Interaction geometry and ground-state properties of sparse quantum lattice models

• URL: http://arxiv.org/abs/2606.20387v1
• Date: Thu, 18 Jun 2026 15:44:34 GMT
• Title: Interaction geometry and ground-state properties of sparse quantum lattice models
• Abstract summary: We show how symmetry and frustration in graph connectivity can drive, suppress, and reshape ground-state phase transitions.<n>We find that phase structure and criticality are governed by the same effective-geometry principle, unifying our framework for experimentally motivated long-range quantum systems.
• Score: 2.2933318919445607
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate how interaction geometry shapes the low-energy phases of sparse tunable long-range quantum models. We focus on a class of graphs whose degree grows logarithmically with system size, and show how symmetry and frustration in graph connectivity can drive, suppress, and reshape ground-state phase transitions. The central examples are power-of-$p$ graphs, where even and odd values of $p$ exhibit qualitatively distinct behaviour: even-$p$ graphs inherit the rich phase structure of the power-of-two model, while odd-$p$ graphs are governed by geometric frustration. Fibonacci graphs provide a contrasting case, lacking the discrete self-similarity of the power-of-$p$ family but exhibiting a direct geometric mapping between the short- and long-range limits. Across our models, we find that phase structure and criticality are governed by the same effective-geometry principle, unifying our framework for experimentally motivated long-range quantum systems.

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