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arXiv · 2608.15806

Longitudinal-Field-Driven Transition in a non-integrable Non-Hermitian Transverse-Field Ising Chain via RBMs

M. E. Ateuafack·M. R. Kamsap·J. T. Diffo·L. C. Fai·M. N. Jipdi
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Abstract

We investigate the ground-state properties and quantum critical behavior of a non-Hermitian transverse-field Ising chain subjected to longitudinal and complex transverse magnetic fields. To address this interacting many-body problem, we employ real-valued neural quantum states based on Restricted Boltzmann Machines (RBMs), optimized using Variational Monte Carlo (VMC) sampling. Spectral analysis of finite chains reveals exceptional points associated with spontaneous parity-time (PT) symmetry breaking. A real-valued RBM framework is developed to reconstruct the ground-state eigenstates of the non-Hermitian Hamiltonian. Benchmark comparisons with exact diagonalization demonstrate that the RBM approach accurately reproduces the ground-state energy, magnetization, and spin-spin correlations. Extending the analysis to larger system sizes, we identify a non-Hermitian quantum phase transition characterized by PT-symmetry breaking and the emergence of magnetic order. Our results establish real-valued neural quantum states as an efficient and scalable framework for investigating critical phenomena in interacting non-Hermitian quantum systems.

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M. E. Ateuafack, M. R. Kamsap, J. T. Diffo, L. C. Fai, M. N. Jipdi. 2026-08-16. Longitudinal-Field-Driven Transition in a non-integrable Non-Hermitian Transverse-Field Ising Chain via RBMs. https://arxiv.org/abs/2608.15806

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