Berlin 2024 – wissenschaftliches Programm
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TT: Fachverband Tiefe Temperaturen
TT 75: Low Dimensional Systems
TT 75.6: Vortrag
Donnerstag, 21. März 2024, 16:15–16:30, H 3007
All product eigenstates in Heisenberg models from a graphical construction — •Felix Gerken1,2, Ingo Runkel3, Christoph Schweigert3, and Thore Posske1,2 — 1I. Institut für Theoretische Physik, Universität Hamburg, Germany — 2The Hamburg Centre for Ultrafast Imaging, Hamburg, Germany — 3Fachbereich Mathematik, Universität Hamburg, Germany
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. In this talk, we present a unified description of 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. The Kirchhoff rules imply a graphical construction procedure for a yet unknown class of potentially strongly, in some cases even extensively, degenerate spin models. The algebraic problem of determining the degeneracy is translated into a graph-theoretic problem. Thus, we find an intriguing connection between graph topology, degeneracy and entanglement. Further, there are hints that the degeneracy is linked to exotic condensates which could be studied in atomic gases and quantum spin lattices.
[1] F. Gerken, I. Runkel, C. Schweigert, T. Posske, arXiv:2310.13158 (2023)
Keywords: Heisenberg model; Graph theory; Product eigenstates; Degeneracy; Quantum spins