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:1503.04664 · New Journal of Physics

Intertwined orders from symmetry projected wavefunctions of repulsively interacting Fermi gases in optical lattices

Alexandre Leprévost, Olivier Juillet, Raymond Frésard

Published Oct 12, 2015• 11 citations
arXivHTMLPDF

Abstract

Unconventional strongly correlated phases of the repulsive Fermi–Hubbard model, which could be emulated by ultracold vapors loaded in optical lattices, are investigated by means of energy minimizations with quantum number projection before variation and without any assumed order parameter. Using a tube-like geometry of optical plaquettes to realize the four-leg ladder Hubbard Hamiltonian, we highlight the intertwining of spin-, charge-, and pair-density waves embedded in a uniform d -wave superfluid background. As the lattice filling increases, this phase emerges from homogenous states exhibiting spiral magnetism and evolves towards a doped antiferromagnet. A concomitant enhancement of long-ranged d -wave pairing correlations is also found. Numerical tests of the approach for two-dimensional clusters are carried out, too.

DOI
10.1088/1367-2630/17/10/103023

Related papers

Intertwined orders of ultracold fermions loaded in two-dimensional optical lattices

Alexandre Leprévost, Olivier Juillet, Raymond Frésard

The generic quantum phase diagram of repulsively interacting spin-1/2 ultracold atoms, moving in a two-dimensional optical lattice, is investigated by means of unbiased energy minimizations with symmetry-adapted unrestricted wavefunctions. In the strongly correlated regime, we highlight the intertwining of spin-, charge-, and pair-density waves embedded in a uniform d-wave superfluid background. As the lattice filling increases, this phase emerges from homogenous states exhibiting spiral magnetism and evolves towards a doped antiferromagnet. A concomitant enhancement of long-ranged d-wave pairing correlations is also found. Nevertheless, superfluidity is suppressed when the charge period and the inverse of the hole doping from half-filling are commensurate. Numerical tests of the approach are carried out, too.

arXiv:1503.04664?context=cond-mat.quant-gas•Mar 16, 2015•0 citations

Magnetic Order And Dimensional Crossover In Optical Lattices With Repulsive Interaction

Jie Xu

One of the most interesting and challenging problems in physics is understanding strongly correlated many-body systems, where strong interactions can yield many remarkable phenomena such as superfluidity in 4He, high-temperature superconductivity, etc. In order to attack these problems, we often need to reduce the complexity of the systems to simple models in hopes of getting better insights into the properties of the systems. The Hubbard model, the focus of this dissertation, is one of the most famous examples of such model, which describes a tunneling of electrons between nearest neighbor sites of a lattice with on-site interactions. This simple model is an important concept in condensed matter physics and provides rich understandings of electronic and magnetic properties of materials. Despite its simplicity, there is no general analytical solution to the Hubbard model beyond 1D.;The discovery of ultracold atoms and optical lattices opens up the possibility of emulating the Hubbard model in experiments. Optical lattices provide an ideal realization of the Hubbard model where relevant parameters can be tuned systematically. It makes theoretical studies of the Hubbard model increasingly attractive since a direct comparison between theoretical calculations and experimental results becomes more and more possible.;In this dissertation, the ground-state properties of the repulsive Hubbard model for weak to intermediate interaction strengths in two, three dimensions and their dimensional crossover are studied within the mean field theory. We show that the system exhibits unidirectional spin-density wave (SDW) order with antiferromagnetic correlations and a long wavelength modulation. The modulating wave is along the [0011-direction at low interaction strength U/t and along the [1111-direction at higher U/t. The evolution of the wavelength of the SDW is determined as a function of U/t, the density, and t⊥/t. With an analysis of the pairing of spins based on nesting and deformation of the Fermi surface, we discuss how these results can be rationalized and how a simple, predictive model can be constructed for the properties of the SDW states.

•Jan 1, 2013•0 citations

Repulsive fermions in optical lattices: Phase separation versus coexistence of antiferromagnetism and d -wave superfluidity

S. Y. Chang, Sandeep Pathak, Nandini Trivedi

We investigate a system of fermions on a two-dimensional optical square lattice in the strongly repulsive coupling regime. In this case, the interactions can be controlled by laser intensity as well as by Feshbach resonance. We compare the energetics of states with resonating valence bond $d$-wave superfluidity, antiferromagnetic long-range order, and a homogeneous state with coexistence of superfluidity and antiferromagnetism. Using a variational formalism, we show that the energy density of a hole ${e}_{\mathrm{hole}}(x)$ has a minimum at doping $x={x}_{c}$ that signals phase separation between the antiferromagnetic and $d$-wave paired superfluid phases. The energy of the phase-separated ground state is, however, found to be very close to that of a homogeneous state with coexisting antiferromagnetic and superfluid orders. We explore the dependence of the energy on the interaction strength and on the three-site hopping terms and compare with the nearest-neighbor hopping t-J model.

