Closest Accessible Symmetry reduction: a tool for Hamiltonian interpolation analysis
Abstract
We introduce a framework for analysing the spectrum of Hamiltonian interpolations without heavily relying on discretising the interpolation parameter. The method is based on the concept of accessible symmetries: a problem-class-dependent family of certifiable reflections that induce bipartitions of the Hilbert space. At each step, the interpolation Hamiltonian is projected onto the sectors of the accessible symmetry that is closest to being satisfied, yielding a hierarchy of weakly coupled pseudo-eigenspaces together with explicit residual couplings between them. We show that this representation captures qualitative signatures of quantum phase transitions, provides estimates of their location, and offers insights into their nature. The quality of the approximation is controlled by the compatibility between the accessible symmetry family and the problem instance. Although motivated in spirit by adiabatic quantum computation, our approach applies more broadly to the study of Hamiltonian phase diagrams, providing a new perspective on the spectral reorganisation of many-body quantum systems.
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BibTeX
@misc{palacios2026closest,
title = {{Closest Accessible Symmetry reduction: a tool for Hamiltonian interpolation analysis}},
author = {Ana Palacios and Artur Garcia-Saez and Arnau Riera and Marta P. Estarellas},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.18161},
eprint = {2606.18161},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.18161},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Closest Accessible Symmetry reduction: a tool for Hamiltonian interpolation analysis
AU - Ana Palacios
AU - Artur Garcia-Saez
AU - Arnau Riera
AU - Marta P. Estarellas
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2606.18161
UR - https://arxiv.org/abs/2606.18161
AB - We introduce a framework for analysing the spectrum of Hamiltonian interpolations without heavily relying on discretising the interpolation parameter. The method is based on the concept of accessible symmetries: a problem-class-dependent family of certifiable reflections that induce bipartitions of the Hilbert space. At each step, the interpolation Hamiltonian is projected onto the sectors of the accessible symmetry that is closest to being satisfied, yielding a hierarchy of weakly coupled pseudo-eigenspaces together with explicit residual couplings between them. We show that this representation captures qualitative signatures of quantum phase transitions, provides estimates of their location, and offers insights into their nature. The quality of the approximation is controlled by the compatibility between the accessible symmetry family and the problem instance. Although motivated in spirit by adiabatic quantum computation, our approach applies more broadly to the study of Hamiltonian phase diagrams, providing a new perspective on the spectral reorganisation of many-body quantum systems.
ER -