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

APS March Meeting Abstracts

Mott transition in the square-lattice SU(4) fermionic Hubbard model with a {\pi}-flux gauge field

Zhichao Zhou, Congjun Wu, Yu Wang

Published Dec 22, 2017• 0 citations
OpenAlex

Abstract

Inspired by recent ultracold atom experiments in both the synthetic gauge field and the SU(2N) symmetry, by employing the large-scale projector quantum Monte Carlo simulations, we investigate the ground state properties of the square-lattice SU(4) fermionic Hubbard model with a {\pi}-flux gauge field. In the noninteracting limit, the ground state is the gapless Dirac semimetal. With the increase of repulsive interaction, we show that, in the presence of a {\pi}-flux gauge field per plaquette, a Mott transition occurs from the semimetal to the valence bond solid phase, accompanied by the breaking of $Z_4$ discrete symmetry. The phase transition point and the critical exponent have also been estimated by the finite size scaling of numerical data. Interestingly, in the strong coupling limit we have analyzed the role of ring exchange terms for the order formation of the ground state by perturbation theory.

Related papers

Mott transition in the π -flux SU(4) Hubbard model on a square lattice

Zhichao Zhou, Congjun Wu, Yu Wang

With increasing repulsive interaction, we show that a Mott transition occurs from the semimetal to the valence bond solid, accompanied by the ${Z}_{4}$ discrete symmetry breaking. Our simulations demonstrate the existence of a second-order phase transition, which confirms the Ginzburg-Landau analysis. The phase transition point and the critical exponent $\ensuremath{\eta}$ are also estimated. To account for the effect of a $\ensuremath{\pi}$ flux on the ordering in the strong-coupling regime, we analytically derive by the perturbation theory the ring-exchange term, which is the leading-order term that can reflect the difference between the $\ensuremath{\pi}$-flux and zero-flux $SU(4)$ Hubbard models.

arXiv:1712.08365•Physical review. B./Physical review. B•May 14, 2018•27 citations

Mott insulating states of the anisotropic SU(4) Dirac fermions

Han Xu, Yu Wang, Zhichao Zhou +1 more

We employ the large-scale quantum Monte Carlo simulations to investigate the Mott-insulating states of the half-filled SU(4) Hubbard model on the square lattice with a staggered-flux pattern. The noninteracting band structure that evolves from a nested Fermi surface at zero flux to isotropic Dirac cones at $\ensuremath{\pi}$ flux, exhibits anisotropic Dirac cones as the flux varies in between. Our simulations show transitions between the three phases of the Dirac semimetal, antiferromagnet, and valence-bond solid. A direct continuous transition between the antiferromagnetic phase and the valence-bond-solid phase is realized via varying the flux in the Mott regime. The simulated critical exponents remarkably agree with those of SU(4) $J\text{\ensuremath{-}}Q$ model. Inside the valence-bond-solid phase induced by the flux, the plaquette valence-bond state with vanishing single-particle gap is identified. At strong coupling, the valence-bond-solid phase disappears and the Mott-insulating state is always accompanied by antiferromagnetic ordering, regardless of the magnitude of the flux.

arXiv:1912.11791•Physical review. B./Physical review. B•Mar 21, 2024•5 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

Dirac fermions with plaquette interactions. I. SU(2) phase diagram with Gross-Neveu and deconfined quantum criticalities

Yuan Da Liao, Xiao Yan Xu, Zi Yang Meng +1 more

We investigate the ground state phase diagram of an extended Hubbard model with a $\ensuremath{\pi}$-flux hopping term at half filling on a square lattice, with unbiased large-scale auxiliary-field quantum Monte Carlo simulations. As a function of interaction strength, there emerges an intermediate phase which realizes two interaction-driven quantum critical points, with the first between the Dirac semimetal and an insulating phase of weak valence bond solid (VBS) order, and the second separating the VBS order and an antiferromagnetic insulating phase. These intriguing quantum critical points are respectively bestowed with Gross-Neveu and deconfined quantum criticalities, and the critical exponents ${\ensuremath{\eta}}_{\text{VBS}}=0.6(1)$ and ${\ensuremath{\eta}}_{\text{AFM}}=0.58(3)$ at a deconfined quantum critical point satisfy the conformal field theory bootstrap bound. We also investigate the dynamical properties of the spin excitation and find the spin gap open near the first transition and closed at the second. The relevance of our findings in realizing deconfined quantum criticality in fermion systems and the implication to lattice models with further extended interactions such as those in quantum moir\'e systems, are discussed.

