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:1402.4569 · Physical Review Letters

Strong Interaction Effects and Criticality of Bosons in Shaken Optical Lattices

Wei Zheng, Boyang Liu, Jiao Miao, Cheng Chin, Hui Zhai

Published Oct 10, 2014• 33 citations
arXivHTMLPDF

Abstract

We study the quantum phase transitions and identify a tricritical point between a normal Bose superfluid, a superfluid that breaks additional Z(2) Ising symmetry, and a Mott insulator in a recent shaken optical lattice experiment. We show that near the transition between normal and Z(2) symmetry breaking superfluids, bosons can condense into a momentum state with high or even locally maximum kinetic energies due to the interaction effect. We present a general low-energy effective field theory that treats both the superfluid transition and the Ising transition in a uniform framework. Using the perturbative renormalization group method, we find that the critical behavior of the quantum phase transition belongs to a universality class different from that of a dilute Bose gas.

DOI
10.1103/physrevlett.113.155303

Related papers

Quantum phase transition of bosons in a shaken optical lattice

Jiao Miao, Boyang Liu, Wei Zheng

Recently, the lattice shaking technique has been used to couple different Bloch bands resonantly. For the one-dimensional (1D) case in which shaking is along only one direction, experimental observation of domain-wall formation has been explained by superfluid Ising transition. Inspired by these, we generalize to a two-dimensional case in which shaking is along two orthogonal directions. Analogous to the 1D case, we find three different phases, the normal superfluid (NSF) phase, the ${D}_{4}$ symmetry-breaking superfluid $({D}_{4}\mathrm{SF})$ phase, and the Mott insulator (MI) phase. Furthermore, we demonstrate that an interaction effect induced by inhomogeneous band mixing can modify the critical shaking amplitude. Unlike in the 1D case, shaking types also can modify the critical shaking amplitude. We also construct a low-energy effective field theory to study the quantum criticality of bosons near the tricritical point of NSF, ${D}_{4}\mathrm{SF}$, and MI phases. Moreover, we find a Bose liquid with anisotropically algebraic order and propose to change a Bose-Einstein condensate into a noncondensed Bose liquid by tuning the shaking amplitude approaching the critical value.

arXiv:1501.04785•Physical Review A•Mar 17, 2015•11 citations

Quantum criticality of a Bose gas in an optical lattice near the Mott transition

Adam Rançon, N. Dupuis

We derive the equation of state of bosons in an optical lattice in the framework of the Bose-Hubbard model. Near the density-driven Mott transition, the expression of the pressure $P(\ensuremath{\mu},T)$ versus chemical potential and temperature is similar to that of a dilute Bose gas but with renormalized mass ${m}^{*}$ and scattering length ${a}^{*}$. Here ${m}^{*}$ is the mass of the elementary excitations at the quantum critical point governing the transition from the superfluid phase to the Mott-insulating phase, while ${a}^{*}$ is related to their effective interaction at low energy. We use a nonperturbative renormalization-group approach to compute these parameters as a function of the ratio $t/U$ between hopping amplitude and on-site repulsion.

arXiv:1107.1314•Physical Review A•Jan 4, 2012•13 citations

Extended Bose-Hubbard model in a shaken optical lattice

Jiao Miao

We study an extended Bose-Hubbard model with next-nearest-neighbor (NNN) hopping in a shaken optical lattice. We show how mean-field phase diagram evolves with the change of NNN hopping amplitude ${t}_{2}$, which can be easily tuned via shaking amplitude. As ${t}_{2}$ increases, a ${Z}_{2}$-symmetry-breaking superfluid $({Z}_{2}\mathrm{SF})$ phase emerges at the bottom of the Mott lobs. The tricritical points between normal superfluid, ${Z}_{2}\mathrm{SF}$, and Mott insulator (MI) phases are identified. We further demonstrate the tricritical point can be tuned to the tip of the Mott lobe, in which case a new critical behavior has been predicted. Within random-phase approximation, excitation spectra in the three phases are obtained, which indicate how the phase transitions occur.

arXiv:1506.04539•Physical Review A•Aug 24, 2015•4 citations

Quantum critical behavior of ultracold bosons in the two-dimensional Bose-Hubbard lattice

Ulli Pohl, Sayak Ray, Johann Kroha

We investigate the temperature-dependent behavior emerging in the vicinity of the superfluid (SF) to Mott insulator (MI) transition of interacting bosons in a two-dimensional optical lattice, described by the Bose-Hubbard model. The equilibrium phase diagram at finite temperatures is computed by means of the cluster mean-field theory (CMF) where the effect of non-local correlations is analyzed systematically by finite-size scaling of the cluster size. The phase diagram exhibits a rich structure including a transition and a crossover of the SF and MI phases respectively to a normal fluid (NF) state at finite temperature. In order to characterize these phases, and the NF transition and crossover scales, we calculate, in addition to the condensate amplitude, the superfluid fraction, sound velocity and compressibility. The phase boundaries obtained by CMF with finite-size scaling agree quantitatively with quantum Monte Carlo (QMC) results as well as with experiments. The von Neumann entanglement entropy of a cluster exhibits critical enhancement near the SF-MI quantum critical point (QCP). We also discuss the behavior of the transition lines near this QCP at the particle-hole symmetric point located at the tip of a Mott lobe as well as away from particle-hole symmetry.

