ORCID Profile
0000-0003-2303-7589
Current Organisation
University of Oxford
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Publisher: American Physical Society (APS)
Date: 10-08-2022
Publisher: American Physical Society (APS)
Date: 12-08-2010
Publisher: American Astronomical Society
Date: 15-03-2012
Publisher: American Physical Society (APS)
Date: 10-07-2018
Publisher: Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften
Date: 04-06-2020
DOI: 10.22331/Q-2020-06-04-278
Abstract: 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 ex le of a new model previously unknown to be solvable by free fermions.
Publisher: Springer Science and Business Media LLC
Date: 29-10-2021
Publisher: American Physical Society (APS)
Date: 15-12-2015
Location: United States of America
Location: United Kingdom of Great Britain and Northern Ireland
No related grants have been discovered for Adrian Chapman.