 |
Center for Nonlinear Studies |
Finding exact solutions to spin models is a fundamental problem of many-body physics. A workhorse technique for exact solution methods is mapping to an effective description by noninteracting fermions. The paradigmatic example of this is the Jordan-Wigner transformation for finding an exact solution to the one-dimensional XY model. Another important example is the exact free-fermion solution to the two-dimensional Kitaev honeycomb model. I will describe a framework for recognizing free-fermion-solvable spin models utilizing the tools of graph theory. Our first main result relies on a connection to the graph-theoretic problem of recognizing line graphs, which has been solved optimally. This characterization reveals a complete set of frustration structures which obstruct a free-fermion solution. We further give a classification of the Pauli symmetries that can be present in spin models with such a free-fermion solution. I will next give a generalization of this result beyond the setting of the Jordan-Wigner transformation to a family of models whose associated graphs contain neither claws nor even holes. We expect this characterization to motivate a renewed exploration of free-fermion-solvable models.
Host: Gopi Muraleedharan