Extended Thouless-Anderson-Palmer method for fermions on frustrated lattices

Mean field theory (MFT) is an effective theoretical tool

to study the qualitative phase diagram of strongly correlated

many-body models. Mean field methods have been particularly useful in the

study of interacting fermions, where charge, spin,

orbital degrees of freedom, and geometric frustration compete

to determine the model's emergent low temperature phases. The key

reason for MFT's success when applied to complicated electron

Hamiltonians is the method ignores fluctuations in the degrees of

freedom. Exact, or more rigorous, methods that include

fluctuations are often restricted to select regions

of the phase diagram because of inherent features of the method.

For example, quantum Monte Carlo (QMC) methods for interacting electrons

can experience a severe sign problem, which prohibits the generation

of meaningful simulation results. A systematic approach to extend

MFT beyond the Gaussian limit was developed by A. Georges

and J. S. Yeddeia (J. Phys. A: Math. Gen. 24, 2173 (1991)), where

they generalized the Thouless-Anderson-Plamer method

first applied to spin glasses (Phil. Mag. 35, 593 (1977))

(eTAP). In this presentation we motivate the application of the eTAP

approach to the frustrated 2D Hubbard model and present preliminary

results.