Emergent symmetries and coexisting orders in Dirac fermion systems

We consider interacting $(2+1)$-dimensional Dirac fermions with competing symmetry-breaking electronic instabilities, as described by relativistic quantum field theories of the Gross-Neveu-Yukawa flavor with anticommuting mass terms. We demonstrate, using a combination of nonperturbative field-theoretical analysis and an adapted quantum Monte Carlo approach, that such systems exhibit a strong-coupling quantum multicritical fixed point with an emerging enhanced symmetry. Moreover, an extended phase coexistence regime expands out from this high-symmetry point. Our results disagree with recent results on the presence of a deconfined quantum criticality in $(2+1)$-dimensional Dirac fermions for the particular case of $O\left(3\right)$ Néel and $Z_2$ Kekulé symmetry-breaking instabilities on the graphene lattice. The robustness of these phenomena with respect to the microscopic symmetries furthermore demonstrates their relevance for a wide range of Dirac materials of current interest, from both theory and ongoing experiments.

Figure 1

Phase diagrams from FRG for $N_1=1, N_2=1$ (left), $N_1=3, N_2=1$ (middle), and $N_1=3, N_2=2$ (right). Tuning parameters $\delta m_i^2$ measure the distance from the IFP, $\mathrm{DSM}$ denotes the Dirac semimetal regime, and other phases are labeled by the broken symmetry. Solid lines are continuous transitions, and coexistence regions are shown in shaded orange. Within the white areas, the FRG flow is numerically unstable.

Figure 2

QMC phase diagram of the $O\left(3\right)\oplus {\mathbb{Z}}_2$ model $H$ in terms of the parameters $(U,1/h)$ of the underlying fermionic model ($\xi =0.5, J_I=1, t=1$). The coexistence region is shown in shaded orange. The inset shows the honeycomb lattice with the modulated pattern ${\xi }_{ij}=-\xi ,0,+\xi$ in different colors. Open (solid) circles denote Heisenberg (Ising) spins.

Figure 3

Finite-size scaling of $m_{\mathrm{H}}$ and $m_{\mathrm{I}}$ for $h$ in the transition region of $H$ for $U=7$ ($\xi =0.5, J_I=1, t=1$). Dashed lines show the asymptotic scalings $m_j\propto N_j^{-{\beta }_j/2{\nu }_j}$ for $j=\mathrm{I},\mathrm{H}$, with ${\beta }_j, {\nu }_j$ as of Ref. [69]. For clarity, the values for $m_{\mathrm{I}}$ were multiplied by a factor of 2. The lowest and highest shown values of $h$ are given, as well as the near-critical $h$ values.