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arXiv:1710.03365 · Physical review. B./Physical review. B

Quantum phase transitions of multispecies Dirac fermions

Huaiming Guo, Lei Wang, Richard T. Scalettar

Published Jun 28, 2018• 16 citations
arXivHTMLPDF

Abstract

We use the determinant quantum Monte Carlo method (DQMC) to study the interaction-driven semimetal to antiferromagnetic insulator transition in a $\ensuremath{\pi}$-flux Hamiltonian with modulated hoppings, a model which has two species of Dirac fermions. It is found that the critical interaction strength ${U}_{c}$ is decreased by reducing the velocity of the outer Dirac cone, while the inner cone velocity fixes the bandwidth. Although ${U}_{c}$ is monotonic, at fixed inverse temperature $\ensuremath{\beta}$ the antiferromagnetic (AF) structure factor has a maximum as a function of the hopping modulation. We also study the corresponding strong coupling (Heisenberg model) limit, where the sublattice magnetization is enhanced by the alternation of the exchange couplings. The AF order is shown to be nonmonotonic, and maximal at an intermediate degree of anisotropy, in qualitative agreement with the Hubbard model. These results quantify the effect of the velocities on the critical interaction strength in Dirac fermion systems and enable an additional degree of control which will be useful in studying strong correlation physics in ultracold atoms in optical lattices.

