Determinant quantum Monte Carlo simulation of the non-Hermitian Hubbard model

While quantum mechanics is ordinarily carried out with Hermitian Hamiltonians, non-Hermitian Hamiltonians can arise. Examples include clever mappings of Hermitian problems (the Hatano-Nelson model), open quantum systems, or even efforts to relax the postulates of quantum mechanics (work by Carl Bender). Common many applications of non-Hermitian quantum mechanics is a need for a real Hamiltonian spectrum. This makes it difficult to write down a non-Hermitian Hubbard Hamiltonian (a standard Hubbard Hamiltonian but with asymmetric hoppings) with real eigenvalues for testing numerically. Numerical experiments find that a 2-chain Hatano-Nelson model with a parameter controlling the amount of non-Hermiticity present in the system exhibits a real spectrum. We have performed determinant quantum Monte Carlo (DQMC) simulations on this model, a method tried and tested on the Hermitian Hubbard model. In this talk I will present results for the energy, double occupancy, and spin-spin correlation functions as the non-Hermiticity is varied. I will also describe details of Monte Carlo efficiency (equilibration time, autocorrelation time), and numerical accuracy (Trotter error).