Motivated by recent experimental findings of correlating insulator and superconductor behavior in twisted bilayer graphene, the authors study a cluster charge interaction model on a honeycomb lattice. The cluster charge is defined on the dual lattice of honeycomb to mimic charge centers forming a triangular lattice found in experiments. Based on unbiased sign-problem-free quantum Monte Carlo simulations, the authors determine the phase diagram for this model. It features a fermionic quantum critical point with chiral XY universality and a Kekul\'e valence bond solid phase at intermediate interaction, which may be related to the correlating insulator phase found in experiments. This is an example of the rich phases found in a simple model without artificial design.
Two-dimensional van der Waals materials offer a highly tunable platform for engineering electronic band structures and interactions. By employing techniques such as twisting, gating, or applying pressure, these systems enable precise control over the electronic excitation spectrum. In moir\'e bilayer graphene, the tunability facilitates the transition from a symmetric Dirac semimetal phase through a quantum critical point into an interaction-induced long-range ordered phase with a finite band gap. At charge neutrality, the ordered state proposed to emerge from twist-angle tuning is the Kramers intervalley-coherent insulator. In this case, the transition falls into the quantum universality class of the relativistic Gross-Neveu-XY model in
2+1 dimensions. Here, we refine estimates for the critical exponents characterizing this universality class using an expansion around the lower critical space-time dimension of two. We compute the order-parameter anomalous dimension ${\ensuremath{\eta}}_{\ensuremath{\varphi}}$ and the correlation-length exponent $\ensuremath{\nu}$ at one-loop order, and the fermion anomalous dimension ${\ensuremath{\eta}}_{\ensuremath{\psi}}$ at two-loop order. Combining these results with previous findings from the expansion around the upper critical dimension, we obtain improved estimates for the universal exponents in
2+1 dimensions via Pad\'e interpolation. For
Nf=4 four-component Dirac fermions, relevant to moir\'e bilayer graphene, we estimate $1/\ensuremath{\nu}=0.916(5), {\ensuremath{\eta}}_{\ensuremath{\varphi}}=0.926(13)$, and ${\ensuremath{\eta}}_{\ensuremath{\psi}}=0.0404(13)$. For
Nf=2, potentially relevant to recent tetralayer
WSe2 experiments, the Gross-Neveu-XY fixed point may be unstable owing to a fixed-point collision at
Nf,c, with ${N}_{\text{f,c}}=1+\sqrt{2}+\mathcal{O}(\ensuremath{\epsilon})$ in the expansion around the lower critical dimension.
Twisted bilayer graphene is an exciting platform for exploring correlated quantum phases, extremely tunable with respect to both the single-particle bands and the interaction profile of electrons. Here, we investigate the phase diagram of twisted bilayer graphene as described by an extended Hubbard model on the honeycomb lattice with two fermionic orbitals (valleys) per site. Besides the special extended cluster interaction
Q, we incorporate the effect of gating through an on-site Hubbard-interaction
U. Within quantum Monte Carlo, we find valence-bond solid, Nel-valley antiferromagnetic or charge-density wave phases. Further, we elucidate the competition of these phases by noticing that the cluster interaction induces an exotic constraint on the Hilbert space, which we dub the cluster rule, in analogy to the famous pyrochlore spin-ice rule. Formulating the perturbative Hamiltonian by projecting into the cluster-rule manifold, we perform exact diagonalization and construct the fixed-point states of the observed phases. Finally, we compute the local electron density patterns as signatures distinguishing these phases, which could be observed with scanning tunneling microscopy. Our paper capitalizes on the notion of cluster constraints in the extended Hubbard model of twisted bilayer graphene and suggests a scheme towards realization of several symmetry-breaking insulating phases in a twisted-bilayer graphene sheet.
Both insulating and conducting electronic behaviors have been experimentally seen in clean bilayer graphene samples at low temperature, and there is still no consensus on the nature of the interacting ground state at half filling and in the absence of a magnetic field. Theoretically, several possibilities for the insulating ground states have been predicted for weak interaction strength. However, a recent renormalization-group calculation on a Hubbard model for charge-neutral bilayer graphene with short-range interactions suggests the emergence of low-energy Dirac fermions that would stabilize the metallic phase for weak interactions. Using a nonperturbative projective quantum Monte Carlo, we calculate the ground state for bilayer graphene using a realistic model for the Coulomb interaction that includes both short-range and long-range contributions. We find that a finite critical on-site interaction is needed to gap bilayer graphene and the transition belongs to the Gross-Neveu universality class, thereby confirming the Hubbard model expectations even in the presence of a long-range Coulomb potential, in agreement with our theoretical analysis. In addition, we also find that the critical on-site interactions necessary to destabilize the metallic ground state decrease with increasing interlayer coupling.
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.
The rich phenomenology of twisted bilayer graphene (TBG) near the magic angle is believed to arise from electron correlations in topological flat bands.An unbiased approach to this problem is highly desirable, but also particularly challenging, given the multiple electron flavors, the topological obstruction to defining tight-binding models, and the long-ranged Coulomb interactions.While numerical simulations of realistic models have thus far been confined to zero temperature, typically excluding some spin or valley species, analytic progress has relied on fixed point models away from the realistic limit.Here, we present unbiased Monte Carlo simulations of realistic models of magic-angle TBG at charge neutrality.We establish the absence of a sign problem for this model in a momentumspace approach and describe a computationally tractable formulation that applies even on breaking chiral symmetry and including band dispersion.Our results include (i) the emergence of an insulating Kramers intervalley coherent ground state in competition with a correlated semimetal phase, (ii) detailed temperature evolution of order parameters and electronic spectral functions that reveal a "pseudogap" regime, in which gap features are established at a higher temperature than the onset of order, and (iii) predictions for electronic tunneling spectra and their evolution with temperature.Our results pave the way towards uncovering the physics of magic-angle graphene through exact simulations of over a hundred electrons across a wide temperature range.