A New Graphical Method for Designing Exactly Solvable Models

Exactly solvable lattice spin models have played important roles in physics. Since Onsager’s work, some lattice spin models were exactly solved by treated as free fermion models (FFMs). For example, the one-dimensional XY model, the one-dimensional transverse field Ising model, and the Kitaev’s two-dimensional honeycomb lattice model (KHLM) can be solved in this way ([1],[2]).
Based on these facts, in this talk we will present a new method to obtain a series of solvable models that include the Jordan-Wigner transformation and the Kitaev’s method of the KHLM as special cases [3]. For any given well-behaved graphs, we can construct FFMs corresponding to them. We can also design a set of operators from them. Therefore, we can create a lot of exactly solvable Hamiltonians. By this method we will introduce new solvable models, containing three-dimensional lattice models and spin systems corresponding to a fractal-like graph.

[1] A. Kitaev and C. Laumann, arXiv:0904.2771.
[2] K. Minami, Nucl. Phys. B 939 (2019) 465.
[3] M. Ogura et al., in preparation.