From symmetries to commutant algebras in standard Hamiltonians
نویسندگان
چکیده
In this work, we revisit several families of standard Hamiltonians that appear in the literature and discuss their symmetries conserved quantities language commutant algebras. particular, start with defined by parts are local, study algebra operators separately commute each part. The models include spin-1/2 Heisenberg model its deformations, types spinless spinful free-fermion models, Hubbard model. This enables a decomposition Hilbert space into dynamically disconnected sectors reduce to conventional quantum number for regular symmetries. addition, find examples non-standard even some simple cases, which demonstrates need enlarge usual definitions quantities. case is related decompositions via irreducible representations certain Lie groups proposed earlier works, while perspective applies more broadly, particular also arbitrary interacting models. Further, von Neumann Double Commutant Theorem (DCT) systematic construction local given symmetry or algebra, potentially eliminating "brute-force" numerical searches carried out literature, show such applications DCT. paper paves way both exact scars characterization terms symmetries, pursued parallel paper.
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ژورنال
عنوان ژورنال: Annals of Physics
سال: 2023
ISSN: ['1096-035X', '0003-4916']
DOI: https://doi.org/10.1016/j.aop.2023.169384