arXiv:2204.04884•Physical review. B./Physical review. B•Aug 4, 2022•22 citations

Fermionic quantum criticality in honeycomb and π -flux Hubbard models: Finite-size scaling of renormalization-group-invariant observables from quantum Monte Carlo

Francesco Parisen Toldin, Martin Hohenadler, Fakher F. Assaad +1 more

We numerically investigate the critical behavior of the Hubbard model on the honeycomb and the $\ensuremath{\pi}$-flux lattice, which exhibits a direct transition from a Dirac semimetal to an antiferromagnetically ordered Mott insulator. We use projective auxiliary-field quantum Monte Carlo simulations and a careful finite-size scaling analysis that exploits approximately improved renormalization-group-invariant observables. This approach, which is successfully verified for the three-dimensional XY transition of the Kane-Mele-Hubbard model, allows us to extract estimates for the critical couplings and the critical exponents. The results confirm that the critical behavior for the semimetal to Mott insulator transition in the Hubbard model belongs to the Gross-Neveu-Heisenberg universality class on both lattices.

arXiv:1411.2502•Physical Review B•Apr 6, 2015•197 citations

Dirac fermions with plaquette interactions. III. SU(N) phase diagram with Gross-Neveu criticality and first-order phase transition

Yuan Da Liao, Xiao Yan Xu, Zi Yang Meng +1 more

Inspired by our recent works on SU(2) and SU(4) Dirac fermions subjected to plaquette interactions on square lattice, here we extend the large-scale quantum Monte Carlo investigations to the phase diagram of correlated Dirac fermions with SU(6) and SU(8) symmetries subjected to the plaquette interaction on the same lattice. From SU(2) to SU(8), the rich phase diagram exhibits a plethora of emerging quantum phases, such as Dirac semimetals, antiferromagnetic Mott insulators, valence bond solids (VBSs), and Dirac spin liquid and phase transitions, including Gross-Neveu chiral transitions with emergent continuous symmetry, deconfined quantum criticality, and the first-order transition between an interaction-driven columnar VBS and a plaquette VBS. These rich phenomena coming from simple-looking lattice models firmly convey the message that the interplay between the $\mathrm{SU}(N)$ Dirac fermions (with enhanced internal symmetries) and extended plaquette interactions (beyond the on-site Hubbard type) is the new playground to synthesize novel highly entangled quantum matter both at the model level and with experimental feasibilities.

