Characterization of solvable spin models via graph invariants
| Autor: | Steven T. Flammia, Adrian Chapman |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Computer Science::Machine Learning
Pure mathematics Physics and Astronomy (miscellaneous) FOS: Physical sciences Computer Science::Digital Libraries 01 natural sciences 010305 fluids & plasmas law.invention Condensed Matter - Strongly Correlated Electrons Statistics::Machine Learning symbols.namesake Operator (computer programming) Pauli exclusion principle law 0103 physical sciences Line graph 010306 general physics Mathematics Spin-½ Quantum Physics Strongly Correlated Electrons (cond-mat.str-el) Parity (physics) Fermion lcsh:QC1-999 Atomic and Molecular Physics and Optics Homogeneous space Computer Science::Mathematical Software symbols Graph (abstract data type) Quantum Physics (quant-ph) lcsh:Physics |
| Zdroj: | Quantum, Vol 4, p 278 (2020) |
| DOI: | 10.48550/arxiv.2003.05465 |
| Popis: | Exactly solvable models are essential in physics. For many-body spin-1/2 systems, an important class of such models consists of those that can be mapped to free fermions hopping on a graph. We provide a complete characterization of models which can be solved this way. Specifically, we reduce the problem of recognizing such spin models to the graph-theoretic problem of recognizing line graphs, which has been solved optimally. A corollary of our result is a complete set of constant-sized commutation structures that constitute the obstructions to a free-fermion solution. We find that symmetries are tightly constrained in these models. Pauli symmetries correspond to either: (i) cycles on the fermion hopping graph, (ii) the fermion parity operator, or (iii) logically encoded qubits. Clifford symmetries within one of these symmetry sectors, with three exceptions, must be symmetries of the free-fermion model itself. We demonstrate how several exact free-fermion solutions from the literature fit into our formalism and give an explicit example of a new model previously unknown to be solvable by free fermions. Comment: 19 pages, 4 tables, 5 figures |
| Databáze: | OpenAIRE |
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