Non-Hermitian Strongly Interacting Dirac Fermions

Exotic quantum phases and phase transition in the strongly interacting Dirac systems have attracted tremendous interests. On the other hand, non-Hermitian physics, usually associated with dissipation arising from the coupling to environment, emerges as a frontier of modern physics in recent years. In this Letter, we investigate the interplay between non-Hermitian physics and strong correlation in Dirac-fermion systems. We generalize the projector quantum Monte-Carlo (PQMC) algorithm to the non-Hermitian interacting fermionic systems. Employing PQMC simulation, we decipher the ground-state phase diagram of the honeycomb Hubbard model with spin resolved non-Hermitian asymmetric hopping processes. The antiferromagnetic (AFM) ordering induced by Hubbard interaction is enhanced by the non-Hermitian asymmetric hopping. Combining PQMC simulation and renormalization group analysis, we reveal that the quantum phase transition between Dirac semi-metal and AFM phases belongs to Hermitian chiral XY universality class, implying that a Hermitian Gross-Neveu transition is emergent at the quantum critical point although the model is non-Hermitian.

Figure 1

(a) Schematic figure of non-Hermitian asymmetry hopping: red (blue) circles represent the sites in $A(B)$ sublattice. Only nearest-neighbor hopping is considered and $\delta$ is the asymmetric hopping amplitude. The hopping amplitude is $t-\delta (-1{)}^{\sigma }$ from the $A$ site to the $B$ site, and $t+\delta (-1{)}^{\sigma }$ from the $B$ site to the $A$ site, where $(-1{)}^{\sigma }=1(-1)$ if spin polarization of the electron is $\uparrow (\downarrow )$. (b) The ground-state phase diagram of model Eq. (1) on honeycomb lattice.

Figure 2

The log-log plot of XY-AFM static structure factor $S_{\mathrm{AFM}}^{\mathrm{XY}}$ versus Hubbard interaction $U$ close to the DSM-AFM transition: (a) $\delta =0.2$, $U_c\approx 3.8$. (b) $\delta =0.4$, $U_c\approx 3.55$. (c) $\delta =0.6$, $U_c\approx 3.16$. The largest system size is $L=24$. The more accurate results of $U_c$ are accessed from correlation-length ratio, as shown in Fig. 3. The results of $U_c$ obtained by different approaches are approximately consistent with each other. (d) XY-AFM structure factor $S_{\mathrm{AFM}}^{\mathrm{XY}}$ versus $\delta$ at fixed $U=3.6$. The results for finite size $L=12$, 15, 18, 21 and thermodynamic limit $L\to \infty$ extrapolated by the polynomial fitting of $S_{\mathrm{AFM}}^{\mathrm{XY}}$ versus $1/L$ as $S_{\mathrm{AFM}}^{\mathrm{XY}}=a+b/L^c$.

Figure 3

Correlation-length ratio for AFM order versus Hubbard interaction strength $U$ for different $\delta$. (a) $\delta =0.2$, $U_c=3.8$; (b) $\delta =0.4$, $U_c=3.55$; (c) $\delta =0.6$, $U_c=3.16$; (d) $\delta =0.8$, $U_c=2.4$.

Figure 4

Finite-size scaling analysis for the quantum critical point between DSM and AFM phases for $\delta =0.4$. (a) Log-log plot for AFM structure factors versus $1/L$ at $U_c=3.55$. The slope of the fitted line yields anomalous dimension $\eta =0.60\pm 0.03$. (b) The data collapse analysis for the rescaled AFM structure factors versus $(U/U_c-1)L^{1/\nu }$ for system sizes $L=15$, 18, 21, 24. The results of critical exponents $\eta =0.60\pm 0.03$ and $\nu =1.07\pm 0.02$ are consistent with the chiral-XY universality class within the error bar.