Quantum models with the Yang-Lee phase transition
Abstract
In this article, we present four different 1+1D quantum models that realize the Yang-Lee (YL) phase transition under a deformation that preserves PT symmetry. These are the antiferromagnetic Ising spin chain in transverse and longitudinal magnetic fields, the massive Schwinger model, the Blume-Capel model, and the three-state quantum clock model. Using the state-operator correspondence, we identify the YL critical point, compute the scaling dimensions of the lowest operators in each model, and find perfect agreement with the exact results for the YL criticality in two dimensions. Using bosonization for the Schwinger model and the Polyakov-Hubbard transformation for the other models, we show that in all of these quantum models the YL critical point is described, as expected, by a massless bosonic field with an i ϕ3 interaction. In the quantum clock model, this critical field interacts with a massive bosonic field, and we identify the massless and massive states in the Hamiltonian spectrum. In addition, we numerically compute the two-point function of ϕ at the Yang-Lee critical point and show that it grows with distance, in agreement with theoretical expectations.
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BibTeX
@misc{cruz2026quantum,
title = {{Quantum models with the Yang-Lee phase transition}},
author = {Erick Arguello Cruz and Grigory Tarnopolsky},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.19732},
eprint = {2606.19732},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.19732},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantum models with the Yang-Lee phase transition
AU - Erick Arguello Cruz
AU - Grigory Tarnopolsky
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2606.19732
UR - https://arxiv.org/abs/2606.19732
AB - In this article, we present four different 1+1D quantum models that realize the Yang-Lee (YL) phase transition under a deformation that preserves PT symmetry. These are the antiferromagnetic Ising spin chain in transverse and longitudinal magnetic fields, the massive Schwinger model, the Blume-Capel model, and the three-state quantum clock model. Using the state-operator correspondence, we identify the YL critical point, compute the scaling dimensions of the lowest operators in each model, and find perfect agreement with the exact results for the YL criticality in two dimensions. Using bosonization for the Schwinger model and the Polyakov-Hubbard transformation for the other models, we show that in all of these quantum models the YL critical point is described, as expected, by a massless bosonic field with an i ϕ^3 interaction. In the quantum clock model, this critical field interacts with a massive bosonic field, and we identify the massless and massive states in the Hamiltonian spectrum. In addition, we numerically compute the two-point function of ϕ at the Yang-Lee critical point and show that it grows with distance, in agreement with theoretical expectations.
ER -