https://doi.org/10.1140/epjb/s10051-025-01103-0
Research - Condensed Matter
Characterizing the phase transition of anomalous Dicke model via Loschmidt echo and studying different phases in 1D and 2D lattice structures
1
Shiyan Key Laboratory of Electromagnetic Induction and Energy Saving Technology and Shiyan Key Laboratory of Quantum Information and Precision Optics, Hubei Key Laboratory of Energy Storage and Power Battery and Hubei Key Laboratory of Automotive Power Train and Electronic Control, Hubei University of Automotive Technology, 442002, Shiyan, China
2
School of Electronic Information and Electrical Engineering, Shangluo University, 726000, Shangluo, China
3
Hubei Provincial Northwest New Energy Vehicle Industry Technology Research Institute, 442002, Shiyan, China
Received:
28
August
2025
Accepted:
22
November
2025
Published online:
6
December
2025
This paper introduces a theoretical method for characterizing the quantum phase transitions (QPTs) of the anomalous Dicke model (ADM) by employing the Loschmidt echo (LE) to access the photon number variance. The ADM features a normal phase (NP) and two superradiant phases: electric (SEP) and magnetic (SMP), respectively. We further extend the ADM to one-dimensional (1D) chain-like and two-dimensional (2D) square-like lattice structures. Analysis of the energy bands in these lattice models reveals the emergence of unstable phases, which are primarily induced by photon–photon hopping interactions between adjacent cavities, namely the dispersion relation. We map the unstable phases onto the phase diagram and analyze the boundaries between different phases, along with the properties of the energy bands within each phase region. This work provides valuable insights into the applications of QPTs and quantum manipulations through the unconventional Dicke-lattice model.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