•Jun 28, 2021•0 citations

Strong-coupling random-phase-approximation theory of a Bose gas near the superfluid–Mott-insulator transition: Universal thermodynamics and two-body contact

N. Dupuis, Moksh Bhateja, Adam Rançon

We present a strong-coupling expansion of the Bose-Hubbard model based on a mean-field treatment of the hopping term, while onsite fluctuations are taken into account exactly. This random phase approximation describes the universal features of the generic Mott-insulator--superfluid transition (induced by a density change) and the superfluid state near the phase transition. The critical quasiparticles at the quantum critical point have a quadratic dispersion with an effective mass ${m}^{*}$ and their mutual interaction is described by an effective $s$-wave scattering length ${a}^{*}$. The singular part of the pressure takes the same form as in a dilute Bose gas, provided we replace the boson mass $m$ and the scattering length in vacuum $a$ by ${m}^{*}$ and ${a}^{*}$, and the density $n$ by the excess density $|n\ensuremath{-}{n}_{\mathrm{MI}}|$ of particles (or holes) with respect to the Mott insulator. We define a universal two-body contact ${C}_{\mathrm{univ}}$ that controls the high-momentum tail $\ensuremath{\sim}1/{|\mathbf{k}|}^{4}$ of the singular part ${n}_{\mathbf{k}}^{\mathrm{sing}}$ of the momentum distribution. We also apply the strong-coupling RPA to a lattice model of hard-core bosons and find that the high-momentum distribution is controlled by a universal contact, in complete agreement with the Bose-Hubbard model. Finally, we discuss a continuum model of bosons in an optical lattice and define two additional two-body contacts: a short-distance universal contact ${C}_{\mathrm{univ}}^{\mathrm{sd}}$ which controls the high-momentum tail of ${n}_{\mathbf{k}}^{\mathrm{sing}}$ at scales larger than the inverse lattice spacing, and a full contact $C$, which controls the high-momentum tail of the full-momentum distribution ${n}_{\mathbf{k}}$.

arXiv:2501.14887•Physical Review A•Sep 11, 2025•2 citations

Quantum XY criticality in a two-dimensional Bose gas near the Mott transition

Adam Rançon, N. Dupuis

We derive the equation of state of a two-dimensional Bose gas in an optical lattice in the framework of the Bose-Hubbard model. We focus on the vicinity of the multicritical points where the quantum phase transition between the Mott insulator and the superfluid phase occurs at fixed density and belongs to the three-dimensional XY model universality class. Using a nonperturbative renormalization-group approach, we compute the pressure $P(μ,T)$ as a function of chemical potential and temperature. Our results compare favorably with a calculation based on the quantum O(2) model -- we find the same universal scaling function -- and allow us to determine the region of the phase diagram in the vicinity of a quantum multicritical point where the equation of state is universal. We also discuss the possible experimental observation of quantum XY criticality in a ultracold gas in an optical lattice.