arXiv:1103.5725•Physical Review A•Jan 18, 2012•1 citation

Exotic spin, charge and pairing correlations of the two-dimensional doped Hubbard model: A symmetry-entangled mean-field approach

Olivier Juillet, Raymond Frésard

Intertwining of spin, charge, and pairing correlations in the repulsive two-dimensional Hubbard model is shown through unrestricted variational calculations, with projected wave functions free of symmetry breaking. A crossover from incommensurate antiferromagnetism to stripe order naturally emerges in the hole-doped region when increasing the on-site coupling. Although effective attractive pairing interactions are identified, they are strongly fragmented in several modes including $d$-wave pairing and more exotic channels related to an underlying stripe. We demonstrate that the entanglement of a mean-field wave function by symmetry restoration can largely account for interaction effects, and that our approach is exact for a two-site cluster.

arXiv:1208.6277•Physical Review B•Mar 25, 2013•10 citations

Hubbard-model calculations of phase separation in optical lattices

H. Heiselberg

Antiferromagnetic, Mott-insulator, $d$-wave, and gossamer superfluid phases are calculated for two-dimensional (2D) square lattices from the extended Hubbard $(t\text{\ensuremath{-}}J\text{\ensuremath{-}}U)$ model using the Gutzwiller projection method and renormalized mean-field theory. The phase separation between antiferromagnetic and $d$-wave superfluid phases is found near half filling when the on-site repulsion exceeds $U\ensuremath{\gtrsim}7.3t$ and coincides with a first-order transition in the double occupancy. The phase separation is thus predicted for 2D optical lattices with ultracold Fermi atoms whereas it is inhibited in cuprates by Coulomb frustration which instead may lead to stripes. In a confined optical lattice the resulting density distribution is discontinuous and with extended Mott plateau which enhances the antiferromagnetic phase but suppresses the superfluid phase. Observation of Mott-insulator, antiferromagnetic, stripe, and superfluid phases in density and momentum distributions and correlations is discussed.

arXiv:0811.4696•Physical Review A•Jun 5, 2009•14 citations

Exotic magnetic orders for high-spin ultracold fermions

E. Szirmai, Maciej Lewenstein

We study Hubbard models for ultracold bosonic or fermionic atoms loaded into an optical lattice. The atoms carry a high spin F> 1/2, and interact on site via strong repulsive Van der Waals forces. Making convenient rearrangements of the interaction terms, and exploiting their symmetry properties, we derive low-energy effective models with nearest-neighbor interactions, and their properties. We apply our method to F =3/2, and 5/2 fermions on two-dimensional square lattice at quarter, and 1/6 fillings, respectively, and investigate mean-field equations for repulsive couplings. We find for F =3/2 fermions that the plaquette state appearing in the highly symmetric SU (4) case does not require fine tuning, and is stable in an extended region of the phase diagram. This phase competes with an SU (2) flux state, that is always suppressed for repulsive interactions in the absence of external magnetic field. The SU (2) flux state has, however, lower energy than the plaquette phase, and stabilizes in the presence of weak applied magnetic field. For F =5/2 fermions a similar SU (2) plaquette phase is found to be the ground state without external magnetic field.

