Related papers: Closest Accessible Symmetry reduction: a tool for Hamiltonian interpolation analysis

Closest Accessible Symmetry reduction: a tool for Hamiltonian interpolation analysis

URL: http://arxiv.org/abs/2606.18161v1
Date: Tue, 16 Jun 2026 16:59:49 GMT
Title: Closest Accessible Symmetry reduction: a tool for Hamiltonian interpolation analysis
Abstract summary: We introduce a framework for analysing the spectrum of Hamiltonians without heavily relying on discretising the parameter.<n>We show that this representation captures qualitative signatures of quantum phase transitions.<n>Although motivated in spirit by adiabatic quantum computation, our approach applies more broadly to the study of Hamiltonian phase diagrams.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
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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