Quantum Monte Carlo method on asymptotic Lefschetz thimbles for quantum spin systems: An application to the Kitaev model in a magnetic field

The quantum Monte Carlo method on asymptotic Lefschetz thimbles is a numerical algorithm devised specifically for alleviation of the sign problem appearing in simulations many-body systems. In this method, alleviated by shifting integration domain auxiliary fields, appearing, example, conventional determinant from real space to an appropriate manifold complex space. Here, we extend spin models with generic two-spin interactions, using Hubbard-Stratonovich transformation decouple exchange interactions and Popov-Fedotov map spins fermions. As demonstration, apply Kitaev model magnetic field whose ground state predicted deliver topological liquid non-Abelian anyonic excitations. To illustrate how visualize space, together saddle points zeros fermion determinant. We benchmark our low-temperature region show that action recovered considerably unbiased results are obtained sufficient precision.