Universal Quantum Criticality from a Gaussian Variational Manifold
Abstract
Universal behavior at continuous phase transitions is encoded in long-wavelength fixed-point theories controlled by dimensionality and symmetries. It is a central question for which systems this universal behavior and the underlying long-wavelength description can be captured by a noninteracting theory allowing for analytical and accurate predictions. In this work we provide a systematic procedure for obtaining the best noninteracting fermionic description of a quantum phase transition through fermionic Gaussian states. We demonstrate the performance of our procedure for the interacting long-range transverse-field Ising chain. This formulation reduces the problem to a self-consistent Euler equation that yields a critical line in close agreement with independent numerical benchmarks, while its singular momentum structure provides analytic predictions for continuously varying critical properties. Yet exact diagonalization shows that Gaussian-state fidelity to the exact ground state is poorest, and non-Gaussianity strongest, near the transition. Thus, accurate predictions for critical properties can emerge from the Gaussian variational description even where its microscopic wave-function approximation is weakest.
Related
- Variational Multi-Gaussian Quantum Trajectories
- Equivalence of maximal and generic reachability for non-universal Variational Quantum Circuits
- Emergent Scaling Symmetry and Universal Interior Criticality of Scalarized Black Holes
- From Equilibrium Criticality to Universal Collective Phases through Nonreciprocal Coupling of Ordered Systems
- The Global Geometry of the Gaussian Bures Manifold: Admissible Domain, Spectral Boundary, and Asymptotic Classicality
BibTeX
@misc{khasseh2026universal,
title = {{Universal Quantum Criticality from a Gaussian Variational Manifold}},
author = {Reyhaneh Khasseh and Fabian Ballar Trigueros and Markus Heyl and M. A. Rajabpour},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26246},
eprint = {2610.26246},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26246},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Universal Quantum Criticality from a Gaussian Variational Manifold
AU - Reyhaneh Khasseh
AU - Fabian Ballar Trigueros
AU - Markus Heyl
AU - M. A. Rajabpour
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26246
UR - https://arxiv.org/abs/2610.26246
AB - Universal behavior at continuous phase transitions is encoded in long-wavelength fixed-point theories controlled by dimensionality and symmetries. It is a central question for which systems this universal behavior and the underlying long-wavelength description can be captured by a noninteracting theory allowing for analytical and accurate predictions. In this work we provide a systematic procedure for obtaining the best noninteracting fermionic description of a quantum phase transition through fermionic Gaussian states. We demonstrate the performance of our procedure for the interacting long-range transverse-field Ising chain. This formulation reduces the problem to a self-consistent Euler equation that yields a critical line in close agreement with independent numerical benchmarks, while its singular momentum structure provides analytic predictions for continuously varying critical properties. Yet exact diagonalization shows that Gaussian-state fidelity to the exact ground state is poorest, and non-Gaussianity strongest, near the transition. Thus, accurate predictions for critical properties can emerge from the Gaussian variational description even where its microscopic wave-function approximation is weakest.
ER -