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arXiv:1512.03994 · Physical review. B./Physical review. B

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

Zhichao Zhou, Da Wang, Zi Yang Meng, Yu Wang, Congjun Wu

Published Jun 29, 2016• 69 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.93.245157

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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 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.
We investigate the SU(2N)\mathrm{SU}(2N)SU(2N) symmetry effects with 2N>22N>22N>2 on the two-dimensional interacting Dirac fermions at finite temperatures, including the valence-bond-solid transition, the Pomeranchuk effect, the compressibility, and the uniform spin susceptibility, by performing the determinant quantum Monte Carlo simulations of the half-filled SU(2N)\mathrm{SU}(2N)SU(2N) Hubbard model on a honeycomb lattice. The columnar valence-bond-solid (cVBS) phase only breaks the threefold discrete symmetry and thus can survive at finite temperatures. The disordered phase in the weak coupling regime is the thermal Dirac semi-metal state, while in the strong coupling regime it is largely a Mott state in which the cVBS order is thermally melted. The calculated entropy-temperature relations for various values of the Hubbard interaction UUU show that the Pomeranchuk effect occurs when the specific entropy is below a characteristic value of S∗{S}^{*}S∗---the maximal entropy per particle from the spin channel of local moments. The SU(2N)\mathrm{SU}(2N)SU(2N) symmetry enhances the Pomeranchuk effect, which facilitates the interaction-induced adiabatic cooling. Our work sheds light on future explorations of novel states of matter with ultracold large-spin alkaline fermions.
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.
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.
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 ${\ensuremath{\eta}}_{\mathrm{VBS}}=0.98\ifmmode\pm\else\textpm\fi{}0.01$.
The Hubbard model encapsulates the physics of strongly correlated quantum systems in its most basic form. It has been studied intensively in the context of the high-temperature superconductivity. A number of novel phases were recently proposed for Hubbard-like models on the honeycomb lattice, the structure of graphene. We analyzed the Hubbard model of spin- 12\frac{1}{2}21​ fermions on the honeycomb lattice at half-filling using large-scale quantum Monte Carlo simulations. We find that the weak coupling semimetal and the antiferromagnetic Mott insulator at strong interaction are separated by an extended gapped phase in an intermediate coupling regime. Exploring excitation gaps, various correlation functions as well as probing for flux quantization, we conclude that a quantum spin liquid, lacking any conventional order, emerges with local charge and spin correlations, best described by a resonating valence bonds state.