Fates of Exact Finite-N First-Order Transitions: Coherent Suppression versus Spectral-Collapse Termination
Abstract
Symmetry-protected ground-state crossings can produce exact first-order transitions (FOTs) even at finite N, in contrast to continuous transitions governed by soft-mode criticality. We establish exact Juddian ground-state crossings for arbitrary finite N in the one- and two-photon anisotropic Dicke models and identify a common two-channel structure: the eigenvalues of the coupling matrix set the local normal-state instability thresholds, whereas its determinant fixes the exact crossing. Despite this common structure, the resulting FOTs have distinct fates determined by the bosonic response. In the one-photon model, the overlap between coherent Juddian branches vanishes in the thermodynamic or infinite frequency-ratio limits, asymptotically suppressing the FOT cusp. In the two-photon model, squeezed Juddian states lose normalizability at spectral collapse, thereby terminating the physical FOT line at finite N. Although the cusp strength tends to zero as the endpoint is approached, the terminating FOT retains a collective spectral signature: the different-parity gap is predicted to close with an N-dependent exponent μN=(2N+3)/4, one greater than the cusp termination exponent. By contrast, the same-parity soft mode retains N-independent square-root scaling and governs the critical response. Thus spectral collapse can terminate an exact finite-N FOT while preserving its collective imprint in the parity-resolved spectrum.
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BibTeX
@misc{li2026fates,
title = {{Fates of Exact Finite-$N$ First-Order Transitions: Coherent Suppression versus Spectral-Collapse Termination}},
author = {Jiong Li and Li-Wei Duan and Qing-Hu Chen and Hai-Qing Lin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27780},
eprint = {2610.27780},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27780},
}
RIS
TY - UNPB
TI - Fates of Exact Finite-N First-Order Transitions: Coherent Suppression versus Spectral-Collapse Termination
AU - Jiong Li
AU - Li-Wei Duan
AU - Qing-Hu Chen
AU - Hai-Qing Lin
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.27780
UR - https://arxiv.org/abs/2610.27780
AB - Symmetry-protected ground-state crossings can produce exact first-order transitions (FOTs) even at finite N, in contrast to continuous transitions governed by soft-mode criticality. We establish exact Juddian ground-state crossings for arbitrary finite N in the one- and two-photon anisotropic Dicke models and identify a common two-channel structure: the eigenvalues of the coupling matrix set the local normal-state instability thresholds, whereas its determinant fixes the exact crossing. Despite this common structure, the resulting FOTs have distinct fates determined by the bosonic response. In the one-photon model, the overlap between coherent Juddian branches vanishes in the thermodynamic or infinite frequency-ratio limits, asymptotically suppressing the FOT cusp. In the two-photon model, squeezed Juddian states lose normalizability at spectral collapse, thereby terminating the physical FOT line at finite N. Although the cusp strength tends to zero as the endpoint is approached, the terminating FOT retains a collective spectral signature: the different-parity gap is predicted to close with an N-dependent exponent μ_N=(2N+3)/4, one greater than the cusp termination exponent. By contrast, the same-parity soft mode retains N-independent square-root scaling and governs the critical response. Thus spectral collapse can terminate an exact finite-N FOT while preserving its collective imprint in the parity-resolved spectrum.
ER -