Emergent symmetries and coexisting orders in Dirac fermion systems

TL;DR

This paper investigates the phase diagram and critical behavior of 2D Dirac fermions coupled to two order parameters, revealing emergent symmetries and continuous transitions between ordered phases through theoretical and numerical methods.

Contribution

It provides a non-perturbative analysis and quantum Monte Carlo simulations to refine understanding of emergent symmetries and phase transitions in Dirac fermion systems with multiple order parameters.

Findings

Support for robust emergent symmetry at multicritical points

Transition between ordered phases occurs via continuous transitions

Presence of coexistence regimes in the phase diagram

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 $N_2$.