Abstract
The quantum phase diagram and critical behavior of two-dimensional Dirac fermions coupled to two compatible order-parameter fields with $O(N_1)\oplus O(N_2)$ symmetry is investigated. Recent numerical studies of such systems have reported evidence for non-Landau-Ginzburg-Wilson transitions and emergent $O(N_1+N_2)$ symmetry between the two ordered states, which has been interpreted within a scenario of deconfined quantum criticality in (2+1)-dimensional Dirac materials. Here, we provide two theoretical approaches to refine the phase diagrams of such systems. In the immediate vicinity of the multicritical point between the ordered phases and the semimetallic phase, we employ a non-perturbative field-theoretical analysis based on the functional renormalization group. For the particular case of $N_1=3$, $N_2=1$, we perform a large-scale quantum Monte Carlo analysis of the strong-coupling region, where both orders meet. Our findings support the robust emergence of enhanced symmetry at the multicritical point and suggest the transition between the two ordered phases to take place via a sequence of continuous transitions. In particular, we find that intermediate regimes of coexistence are present in the phase diagram for all values of $N_1$ and $N_2$.
Highlights
Recent advances in the fabrication of two-dimensional electron systems, such as in twisted bilayer graphene, have exhibited the emergence of strongly correlated states [1,2], which are reminiscent of other material classes, e.g., the transition-metal oxides, where the interplay of competing electronic instabilities leads to rich phase diagrams [3,4]
In order to arrive at such general conclusions, we consider the generic case of (2+1)-dimensional Dirac fermions coupled to two order parameters (OPs) with O(N1) ⊕ O(N2) symmetry, following two different and complementary routes: the nonperturbative functional renormalization group (RG) approach (FRG) [33], and a refined quantum Monte Carlo (QMC) analysis for the model in Ref. [19]
We studied (2 + 1)-dimensional Dirac fermions coupled to two compatible OPs with O(N1) and O(N2) symmetry in the vicinity of the multicritical isotropic fixed point, providing an emergent O(N1 + N2) symmetry
Summary
Emilio Torres ,1 Lukas Weber ,2 Lukas Janssen ,3 Stefan Wessel ,2 and Michael M. Recent advances in the fabrication of two-dimensional electron systems, such as in twisted bilayer graphene, have exhibited the emergence of strongly correlated states [1,2], which are reminiscent of other material classes, e.g., the transition-metal oxides, where the interplay of competing electronic instabilities leads to rich phase diagrams [3,4] These findings have renewed interest in the symmetry-broken phases of correlated Dirac fermions, due to the evidence of gap openings near charge neutrality [5,6,7,8,9]. (ii) their relation to the apparent emergence of unconventional criticality in such systems This Rapid Communication solves both of these issues by identifying the generic features of Dirac fermions interacting with the quantum fluctuations of competing symmetrybreaking order parameters using two complementary, nonperturbative approaches. Our approach facilitates a study of the phases with broken symmetry and we find robust indications for an
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