Collective excitations of the U (1)-symmetric exciton insulator in a cavity - Lenk, Katharina; Eckstein, Martin (Physical Review B, 2020)
We investigate the equilibrium state and the collective modes of an excitonic insulator (EI) in a Fabry-Pérot cavity. In an EI, two bands of a semiconductor or semimetal spontaneously hybridize due to the Coulomb interaction between electrons and holes, leading to the opening of a gap. The coupling to the electromagnetic field reduces the symmetry of the system with respect to phase rotations of the excitonic order parameter from U(1) to Z2. While the reduction to a discrete symmetry would, in general, lead to a gapped phase mode and enhance the stability of the ordered phase, the coupling to the cavity leaves the mean-field ground state unaffected. Its energy remains invariant under U(1) phase rotations, in spite of the lower Z2 symmetry imposed by the cavity. In a dipolar gauge, this can be traced back to the balancing of the linear light-matter coupling and the dipolar self-interaction at zero frequency. At nonzero frequency, however, the collective excitations do reflect the lower Z2 symmetry. While our model is studied using a mean-field decoupling of the light-matter approximation (which is exact in the single-mode limit), the results show that fluctuations beyond mean field could play a crucial role in finding the true phase at finite temperature.
CRIS-Team Scopus Importer:2020-12-11

Dynamical mean-field study of a photon-mediated ferroelectric phase transition - Lenk, Katharina; Li, Jiajun; Werner, Philipp; Eckstein, Martin (Physical Review B, 2022)
The interplay of light and matter gives rise to intriguing cooperative effects in quantum many-body systems. This is even true in thermal equilibrium, where the electromagnetic field can hybridize with collective modes of matter, and virtual photons can induce interactions in the solid. Here, we show how these light-mediated interactions can be treated using the dynamical mean-field theory formalism. We consider a minimal model of a two-dimensional material that couples to a surface plasmon polariton mode of a metal-dielectric interface. Within the mean-field approximation, the system exhibits a ferroelectric phase transition that is unaffected by the light-matter coupling. Bosonic dynamical mean-field theory provides a more accurate description and reveals that the photon-mediated interactions enhance the ferroelectric order and stabilize the ferroelectric phase.
CRIS-Team WoS Importer:2023-01-13

Vertex-Based Diagrammatic Treatment of Light-Matter-Coupled Systems - Kim, Aaram J.; Lenk, Katharina; Li, Jiajun; Werner, Philipp; Eckstein, Martin (Physical Review Letters, 2023)
We propose a diagrammatic Monte Carlo approach for quantum impurity models, which can be regarded as a generalization of the strong-coupling expansion for fermionic impurity models. The algorithm is based on a self-consistently computed three-point vertex and a stochastically sampled four-point vertex, and it allows one to obtain numerically exact results in a wide parameter regime. The performance of the algorithm is demonstrated with applications to a spin-boson model representing an emitter in a waveguide. As a function of the coupling strength, the spin exhibits a delocalization-localization crossover at low temperatures, signaling a qualitative change in the real-time relaxation. In certain parameter regimes, the response functions of the emitter coupled to the electromagnetic continuum can be described by an effective Rabi model with appropriately defined parameters. We also discuss the spatial distribution of the photon density around the emitter.
CRIS-Team Scopus Importer:2023-02-10