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arXiv:2603.13657

Superradiant strongly correlated quantum states in cavity Hubbard model

Kang Wang, Wei-Xuan Chang, Cheng-Yu Bi, Zi Cai, Zi-Xiang Li

Published Mar 13, 2026• 0 citations
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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.

DOI
10.48550/arxiv.2603.13657

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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/πππ-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.
The superfluid to Mott insulator transition and the superradiant transition are textbook examples of quantum phase transition and coherent quantum optics, respectively. Recent experiments in ETH and Hamburg have succeeded in loading degenerate bosonic atomic gases in optical lattices inside a cavity, which enables the first experimental study of the interplay between these two transitions. In this Rapid Communication we present the theoretical phase diagram for the ETH Zurich experimental setup, and determine the phase boundaries and the orders of the phase transitions between the normal superfluid phase, the superfluid with superradiant light, the normal Mott insulator, and the Mott insulator with superradiant light. We find that in contrast to the second-order superradiant transition in a weakly interacting Bose condensate, strong correlations in the superfluid nearby a Mott transition can render the superradiant transition to a first-order one. Our results will stimulate further experimental studies of interactions between cavity light and strongly interacting quantum matter.
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In this thesis we apply recently developed, as well as sophisticated quantum Monte Carlo methods to numerically investigate models of strongly correlated electron systems on honeycomb structures. The latter are of particular interest owing to their unique properties when simulating electrons on them, like the relativistic dispersion, strong quantum fluctuations and their resistance against instabilities. This work covers several projects including the advancement of the weak-coupling continuous time quantum Monte Carlo and its application to zero temperature and phonons, quantum phase transitions of valence bond solids in spin-1/2 Heisenberg systems using projector quantum Monte Carlo in the valence bond basis, and the magnetic field induced transition to a canted antiferromagnet of the Hubbard model on the honeycomb lattice. The emphasis lies on two projects investigating the phase diagram of the SU(2) and the SU(N)-symmetric Hubbard model on the hexagonal lattice. At sufficiently low temperatures, condensed-matter systems tend to develop order. An exception are quantum spin-liquids, where fluctuations prevent a transition to an ordered state down to the lowest temperatures. Previously elusive in experimentally relevant microscopic two-dimensional models, we show by means of large-scale quantum Monte Carlo simulations of the SU(2) Hubbard model on the honeycomb lattice, that a quantum spin-liquid emerges between the state described by massless Dirac fermions and an antiferromagnetically ordered Mott insulator. This unexpected quantum-disordered state is found to be a short-range resonating valence bond liquid, akin to the one proposed for high temperature superconductors. Inspired by the rich phase diagrams of SU(N) models we study the SU(N)-symmetric Hubbard Heisenberg quantum antiferromagnet on the honeycomb lattice to investigate the reliability of 1/N corrections to large-N results by means of numerically exact QMC simulations. We study the melting of phases as correlations increase with decreasing N and determine whether the quantum spin liquid found in the SU(2) Hubbard model at intermediate coupling is a specific feature, or also exists in the unconstrained t-J model and higher symmetries.