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arXiv:2609.01340

Quantum phase transitions of the Cavity Heisenberg spin-chain

Lv-Ting Gong, Shao-Fan He, Fu-Quan Dou

quant-phSubmitted Sep 1, 2026• Announced Sep 2, 2026• 0 citations
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Abstract

The interplay between quantum criticality and ergodicity breaking constitutes a central challenge in complex quantum many-body systems. Here, we investigate ground-state quantum phase transitions (QPTs) and excited-state quantum phase transitions (ESQPTs), as well as ergodic-nonergodic transition in the cavity Heisenberg spin-chain (CHS) model. By combining quantum information measures with semiclassical fixed-point analysis, we identify a deformed phase that interpolates between the normal and superradiant phases, featuring a logarithmic nonanalyticity in the density of states (DoS) and two additional jump discontinuities. We further elucidate the spectral-structure mechanism underlying the connection between ESQPTs and the ergodic--nonergodic transition (ENET) via level statistics, participation ratios, and multifractal analysis. Our results provide a general framework for characterizing phase structures and spectral features in light--matter quantum many-body systems.

Comments
14 pages,9 figures

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We investigate the quantum phase transition (QPT) in the XXZ central spin model, which can be described as a spin-12\frac{1}{2}21​ particle coupled to NNN bath spins. In general, the QPT is supposed to occur only in the thermodynamical limit. In contrast, we present that the central spin model exhibits a normal-to-superradiant phase transition in the limit where the ratio of the transition frequency of the central spin to that of the bath spins and the number of bath spins tend to infinity. We give the low-energy effective Hamiltonian analytically in the normal phase and the superradiant phase, and we find that the longitudinal interaction $\mathrm{\ensuremath{\Delta}}$ can significantly influence the excitation number and the coherence of the ground state. These two quantities are remarkably enhanced for the negative longitudinal interaction while suppressed for the positive longitudinal interaction. In addition, the finite-size effect on the central spin model is also illustrated through the mean-field analysis. We further exploit the quantum Fisher information to characterize the QPT and propose a measurement scheme that can be applied in practice. This work builds a connection between the qubit-spin systems and the qubit-field systems, which provides a possibility for the realization of criticality-enhanced quantum sensing in central spin systems.