillings n=1n=1n=1, n=2n=2n=2, and n=3n=3n=3 by studying the single-particle gap, the fidelity susceptibility, and the amplitude of Bloch oscillations via density-matrix renormalization-group methods. We apply a generic scaling procedure for the gap, which allows us to determine the critical points with very high accuracy. We also study how the fidelity susceptibility behaves across the phase transition. Furthermore, we show that in the BHM, and in a system of spinless fermions, the amplitude of Bloch oscillations after a tilt of the lattice vanishes at the critical points. This indicates that Bloch oscillations can serve as a tool to detect the transition point in ongoing experiments with ultracold gases.
delity susceptibility, and the amplitude of Bloch oscillations via densitymatrix renormalization-group methods. We apply a generic scaling procedure for the gap, which allows us to determine the critical points with very high accuracy. We also study how the delity susceptibility behaves across the phase transition. Furthermore, we show that in the BHM, and in a system of spinless fermions, the amplitude of Bloch oscillations after a tilt of the lattice vanishes at the critical points. This indicates that Bloch oscillations can serve as a tool to detect the transition point in ongoing experiments with ultracold gases.
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.
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.
We study the thermodynamics near the generic (density-driven) superfluid--Mott-insulator transition in the three-dimensional Bose-Hubbard model using the nonperturbative renormalization-group approach. At low energy, the physics is controlled by the Gaussian fixed point and becomes universal. Thermodynamic quantities can then be expressed in terms of the universal scaling functions of the dilute Bose gas universality class while the microscopic physics enters only via two nonuniversal parameters, namely, the effective mass m∗{m}^{*}m∗ and the ``scattering length'' a∗{a}^{*}a∗ of the elementary excitations at the quantum critical point between the superfluid and Mott-insulating phases. A notable exception is the condensate density in the superfluid phase which is proportional to the quasiparticle weight Zqp{Z}_{\mathrm{qp}}Zqp​ of the elementary excitations. The universal regime is defined by ${m}^{*}{a}^{*}{}^{2}T\ensuremath{\ll}1$ and ${m}^{*}{a}^{*}{}^{2}|\ensuremath{\delta}\ensuremath{\mu}|\ensuremath{\ll}1$ or, equivalently, $|\overline{n}\ensuremath{-}{\overline{n}}_{c}|{a}^{*}{}^{3}\ensuremath{\ll}1$, where $\ensuremath{\delta}\ensuremath{\mu}=\ensuremath{\mu}\ensuremath{-}{\ensuremath{\mu}}_{c}$ is the chemical potential shift from the quantum critical point $(\ensuremath{\mu}={\ensuremath{\mu}}_{c},\phantom{\rule{0.28em}{0ex}}T=0)$ and $\overline{n}\ensuremath{-}{\overline{n}}_{c}$ the doping with respect to the commensurate density n‾c{\overline{n}}_{c}nc​ of the T=0T=0T=0 Mott insulator. We compute Zqp{Z}_{\mathrm{qp}}Zqp​, m∗{m}^{*}m∗, and a∗{a}^{*}a∗ and find that they vary strongly with both the ratio t/Ut/Ut/U between hopping amplitude and onsite repulsion and the value of the (commensurate) density n‾c{\overline{n}}_{c}nc​. Finally, we discuss the experimental observation of universality and the measurement of Zqp{Z}_{\mathrm{qp}}Zqp​, m∗{m}^{*}m∗, and a∗{a}^{*}a∗ in a cold-atomic gas in an optical lattice.
In a quantum many-body system, dimensionality plays a critical role in determining the type of quantum phase transition. To study the quantum system during dimensional crossover, we studied the Bose-Hubbard model on a cubic lattice with anisotropic hopping by using the high-order symbolic strong-coupling expansion method. The analytic series expanded boundaries between the Mott insulator and the superfluid phase up to eighth order are calculated. The critical exponents are extracted by the Pad\'e resummation method, which clearly shows dimensional crossover behavior. Meanwhile, the critical points at commensurate filling can also be obtained, and they match well with the prediction of renormalization group theory. Finally, the scaling of the gap energy and the whole phase diagram are given, and they can be taken as the benchmark for experiment and numerical simulations in future study.