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:1509.07362 · Physical review. B./Physical review. B

Competing valence bond and symmetry-breaking Mott states of spin- 32 fermions on a honeycomb lattice

Dávid Jakab, E. Szirmai, Maciej Lewenstein, Gergely Szirmai

Published Feb 29, 2016• 8 citations
arXivHTMLPDF

Abstract

We investigate magnetic properties of strongly interacting four component spin-3/2 ultracold fermionic atoms in the Mott insulator limit with one particle per site in an optical lattice with honeycomb symmetry. In this limit, atomic tunneling is virtual, and only the atomic spins can exchange. We find a competition between symmetry-breaking and liquidlike disordered phases. Particularly interesting are valence bond states with bond centered magnetizations, situated between the ferromagnetic and conventional valence bond phases. In the framework of a mean-field theory, we calculate the phase diagram and identify an experimentally relevant parameter region where a homogeneous SU(4) symmetric Affleck-Kennedy-Lieb-Tasaki--like valence bond state is present.

DOI
10.1103/physrevb.93.064434

Related papers

SU(4) Heisenberg model on the honeycomb lattice with exchange-frustrated perturbations: Implications for twistronics and Mott insulators

W. M. H. Natori, Rajah P. Nutakki, Rodrigo G. Pereira +1 more

The SU(4)-symmetric spin-orbital model on the honeycomb lattice was recently studied in connection to correlated insulators such as the ${e}_{g}$ Mott insulator ${\mathrm{Ba}}_{3}{\mathrm{CuSb}}_{2}{\mathrm{O}}_{9}$ and the insulating phase of magic-angle twisted bilayer graphene at quarter filling. Here we provide a unified discussion of these systems by investigating an extended model that includes the effects of Hund's coupling and anisotropic, orbital-dependent exchange interactions. Using a combination of mean-field theory, linear flavor-wave theory, and variational Monte Carlo, we show that this model harbors a quantum spin-orbital liquid over a wide parameter regime around the SU(4)-symmetric point. For large Hund's coupling, a ferromagnetic antiferro-orbital ordered state appears, while a valence-bond crystal combined with a vortex orbital state is stabilized by dominant orbital-dependent exchange interactions.

arXiv:1908.09224•Physical review. B./Physical review. B•Nov 21, 2019•43 citations

Mott insulating states and quantum phase transitions of correlated SU(2N) Dirac fermions

Zhichao Zhou, Da Wang, Zi Yang Meng +2 more

The interplay between charge and spin degrees of freedom in strongly correlated fermionic systems, in particular of Dirac fermions, is a long-standing problem in condensed matter physics. We investigate the competing orders in the half-filled $\mathrm{SU}(2N)$ Hubbard model on a honeycomb lattice, which can be accurately realized in optical lattices with ultracold large-spin alkaline-earth fermions. Employing large-scale projector determinant quantum Monte Carlo simulations, we have explored quantum phase transitions from the gapless Dirac semimetals to the gapped Mott insulating phases in the SU(4) and SU(6) cases. Both of these Mott insulating states are found to be columnar valence bond solid (cVBS) and to be absent of the antiferromagnetic N\'eel ordering and the loop current ordering. Inside the cVBS phases, the dimer ordering is enhanced by increasing fermion components and behaves nonmonotonically as the interaction strength increases. Although the transitions generally should be of first order due to a cubic invariance possessed by the cVBS order, the coupling to gapless Dirac fermions can soften the transitions to second order through a nonanalytic term in the free energy. Our simulations provide important guidance for the experimental explorations of novel states of matter with ultracold alkaline-earth fermions.

arXiv:1512.03994•Physical review. B./Physical review. B•Jun 29, 2016•69 citations

Phase diagram of a frustrated quantum antiferromagnet on the honeycomb lattice: Magnetic order versus valence-bond crystal formation

A. Fabricio Albuquerque, David R. Schwandt, Balázs Hetényi +3 more

We present a comprehensive computational study of the phase diagram of the frustrated $S=1/2$ Heisenberg antiferromagnet on the honeycomb lattice, with second-nearest $({J}_{2})$ and third-neighbor $({J}_{3})$ couplings. Using a combination of exact diagonalizations (EDs) of the original spin model, of the Hamiltonian projected into the nearest-neighbor short-range valence-bond basis, and of an effective quantum dimer model, as well as a self-consistent cluster mean-field theory, we determine the boundaries of several magnetically ordered phases in the region ${J}_{2},{J}_{3}\ensuremath{\in}[0,1]$, and find a sizable magnetically disordered region in between. We characterize part of this magnetically disordered phase as a plaquette valence-bond crystal phase. At larger ${J}_{2}$, we locate a sizable region in which staggered valence-bond crystal correlations are found to be important, either due to genuine valence-bond crystal (VBC) ordering or as a consequence of magnetically ordered phases, which break lattice rotational symmetry. Furthermore, we find that a particular parameter-free Gutzwiller projected tight-binding wave function has remarkably accurate energies compared to finite-size extrapolated ED energies along the transition line from conventional N\'eel to plaquette VBC phases, a fact that points to possibly interesting critical behavior---such as a deconfined critical point---across this transition. We also comment on the relevance of this spin model to model the spin liquid region found in the half filled Hubbard model on the honeycomb lattice.