DOI
10.1103/physrevb.97.235152

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We use the determinant quantum Monte Carlo method (DQMC) to study the interaction-driven semimetal to antiferromagnetic insulator transition in a \ensuremathπ\ensuremath{\pi}\ensuremathπ-flux Hamiltonian with modulated hoppings, a model which has two species of Dirac fermions. It is found that the critical interaction strength Uc{U}_{c}Uc​ is decreased by reducing the velocity of the outer Dirac cone, while the inner cone velocity fixes the bandwidth. Although Uc{U}_{c}Uc​ is monotonic, at fixed inverse temperature \ensuremathβ\ensuremath{\beta}\ensuremathβ the antiferromagnetic (AF) structure factor has a maximum as a function of the hopping modulation. We also study the corresponding strong coupling (Heisenberg model) limit, where the sublattice magnetization is enhanced by the alternation of the exchange couplings. The AF order is shown to be nonmonotonic, and maximal at an intermediate degree of anisotropy, in qualitative agreement with the Hubbard model. These results quantify the effect of the velocities on the critical interaction strength in Dirac fermion systems and enable an additional degree of control which will be useful in studying strong correlation physics in ultracold atoms in optical lattices.
We use determinant quantum Monte Carlo simulations to study the role of electron-electron interactions on three-dimensional (3D) Dirac fermions based on the $\ensuremath{\pi}$-flux model on a cubic lattice. We show that the Hubbard interaction drives the 3D Dirac semimetal to an antiferromagnetic (AF) insulator only above a finite critical interaction strength and the long-range AF order persists up to a finite temperature. We evaluate the critical interaction strength and temperatures using finite-size scaling of the spin structure factor. The critical behaviors are consistent with the (3+1)-dimensional Gross-Neveu universality class for the quantum critical point and 3D Heisenberg universality class for the thermal phase transitions. We further investigate correlation effects in the birefringent Dirac fermion system. It is found that the critical interaction strength Uc{U}_{c}Uc​ is decreased by reducing the velocity of the Dirac cone, quantifying the effect of velocity on the critical interaction strength in 3D Dirac fermion systems. Our findings unambiguously uncover correlation effects in 3D Dirac fermions and may be observed using ultracold atoms in an optical lattice.
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.
Using the determinant quantum Monte Carlo method, we investigate the antiferromagnetic phase transition that is induced by the Zeeman field in a disordered interacting two-dimensional Dirac fermion system. At a fixed interaction strength UUU, the antiferromagnetic correlation is enhanced as the magnetic field increases and, when the magnetic field is larger than a Bc(U){B}_{c}(U)Bc​(U), the antiferromagnetic correlation shall be suppressed by the increased magnetic field. The impact of Zeeman field BBB, Coulomb repulsion UUU, and disorder $\mathrm{\ensuremath{\Delta}}$ is not isolated. The intensity of magnetic field effect on the antiferromagnetic correlation shall be strongly suppressed by disorder. Differently, it will be promoted by weak interaction, but, when UUU becomes larger than Uc=4.5{U}_{c}=4.5Uc​=4.5, the increased interaction will suppress the intensity of this effect and here Uc=4.5{U}_{c}=4.5Uc​=4.5 coincides with the critical strength inducing the metal-Mott insulator transition in a clean system. Moreover, at a fixed magnetic field BBB, strong interaction shall suppress the antiferromagnetic phase rather than promote it.
We present a systematic study of the quantum phase transition from a Dirac semimetal to an antiferromagnetic Mott insulator in the honeycomb-lattice Hubbard model, using finite-temperature auxiliary-field quantum Monte Carlo (AFQMC) simulations. Given the dynamical critical exponent z=1z=1z=1 at criticality, we scale the inverse temperature βββ with the linear system size LLL, i.e., βt=Lβt=Lβt=L (with ttt as the hopping amplitude), to approach the thermodynamic and zero-temperature limits simultaneously. On the algorithmic front, we generalize the fast Fourier transform in path propagation to multi-sublattice systems and employ the delayed update technique in configuration updates to accelerate the AFQMC simulations. These advances enable us to access unprecedented system sizes of up to 352835283528 sites (with L=42L=42L=42 and βt=42βt = 42βt=42). We additionally use twist-averaged boundary conditions to reduce the finite-size effects in computed observables. On the physical side, we determine the Dirac quantum criticality via finite-size scaling analysis of the spin correlations and off-diagonal single-particle Green's function, and locate the critical point at Uc/t=3.731(4)U_c/t=3.731(4)Uc​/t=3.731(4) with the critical exponents ν=1.097(7)ν=1.097(7)ν=1.097(7), ηϕ=0.72(2)η_ϕ=0.72(2)ηϕ​=0.72(2) and ηψ=0.155(6)η_ψ=0.155(6)ηψ​=0.155(6). We further corroborate the critical point by examining several relevant quantities, including the quasiparticle weight, Fermi-liquid parameter, charge compressibility, UUU-derivative of double occupancy, and fidelity susceptibility. Our work establishes an independent benchmark for the chiral Heisenberg Gross-Neveu-Yukawa criticality in the honeycomb Hubbard model, offering a complementary perspective to previous ground-state simulations.
We present quantum Monte Carlo simulations for the chiral Heisenberg Gross-Neveu-Yukawa quantum phase transition of relativistic fermions with N=4 Dirac spinor components subject to a repulsive, local four fermion interaction in (2+1)D. Here we employ a two-dimensional lattice Hamiltonian with a single, spin-degenerate Dirac cone, which exactly reproduces a linear energy-momentum relation for all finite size lattice momenta in the absence of interactions. This allows us to significantly reduce finite size corrections compared to the widely studied honeycomb and π-flux lattices. A Hubbard term dynamically generates a mass beyond a critical coupling of U_{c}=6.76(1) as the system acquires antiferromagnetic order and SU(2) spin rotational symmetry is spontaneously broken. At the quantum phase transition, we extract a self-consistent set of critical exponents ν=0.98(1), η_{ϕ}=0.53(1), η_{ψ}=0.18(1), and β=0.75(1). We provide evidence for the continuous degradation of the quasiparticle weight of the fermionic excitations as the critical point is approached from the semimetallic phase. Finally, we study the effective "speed of light" of the low-energy relativistic description, which depends on the interaction U, but is expected to be regular across the quantum phase transition. We illustrate that the strongly coupled bosonic and fermionic excitations share a common velocity at the critical point.
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.