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arXiv:1912.11791 · Physical review. B./Physical review. B

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

Han Xu, Yu Wang, Zhichao Zhou, Congjun Wu

Published Mar 21, 2024• 5 citations
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Abstract

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.

DOI
10.1103/physrevb.109.125136

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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 \ensuremathπ\ensuremath{\pi}\ensuremathπ 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\ensuremath-QJ\text{\ensuremath{-}}QJ\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 perform large-scale projector determinant quantum Monte Carlo simulations to study the insulating states of the half-filled SU(6) Hubbard model on the square lattice. The transition from the antiferromagnetic state to the valence bond solid state occurs as increasing the Hubbard UUU. In contrast, in the SU(2) and SU(4) cases antiferromagnetism persists throughout the entire interaction range. In the SU(6) case, antiferromagnetism starts to develop in the weak interacting regime based on the Slater mechanism of Fermi surface nesting. As UUU passes a crossover value ${U}^{*}/t\ensuremath{\approx}9$, the single-particle gap scales linearly with UUU, marking the onset of Mott physics. In the Mott regime, antiferromagnetism becomes to be suppressed as UUU increases and vanishes after UUU passes the critical value ${U}_{\mathrm{AF},\mathrm{c}}/t=13.3\ifmmode\pm\else\textpm\fi{}0.05$. The critical exponents are obtained via critical scalings as ${\ensuremath{\nu}}_{\mathrm{AF}}=0.60\ifmmode\pm\else\textpm\fi{}0.02$ and ${\ensuremath{\eta}}_{\mathrm{AF}}=0.44\ifmmode\pm\else\textpm\fi{}0.03$. As UUU further increases, the valence bond solid ordering appears exhibiting the anomalous dimension ${\ensuremath{\eta}}_{\mathrm{VBS}}=0.98\ifmmode\pm\else\textpm\fi{}0.01$.
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.
We study the quantum phases of fermions with an explicit SU(N)-symmetric, Heisenberg-like nearest-neighbor flavor exchange interaction on the honeycomb lattice at half filling. Employing projective (zero temperature) quantum Monte Carlo simulations for even values of N, we explore the evolution from a weak-coupling semimetal into the strong-coupling, insulating regime. Furthermore, we compare our numerical results to a saddle-point approximation in the large-N limit. From the large-N regime down to the SU(6) case, the insulating state is found to be a columnar valence bond crystal, with a direct transition to the semimetal at weak, finite coupling, in agreement with the mean-field result in the large-N limit. At SU(4) however, the insulator exhibits a subtly different valence bond crystal structure, stabilized by resonating valence bond plaquettes. In the SU(2) limit, our results support a direct transition between the semimetal and an antiferromagnetic insulator.
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.
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.