arXiv:1102.5325•Physical Review B•Jul 6, 2011•204 citations

Mott insulating phases and quantum phase transitions of interacting spin- 32 fermionic cold atoms in optical lattices at half filling

Hong-Hao Tu, Guang-Ming Zhang, Lu Yu

We study various Mott insulating phases of interacting spin-$\frac{3}{2}$ fermionic ultracold atoms in two-dimensional square optical lattices at half filling. Using a generalized one-band Hubbard model with hidden SO(5) symmetry, we identify two distinct symmetry breaking phases: the degenerate antiferromagnetic spin-dipole--spin-octupole ordering and spin-quadrupole ordering, depending on the sign of the spin-dependent interaction. These two competing orders exhibit very different symmetry properties, low energy excitations, and topological characterizations. Near the SU(4) symmetric point, a quantum critical state with a $\ensuremath{\pi}$-flux phase may emerge due to strong quantum fluctuations, leading to spin algebraic correlations and gapless excitations.

arXiv:cond-mat/0703284•Physical Review B•Jul 31, 2007•14 citations

Competing chiral orders in the topological Haldane-Hubbard model of spin- 12 fermions and bosons

Ciarán Hickey, P. Rath, Arun Paramekanti

Motivated by experiments on ultracold atoms which have realized the Haldane model for a Chern insulator, we consider its strongly correlated Mott limit with spin-$\frac{1}{2}$ fermions. We find that slave rotor mean-field theory yields gapped or gapless chiral spin liquid Mott insulators. To study competing magnetic orders, we consider the strong coupling effective spin Hamiltonian which includes chiral three-spin exchange. We obtain its classical phase diagram, uncovering various chiral magnetic orders including tetrahedral, cone, and noncoplanar spiral states which can compete with putative chiral quantum spin liquids. We study the effect of thermal fluctuations on these states, identifying crossovers in the spin chirality, and phase transitions associated with lattice symmetry breaking. We also discuss analogous effective spin Hamiltonians for correlated spin-$\frac{1}{2}$ bosons. Finally, we point out possible experimental implications of our results for cold atom experiments.

arXiv:1501.01304•Physical Review B•Apr 13, 2015•36 citations

Competing chiral magnetic orders in the strongly correlated Haldane-Hubbard model

Arun Paramekanti, Ciarán Hickey, Pratik Rath

Motivated by experiments on ultracold atoms which have realized the Haldane model for a Chern insulator, we consider its strongly correlated Mott limit with spin-1/2 fermions. A slave rotor mean field theory suggests the appearance of gapped or gapless chiral spin liquid Mott insulators. To study competing magnetic orders, we consider the strong coupling effective spin Hamiltonian which includes chiral three-spin exchange. We obtain its classical phase diagram, uncovering various chiral magnetic orders including tetrahedral, cone, and noncoplanar spiral states which can compete with putative chiral quantum spin liquids. We study the effect of thermal fluctuations on these states, identifying crossovers in the spin chirality, and phase transitions associated with lattice symmetry breaking. We also discuss analogous effective spin Hamiltonians for correlated spin-1/2 bosons.