arXiv:1307.3436•Europhysics Letters (EPL)•Oct 1, 2013•15 citations
We study the quantum phase transitions and identify a tricritical point between a normal Bose superfluid, a superfluid that breaks additional Z(2) Ising symmetry, and a Mott insulator in a recent shaken optical lattice experiment. We show that near the transition between normal and Z(2) symmetry breaking superfluids, bosons can condense into a momentum state with high or even locally maximum kinetic energies due to the interaction effect. We present a general low-energy effective field theory that treats both the superfluid transition and the Ising transition in a uniform framework. Using the perturbative renormalization group method, we find that the critical behavior of the quantum phase transition belongs to a universality class different from that of a dilute Bose gas.
Recently, the lattice shaking technique has been used to couple different Bloch bands resonantly. For the one-dimensional (1D) case in which shaking is along only one direction, experimental observation of domain-wall formation has been explained by superfluid Ising transition. Inspired by these, we generalize to a two-dimensional case in which shaking is along two orthogonal directions. Analogous to the 1D case, we find three different phases, the normal superfluid (NSF) phase, the D4{D}_{4}D4​ symmetry-breaking superfluid (D4SF)({D}_{4}\mathrm{SF})(D4​SF) phase, and the Mott insulator (MI) phase. Furthermore, we demonstrate that an interaction effect induced by inhomogeneous band mixing can modify the critical shaking amplitude. Unlike in the 1D case, shaking types also can modify the critical shaking amplitude. We also construct a low-energy effective field theory to study the quantum criticality of bosons near the tricritical point of NSF, D4SF{D}_{4}\mathrm{SF}D4​SF, and MI phases. Moreover, we find a Bose liquid with anisotropically algebraic order and propose to change a Bose-Einstein condensate into a noncondensed Bose liquid by tuning the shaking amplitude approaching the critical value.
We derive the equation of state of bosons in an optical lattice in the framework of the Bose-Hubbard model. Near the density-driven Mott transition, the expression of the pressure $P(\ensuremath{\mu},T)$ versus chemical potential and temperature is similar to that of a dilute Bose gas but with renormalized mass m∗{m}^{*}m∗ and scattering length a∗{a}^{*}a∗. Here m∗{m}^{*}m∗ is the mass of the elementary excitations at the quantum critical point governing the transition from the superfluid phase to the Mott-insulating phase, while a∗{a}^{*}a∗ is related to their effective interaction at low energy. We use a nonperturbative renormalization-group approach to compute these parameters as a function of the ratio t/Ut/Ut/U between hopping amplitude and on-site repulsion.
We study an extended Bose-Hubbard model with next-nearest-neighbor (NNN) hopping in a shaken optical lattice. We show how mean-field phase diagram evolves with the change of NNN hopping amplitude t2{t}_{2}t2​, which can be easily tuned via shaking amplitude. As t2{t}_{2}t2​ increases, a Z2{Z}_{2}Z2​-symmetry-breaking superfluid (Z2SF)({Z}_{2}\mathrm{SF})(Z2​SF) phase emerges at the bottom of the Mott lobs. The tricritical points between normal superfluid, Z2SF{Z}_{2}\mathrm{SF}Z2​SF, and Mott insulator (MI) phases are identified. We further demonstrate the tricritical point can be tuned to the tip of the Mott lobe, in which case a new critical behavior has been predicted. Within random-phase approximation, excitation spectra in the three phases are obtained, which indicate how the phase transitions occur.
We investigate the temperature-dependent behavior emerging in the vicinity of the superfluid (SF) to Mott insulator (MI) transition of interacting bosons in a two-dimensional optical lattice, described by the Bose-Hubbard model. The equilibrium phase diagram at finite temperatures is computed by means of the cluster mean-field theory (CMF) where the effect of non-local correlations is analyzed systematically by finite-size scaling of the cluster size. The phase diagram exhibits a rich structure including a transition and a crossover of the SF and MI phases respectively to a normal fluid (NF) state at finite temperature. In order to characterize these phases, and the NF transition and crossover scales, we calculate, in addition to the condensate amplitude, the superfluid fraction, sound velocity and compressibility. The phase boundaries obtained by CMF with finite-size scaling agree quantitatively with quantum Monte Carlo (QMC) results as well as with experiments. The von Neumann entanglement entropy of a cluster exhibits critical enhancement near the SF-MI quantum critical point (QCP). We also discuss the behavior of the transition lines near this QCP at the particle-hole symmetric point located at the tip of a Mott lobe as well as away from particle-hole symmetry.
We present a strong-coupling expansion of the Bose-Hubbard model based on a mean-field treatment of the hopping term, while onsite fluctuations are taken into account exactly. This random phase approximation describes the universal features of the generic Mott-insulator--superfluid transition (induced by a density change) and the superfluid state near the phase transition. The critical quasiparticles at the quantum critical point have a quadratic dispersion with an effective mass m∗{m}^{*}m∗ and their mutual interaction is described by an effective sss-wave scattering length a∗{a}^{*}a∗. The singular part of the pressure takes the same form as in a dilute Bose gas, provided we replace the boson mass mmm and the scattering length in vacuum aaa by m∗{m}^{*}m∗ and a∗{a}^{*}a∗, and the density nnn by the excess density $|n\ensuremath{-}{n}_{\mathrm{MI}}|$ of particles (or holes) with respect to the Mott insulator. We define a universal two-body contact Cuniv{C}_{\mathrm{univ}}Cuniv​ that controls the high-momentum tail $\ensuremath{\sim}1/{|\mathbf{k}|}^{4}$ of the singular part nksing{n}_{\mathbf{k}}^{\mathrm{sing}}nksing​ of the momentum distribution. We also apply the strong-coupling RPA to a lattice model of hard-core bosons and find that the high-momentum distribution is controlled by a universal contact, in complete agreement with the Bose-Hubbard model. Finally, we discuss a continuum model of bosons in an optical lattice and define two additional two-body contacts: a short-distance universal contact Cunivsd{C}_{\mathrm{univ}}^{\mathrm{sd}}Cunivsd​ which controls the high-momentum tail of nksing{n}_{\mathbf{k}}^{\mathrm{sing}}nksing​ at scales larger than the inverse lattice spacing, and a full contact CCC, which controls the high-momentum tail of the full-momentum distribution nk{n}_{\mathbf{k}}nk​.
We derive the equation of state of a two-dimensional Bose gas in an optical lattice in the framework of the Bose-Hubbard model. We focus on the vicinity of the multicritical points where the quantum phase transition between the Mott insulator and the superfluid phase occurs at fixed density and belongs to the three-dimensional XY model universality class. Using a nonperturbative renormalization-group approach, we compute the pressure P(μ,T)P(μ,T)P(μ,T) as a function of chemical potential and temperature. Our results compare favorably with a calculation based on the quantum O(2) model -- we find the same universal scaling function -- and allow us to determine the region of the phase diagram in the vicinity of a quantum multicritical point where the equation of state is universal. We also discuss the possible experimental observation of quantum XY criticality in a ultracold gas in an optical lattice.