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All product eigenstates in Heisenberg models from a graphical construction

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arxiv 2310.13158 v2 pith:KPY2Y3VG submitted 2023-10-19 cond-mat.str-el quant-ph

Felix Gerken , Ingo Runkel , Christoph Schweigert , Thore Posske This is my paper · ORCID
classification cond-mat.str-elquant-ph
keywords spineigenstatesproductdegeneracyheisenberglatticesquantumsystems
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Recently, large degeneracy based on product eigenstates has been found in spin ladders, kagome-like lattices, and motif magnetism, connected to spin liquids, anyonic phases, and quantum scars. We unify these systems by a complete classification of product eigenstates of Heisenberg XXZ Hamiltonians with Dzyaloshinskii-Moriya interaction on general graphs in the form of Kirchhoff rules for spin supercurrent. By this, we construct spin systems with extensive degree of degeneracy linked to exotic condensates which could be studied in atomic gases and quantum spin lattices.

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  1. Exact Quantum Many-Body Scars in 2D Quantum Gauge Models

    cond-mat.str-el 2025-05 conditional novelty 7.0 of 10

    Exact many-body scar eigenstates of a 2D XY model are mapped via Kramers-Wannier duality to exact scars of a Z2 lattice gauge theory.

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