Superradiant strongly correlated quantum states in cavity Hubbard model

Abstract

In cavity quantum materials, entangling strongly correlated electrons with quantum light provides a unique opportunity to explore novel quantum phases and phase transitions absent in conventional solid-state materials. In this study, we develop a sign-problem-free fermion-photon hybrid Quantum Monte Carlo (QMC) algorithm, and use it to systematically investigate the ground-state phase diagram of a two-dimensional cavity Hubbard model. It is shown that the interplay between the electron correlation and photon condensation gives rise to intriguing quantum phases ({\it e.g.} superradiant antiferromagnetic and chiral/$π$-flux states), and different quantum phase transitions, such as a first-order superradiant phase transition and a continuous phase transition with Gross-Neveu universality class. The methodology can be readily generalized to more complicated cavity strongly correlated models.

Figures (8)

• Figure 1: (a) Schematic illustration of a two-dimensional Hubbard model embedded in a gyrotropic cavity. (b)Ground-state phase diagram of the cavity Hubbard model in terms of light-matter coupling $g$ and Hubbard interaction $U/t$. Dashed and solid denote first-order and second-order AFM transitions, respectively. The label GNU marks the second-order phase transition with Gross-Neveu universality class.
• Figure 2: Superradiant phase transition at $U=0$. (a) Squared effective gauge flux $\langle \hat{\Phi}^2 \rangle=\frac{g^2}{N}\langle \hat{X}^2 \rangle$ per plaquette as a function of light-matter coupling $g$. The discontinuous jump at $g_c\approx 2.8$ signals a first-order photon condensation transition. (b) Edge current correlation function. The finite negative value for $g>g_c$ indicates chiral edge currents induced by the emergent magnetic flux.
• Figure 3: Effects of finite Hubbard interaction. (a) and (b) AFM structure factor $S(\pi,\pi)$ and squared effective flux $\langle \Phi^2 \rangle$ as functions of $U$ at $g = 4.0$. The simultaneous discontinuous jumps in both quantities are the hallmark of a single first-order transition. (c) Correlation-length ratio $R_s$ as a function of $U$ at $g = 6.0$ for different system sizes. The crossing of curves for different $L$, shown in the inset, signals a continuous AFM transition at $U \approx 6.4t$. (d) Squared effective flux $\langle \Phi^2 \rangle$ at $g = 6.0$, showing a first-order photon condensation transition at $U\approx 8.6t$. (e) and (f) Histogram of probability distribution of the $S(\pi,\pi)$ at $U = 6.4$ (close to the AFM transition) and $\langle \Phi^2 \rangle$ at $U = 8.15$ (close to the superradiant transition) for $L=12$ system, the former displays a unimodal distribution characteristic of a continuous (second-order) phase transition, while the latter exhibits a bimodal distribution characteristic of a first-order phase transition, $g$ is fixed as $g=6.0$ and the dashed line indicates the average value. (g) and (h) Finite-size scaling of the AFM structure factor $S(\pi,\pi)$ and the squared effective flux $\langle \Phi^2 \rangle$ for different system sizes at $g = 6.0, U=7.4$, confirming the coexistence of AFM order and photon condensation in the intermediate interaction regime.
• Figure 4: Finite-size scaling analysis of the continuous AFM transition at $g=6.0$. Data collapse of the (a) AFM structure factor $S(\pi,\pi)L^{2\beta/\nu}$ and (b) correlation-length ratio $R_s$ as functions of the scaling variable $(U/U_c-1)L^{1/\nu}$. The critical point here is $U_c\approx6.4$. The critical exponents used for the collapse, $\nu = 1.021, \beta=0.743$, are taken from the established values for the chiral Heisenberg Gross-Neveu universality class Sorella16PRX.
• Figure 5: Evolution of physical observables as a function of interaction strength $U$ for different light-matter coupling values $g=2.0, 4.0, 6.0,$ and $10.0$ (arranged from top to bottom). From left to right, each column displays: the squared effective flux $\langle\Phi^2\rangle$, the antiferromagnetic spin structure factor $S(\pi,\pi)$, and the dimensionless correlation-length ratio $R_s$. These results provide further evidence for the competition between magnetic and photonic orders across different parameter regimes.