All product eigenstates in Heisenberg models from a graphical construction

• URL: http://arxiv.org/abs/2310.13158v1
• Date: Thu, 19 Oct 2023 21:13:04 GMT
• Title: All product eigenstates in Heisenberg models from a graphical construction
• Authors: Felix Gerken, Ingo Runkel, Christoph Schweigert, Thore Posske
• Abstract summary: 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.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 can be studied in atomic gases and quantum spin lattices.

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