Kibble-Zurek Dynamics in Two-dimensional Frustrated Systems with a Neural Foundation-state Subspace Method
Abstract
Universal scaling generated when a strongly interacting quantum many-body system is driven across a continuous phase transition provides a dynamical probe of equilibrium criticality. Accessing this regime numerically in two dimensions is challenging because it requires accurate real-time evolution of correlated many-body states over many system sizes and driving rates. We introduce a Neural Foundation-state Subspace (NFS) method for near-adiabatic dynamics. A foundation neural-network quantum state represents the ground-state manifold along the driving path, and a small fidelity-selected subset defines a fixed variational subspace. The many-body Schrödinger equation then reduces to the evolution of a few linear coefficients, with projected operators reusable across ramp times. We validate the method on the two-dimensional transverse-field Ising model, recovering the expected Kibble-Zurek scaling and critical exponents in quantitative agreement with ground-state quantum Monte Carlo estimates. Applied to the frustrated square-lattice J1-J2 Heisenberg model up to 16 × 16 clusters, our approach provides strong numerical evidence of Kibble-Zurek mechanism across the Néel-to-spin-liquid transition at J2/J1=0.49, yielding ν=1.23(15) and η=0.409(19) at fixed z=1, consistent with static estimates and supporting the proposed continuous critical behavior.
Related
- Annealing Dynamics of the Two-Dimensional Fully Frustrated Ising Model
- Triplon dynamics from partial Kondo screening in frustrated heavy-fermion systems
- Dynamics of disordered quantum systems with two- and three-dimensional tensor networks
- Vestigial Nematic Order at Zero Temperature in Two-Dimensional Frustrated Quantum Antiferromagnets
- Three-Dimensional Shankar Skyrmions in Frustrated Antiferromagnets
BibTeX
@misc{mauron2026kibblezurek,
title = {{Kibble-Zurek Dynamics in Two-dimensional Frustrated Systems with a Neural Foundation-state Subspace Method}},
author = {Linda Mauron and Luciano Loris Viteritti and Zakari Denis and Riccardo Rende and Giuseppe Carleo},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05556},
eprint = {2609.05556},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05556},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Kibble-Zurek Dynamics in Two-dimensional Frustrated Systems with a Neural Foundation-state Subspace Method
AU - Linda Mauron
AU - Luciano Loris Viteritti
AU - Zakari Denis
AU - Riccardo Rende
AU - Giuseppe Carleo
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.05556
UR - https://arxiv.org/abs/2609.05556
AB - Universal scaling generated when a strongly interacting quantum many-body system is driven across a continuous phase transition provides a dynamical probe of equilibrium criticality. Accessing this regime numerically in two dimensions is challenging because it requires accurate real-time evolution of correlated many-body states over many system sizes and driving rates. We introduce a Neural Foundation-state Subspace (NFS) method for near-adiabatic dynamics. A foundation neural-network quantum state represents the ground-state manifold along the driving path, and a small fidelity-selected subset defines a fixed variational subspace. The many-body Schrödinger equation then reduces to the evolution of a few linear coefficients, with projected operators reusable across ramp times. We validate the method on the two-dimensional transverse-field Ising model, recovering the expected Kibble-Zurek scaling and critical exponents in quantitative agreement with ground-state quantum Monte Carlo estimates. Applied to the frustrated square-lattice J_1-J_2 Heisenberg model up to 16 × 16 clusters, our approach provides strong numerical evidence of Kibble-Zurek mechanism across the Néel-to-spin-liquid transition at J_2/J_1=0.49, yielding ν=1.23(15) and η=0.409(19) at fixed z=1, consistent with static estimates and supporting the proposed continuous critical behavior.
ER -