Few-cluster solutions of many-fermion problem

Kevin E. Schmidt, Malvin H. Kalos

Kevin E. Schmidt, Malvin H. Kalos

Kevin E. Schmidt, Malvin H. Kalos

Shailesh Chandrasekharan A, U.‐J. Wiese

We present a general strategy to solve the notorious fermion sign problem using cluster algorithms. The method applies to various systems in the Hubbard model family as well as to relativistic fermions. Here it is illustrated for nonrelativistic lattice fermions. A configuration of fermion world lines is decomposed into clusters that contribute independently to the fermion permutation sign. A cluster whose flip changes the sign is referred to as a meron. Configurations containing meron clusters contribute $0$ to the path integral, while all other configurations contribute $1$. The cluster representation describes the partition function as a gas of clusters in the zero-meron sector.

M. C. Gordillo

Abstract We describe the possible states of four-fermion clusters loaded in one-dimensional optical lattices with an additional harmonic confinement when the interactions between particles of different spin are contact-like. We have found that, depending on the depth of the potential well, the wavelength of the laser, and the strength of the repulsive interactions, we can have ground states that have unpaired spins (paramagnetic), all the spins paired (diamagnetic) or a degenerate mixture of different configurations. In this last case, the cluster could be either a metal or a Mott insulator. The characteristics of the ground state can be inferred to some extent from the solutions of non-interacting Schrödinger equations for the same arrangements.

Jeffrey Goldstone

Abstract An exact formal solution is obtained to the problem of a system of fermions in interaction. This solution is expressed in a form which avoids the problem of unlinked clusters in manybody theory. The technique of Feynman graphs is used to derive the series and to define linked terms. The graphs are those appropriate to a system of many fermions and are used to give a new derivation of the Hartree-Fock and Brueckner methods for this problem.