Bulletin of the American Physical Society•Jun 11, 2015•0 citations
We investigate magnetic properties of strongly interacting four component spin-3/2 ultracold fermionic atoms in the Mott insulator limit with one particle per site in an optical lattice with honeycomb symmetry. In this limit, atomic tunneling is virtual, and only the atomic spins can exchange. We find a competition between symmetry-breaking and liquidlike disordered phases. Particularly interesting are valence bond states with bond centered magnetizations, situated between the ferromagnetic and conventional valence bond phases. In the framework of a mean-field theory, we calculate the phase diagram and identify an experimentally relevant parameter region where a homogeneous SU(4) symmetric Affleck-Kennedy-Lieb-Tasaki--like valence bond state is present.
The SU(4)-symmetric spin-orbital model on the honeycomb lattice was recently studied in connection to correlated insulators such as the eg{e}_{g}eg​ Mott insulator Ba3CuSb2O9{\mathrm{Ba}}_{3}{\mathrm{CuSb}}_{2}{\mathrm{O}}_{9}Ba3​CuSb2​O9​ and the insulating phase of magic-angle twisted bilayer graphene at quarter filling. Here we provide a unified discussion of these systems by investigating an extended model that includes the effects of Hund's coupling and anisotropic, orbital-dependent exchange interactions. Using a combination of mean-field theory, linear flavor-wave theory, and variational Monte Carlo, we show that this model harbors a quantum spin-orbital liquid over a wide parameter regime around the SU(4)-symmetric point. For large Hund's coupling, a ferromagnetic antiferro-orbital ordered state appears, while a valence-bond crystal combined with a vortex orbital state is stabilized by dominant orbital-dependent exchange interactions.
The interplay between charge and spin degrees of freedom in strongly correlated fermionic systems, in particular of Dirac fermions, is a long-standing problem in condensed matter physics. We investigate the competing orders in the half-filled SU(2N)\mathrm{SU}(2N)SU(2N) Hubbard model on a honeycomb lattice, which can be accurately realized in optical lattices with ultracold large-spin alkaline-earth fermions. Employing large-scale projector determinant quantum Monte Carlo simulations, we have explored quantum phase transitions from the gapless Dirac semimetals to the gapped Mott insulating phases in the SU(4) and SU(6) cases. Both of these Mott insulating states are found to be columnar valence bond solid (cVBS) and to be absent of the antiferromagnetic N\'eel ordering and the loop current ordering. Inside the cVBS phases, the dimer ordering is enhanced by increasing fermion components and behaves nonmonotonically as the interaction strength increases. Although the transitions generally should be of first order due to a cubic invariance possessed by the cVBS order, the coupling to gapless Dirac fermions can soften the transitions to second order through a nonanalytic term in the free energy. Our simulations provide important guidance for the experimental explorations of novel states of matter with ultracold alkaline-earth fermions.
We present a comprehensive computational study of the phase diagram of the frustrated S=1/2S=1/2S=1/2 Heisenberg antiferromagnet on the honeycomb lattice, with second-nearest (J2)({J}_{2})(J2​) and third-neighbor (J3)({J}_{3})(J3​) couplings. Using a combination of exact diagonalizations (EDs) of the original spin model, of the Hamiltonian projected into the nearest-neighbor short-range valence-bond basis, and of an effective quantum dimer model, as well as a self-consistent cluster mean-field theory, we determine the boundaries of several magnetically ordered phases in the region ${J}_{2},{J}_{3}\ensuremath{\in}[0,1]$, and find a sizable magnetically disordered region in between. We characterize part of this magnetically disordered phase as a plaquette valence-bond crystal phase. At larger J2{J}_{2}J2​, we locate a sizable region in which staggered valence-bond crystal correlations are found to be important, either due to genuine valence-bond crystal (VBC) ordering or as a consequence of magnetically ordered phases, which break lattice rotational symmetry. Furthermore, we find that a particular parameter-free Gutzwiller projected tight-binding wave function has remarkably accurate energies compared to finite-size extrapolated ED energies along the transition line from conventional N\'eel to plaquette VBC phases, a fact that points to possibly interesting critical behavior---such as a deconfined critical point---across this transition. We also comment on the relevance of this spin model to model the spin liquid region found in the half filled Hubbard model on the honeycomb lattice.
We study various Mott insulating phases of interacting spin-32\frac{3}{2}23​ fermionic ultracold atoms in two-dimensional square optical lattices at half filling. Using a generalized one-band Hubbard model with hidden SO(5) symmetry, we identify two distinct symmetry breaking phases: the degenerate antiferromagnetic spin-dipole--spin-octupole ordering and spin-quadrupole ordering, depending on the sign of the spin-dependent interaction. These two competing orders exhibit very different symmetry properties, low energy excitations, and topological characterizations. Near the SU(4) symmetric point, a quantum critical state with a $\ensuremath{\pi}$-flux phase may emerge due to strong quantum fluctuations, leading to spin algebraic correlations and gapless excitations.
Motivated by experiments on ultracold atoms which have realized the Haldane model for a Chern insulator, we consider its strongly correlated Mott limit with spin-12\frac{1}{2}21​ fermions. We find that slave rotor mean-field theory yields gapped or gapless chiral spin liquid Mott insulators. To study competing magnetic orders, we consider the strong coupling effective spin Hamiltonian which includes chiral three-spin exchange. We obtain its classical phase diagram, uncovering various chiral magnetic orders including tetrahedral, cone, and noncoplanar spiral states which can compete with putative chiral quantum spin liquids. We study the effect of thermal fluctuations on these states, identifying crossovers in the spin chirality, and phase transitions associated with lattice symmetry breaking. We also discuss analogous effective spin Hamiltonians for correlated spin-12\frac{1}{2}21​ bosons. Finally, we point out possible experimental implications of our results for cold atom experiments.
Motivated by experiments on ultracold atoms which have realized the Haldane model for a Chern insulator, we consider its strongly correlated Mott limit with spin-1/2 fermions. A slave rotor mean field theory suggests the appearance of gapped or gapless chiral spin liquid Mott insulators. To study competing magnetic orders, we consider the strong coupling effective spin Hamiltonian which includes chiral three-spin exchange. We obtain its classical phase diagram, uncovering various chiral magnetic orders including tetrahedral, cone, and noncoplanar spiral states which can compete with putative chiral quantum spin liquids. We study the effect of thermal fluctuations on these states, identifying crossovers in the spin chirality, and phase transitions associated with lattice symmetry breaking. We also discuss analogous effective spin Hamiltonians for correlated spin-1/2 bosons.