arXiv:1009.4868•Europhysics Letters (EPL)•Mar 1, 2011•34 citations
Unconventional strongly correlated phases of the repulsive Fermi–Hubbard model, which could be emulated by ultracold vapors loaded in optical lattices, are investigated by means of energy minimizations with quantum number projection before variation and without any assumed order parameter. Using a tube-like geometry of optical plaquettes to realize the four-leg ladder Hubbard Hamiltonian, we highlight the intertwining of spin-, charge-, and pair-density waves embedded in a uniform d -wave superfluid background. As the lattice filling increases, this phase emerges from homogenous states exhibiting spiral magnetism and evolves towards a doped antiferromagnet. A concomitant enhancement of long-ranged d -wave pairing correlations is also found. Numerical tests of the approach for two-dimensional clusters are carried out, too.
The generic quantum phase diagram of repulsively interacting spin-1/2 ultracold atoms, moving in a two-dimensional optical lattice, is investigated by means of unbiased energy minimizations with symmetry-adapted unrestricted wavefunctions. In the strongly correlated regime, we highlight the intertwining of spin-, charge-, and pair-density waves embedded in a uniform d-wave superfluid background. As the lattice filling increases, this phase emerges from homogenous states exhibiting spiral magnetism and evolves towards a doped antiferromagnet. A concomitant enhancement of long-ranged d-wave pairing correlations is also found. Nevertheless, superfluidity is suppressed when the charge period and the inverse of the hole doping from half-filling are commensurate. Numerical tests of the approach are carried out, too.
One of the most interesting and challenging problems in physics is understanding strongly correlated many-body systems, where strong interactions can yield many remarkable phenomena such as superfluidity in 4He, high-temperature superconductivity, etc. In order to attack these problems, we often need to reduce the complexity of the systems to simple models in hopes of getting better insights into the properties of the systems. The Hubbard model, the focus of this dissertation, is one of the most famous examples of such model, which describes a tunneling of electrons between nearest neighbor sites of a lattice with on-site interactions. This simple model is an important concept in condensed matter physics and provides rich understandings of electronic and magnetic properties of materials. Despite its simplicity, there is no general analytical solution to the Hubbard model beyond 1D.;The discovery of ultracold atoms and optical lattices opens up the possibility of emulating the Hubbard model in experiments. Optical lattices provide an ideal realization of the Hubbard model where relevant parameters can be tuned systematically. It makes theoretical studies of the Hubbard model increasingly attractive since a direct comparison between theoretical calculations and experimental results becomes more and more possible.;In this dissertation, the ground-state properties of the repulsive Hubbard model for weak to intermediate interaction strengths in two, three dimensions and their dimensional crossover are studied within the mean field theory. We show that the system exhibits unidirectional spin-density wave (SDW) order with antiferromagnetic correlations and a long wavelength modulation. The modulating wave is along the [0011-direction at low interaction strength U/t and along the [1111-direction at higher U/t. The evolution of the wavelength of the SDW is determined as a function of U/t, the density, and t⊥/t. With an analysis of the pairing of spins based on nesting and deformation of the Fermi surface, we discuss how these results can be rationalized and how a simple, predictive model can be constructed for the properties of the SDW states.
We investigate a system of fermions on a two-dimensional optical square lattice in the strongly repulsive coupling regime. In this case, the interactions can be controlled by laser intensity as well as by Feshbach resonance. We compare the energetics of states with resonating valence bond ddd-wave superfluidity, antiferromagnetic long-range order, and a homogeneous state with coexistence of superfluidity and antiferromagnetism. Using a variational formalism, we show that the energy density of a hole ehole(x){e}_{\mathrm{hole}}(x)ehole​(x) has a minimum at doping x=xcx={x}_{c}x=xc​ that signals phase separation between the antiferromagnetic and ddd-wave paired superfluid phases. The energy of the phase-separated ground state is, however, found to be very close to that of a homogeneous state with coexisting antiferromagnetic and superfluid orders. We explore the dependence of the energy on the interaction strength and on the three-site hopping terms and compare with the nearest-neighbor hopping t-J model.
Intertwining of spin, charge, and pairing correlations in the repulsive two-dimensional Hubbard model is shown through unrestricted variational calculations, with projected wave functions free of symmetry breaking. A crossover from incommensurate antiferromagnetism to stripe order naturally emerges in the hole-doped region when increasing the on-site coupling. Although effective attractive pairing interactions are identified, they are strongly fragmented in several modes including ddd-wave pairing and more exotic channels related to an underlying stripe. We demonstrate that the entanglement of a mean-field wave function by symmetry restoration can largely account for interaction effects, and that our approach is exact for a two-site cluster.
Antiferromagnetic, Mott-insulator, ddd-wave, and gossamer superfluid phases are calculated for two-dimensional (2D) square lattices from the extended Hubbard $(t\text{\ensuremath{-}}J\text{\ensuremath{-}}U)$ model using the Gutzwiller projection method and renormalized mean-field theory. The phase separation between antiferromagnetic and ddd-wave superfluid phases is found near half filling when the on-site repulsion exceeds $U\ensuremath{\gtrsim}7.3t$ and coincides with a first-order transition in the double occupancy. The phase separation is thus predicted for 2D optical lattices with ultracold Fermi atoms whereas it is inhibited in cuprates by Coulomb frustration which instead may lead to stripes. In a confined optical lattice the resulting density distribution is discontinuous and with extended Mott plateau which enhances the antiferromagnetic phase but suppresses the superfluid phase. Observation of Mott-insulator, antiferromagnetic, stripe, and superfluid phases in density and momentum distributions and correlations is discussed.
We study Hubbard models for ultracold bosonic or fermionic atoms loaded into an optical lattice. The atoms carry a high spin F> 1/2, and interact on site via strong repulsive Van der Waals forces. Making convenient rearrangements of the interaction terms, and exploiting their symmetry properties, we derive low-energy effective models with nearest-neighbor interactions, and their properties. We apply our method to F =3/2, and 5/2 fermions on two-dimensional square lattice at quarter, and 1/6 fillings, respectively, and investigate mean-field equations for repulsive couplings. We find for F =3/2 fermions that the plaquette state appearing in the highly symmetric SU (4) case does not require fine tuning, and is stable in an extended region of the phase diagram. This phase competes with an SU (2) flux state, that is always suppressed for repulsive interactions in the absence of external magnetic field. The SU (2) flux state has, however, lower energy than the plaquette phase, and stabilizes in the presence of weak applied magnetic field. For F =5/2 fermions a similar SU (2) plaquette phase is found to be the ground state without external magnetic field.