Study of competing phases in the half filled Hubbard-Holstein model by "sign-free" determinantal Langevin simulations

Understanding the properties of strongly correlated models is a challenging problem since many analytical tools cannot be applied due to the complicated nature of the problems. Here, we apply numerical methods in order to investigate the ground state thermodynamic limit properties of the so-called Hubbard-Holstein model in two spatial dimensions. We show that it is possible to perform "sign-problem-free" path integration for the model at half-filling by an appropriate choice of Hubbard-Stratonovich transformation and exact integration of phononic degrees of freedom. We apply an efficient first-order accelerated Langevin dynamics algorithm to evaluate all relevant correlation functions of the model. Preliminary calculations at U/t=4 and U/t=1, ω₀/t=1, indicate a strong competition of antiferromagnetic and charge-density-wave orders.
We observe signatures of a quite extended region around U≈g²/ω₀ without either antiferromagnetic or charge-density-wave orders, separating into two quantum critical points at zero temperature. Furthermore, the phase diagram of the model will be presented for moderate phonon frequencies ω₀. The possible extension of the current technique to finite temperature is under study.