arXiv:2207.13349•Physical review. B./Physical review. B•Oct 31, 2022•15 citations
Inspired by recent ultracold atom experiments in both the synthetic gauge field and the SU(2N) symmetry, by employing the large-scale projector quantum Monte Carlo simulations, we investigate the ground state properties of the square-lattice SU(4) fermionic Hubbard model with a {\pi}-flux gauge field. In the noninteracting limit, the ground state is the gapless Dirac semimetal. With the increase of repulsive interaction, we show that, in the presence of a {\pi}-flux gauge field per plaquette, a Mott transition occurs from the semimetal to the valence bond solid phase, accompanied by the breaking of Z4Z_4Z4​ discrete symmetry. The phase transition point and the critical exponent have also been estimated by the finite size scaling of numerical data. Interestingly, in the strong coupling limit we have analyzed the role of ring exchange terms for the order formation of the ground state by perturbation theory.
With increasing repulsive interaction, we show that a Mott transition occurs from the semimetal to the valence bond solid, accompanied by the Z4{Z}_{4}Z4​ discrete symmetry breaking. Our simulations demonstrate the existence of a second-order phase transition, which confirms the Ginzburg-Landau analysis. The phase transition point and the critical exponent $\ensuremath{\eta}$ are also estimated. To account for the effect of a $\ensuremath{\pi}$ flux on the ordering in the strong-coupling regime, we analytically derive by the perturbation theory the ring-exchange term, which is the leading-order term that can reflect the difference between the $\ensuremath{\pi}$-flux and zero-flux SU(4)SU(4)SU(4) Hubbard models.
We employ the large-scale quantum Monte Carlo simulations to investigate the Mott-insulating states of the half-filled SU(4) Hubbard model on the square lattice with a staggered-flux pattern. The noninteracting band structure that evolves from a nested Fermi surface at zero flux to isotropic Dirac cones at $\ensuremath{\pi}$ flux, exhibits anisotropic Dirac cones as the flux varies in between. Our simulations show transitions between the three phases of the Dirac semimetal, antiferromagnet, and valence-bond solid. A direct continuous transition between the antiferromagnetic phase and the valence-bond-solid phase is realized via varying the flux in the Mott regime. The simulated critical exponents remarkably agree with those of SU(4) $J\text{\ensuremath{-}}Q$ model. Inside the valence-bond-solid phase induced by the flux, the plaquette valence-bond state with vanishing single-particle gap is identified. At strong coupling, the valence-bond-solid phase disappears and the Mott-insulating state is always accompanied by antiferromagnetic ordering, regardless of the magnitude of the flux.
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 investigate the ground state phase diagram of an extended Hubbard model with a $\ensuremath{\pi}$-flux hopping term at half filling on a square lattice, with unbiased large-scale auxiliary-field quantum Monte Carlo simulations. As a function of interaction strength, there emerges an intermediate phase which realizes two interaction-driven quantum critical points, with the first between the Dirac semimetal and an insulating phase of weak valence bond solid (VBS) order, and the second separating the VBS order and an antiferromagnetic insulating phase. These intriguing quantum critical points are respectively bestowed with Gross-Neveu and deconfined quantum criticalities, and the critical exponents ${\ensuremath{\eta}}_{\text{VBS}}=0.6(1)$ and ${\ensuremath{\eta}}_{\text{AFM}}=0.58(3)$ at a deconfined quantum critical point satisfy the conformal field theory bootstrap bound. We also investigate the dynamical properties of the spin excitation and find the spin gap open near the first transition and closed at the second. The relevance of our findings in realizing deconfined quantum criticality in fermion systems and the implication to lattice models with further extended interactions such as those in quantum moir\'e systems, are discussed.
We numerically investigate the critical behavior of the Hubbard model on the honeycomb and the $\ensuremath{\pi}$-flux lattice, which exhibits a direct transition from a Dirac semimetal to an antiferromagnetically ordered Mott insulator. We use projective auxiliary-field quantum Monte Carlo simulations and a careful finite-size scaling analysis that exploits approximately improved renormalization-group-invariant observables. This approach, which is successfully verified for the three-dimensional XY transition of the Kane-Mele-Hubbard model, allows us to extract estimates for the critical couplings and the critical exponents. The results confirm that the critical behavior for the semimetal to Mott insulator transition in the Hubbard model belongs to the Gross-Neveu-Heisenberg universality class on both lattices.
Inspired by our recent works on SU(2) and SU(4) Dirac fermions subjected to plaquette interactions on square lattice, here we extend the large-scale quantum Monte Carlo investigations to the phase diagram of correlated Dirac fermions with SU(6) and SU(8) symmetries subjected to the plaquette interaction on the same lattice. From SU(2) to SU(8), the rich phase diagram exhibits a plethora of emerging quantum phases, such as Dirac semimetals, antiferromagnetic Mott insulators, valence bond solids (VBSs), and Dirac spin liquid and phase transitions, including Gross-Neveu chiral transitions with emergent continuous symmetry, deconfined quantum criticality, and the first-order transition between an interaction-driven columnar VBS and a plaquette VBS. These rich phenomena coming from simple-looking lattice models firmly convey the message that the interplay between the SU(N)\mathrm{SU}(N)SU(N) Dirac fermions (with enhanced internal symmetries) and extended plaquette interactions (beyond the on-site Hubbard type) is the new playground to synthesize novel highly entangled quantum matter both at the model level and with experimental feasibilities.