Fermionic representations of integrable lattice systems

Matteo Beccaria A, Carlo Presilla, Gian Fabrizio De Angelis +1 more

Gohmann, F, Murakami, S, 村上修一 +1 more

We develop a general scheme for the use of Fermi operators within the framework of integrable systems. This enables us to read off a fermionic Hamiltonian from a given solution of the Yang-Baxter equation and to express the corresponding L-matrix and the generators of symmetries in terms of Fermi operators. We illustrate our approach through a number of examples. Our main example is the algebraic Bethe ansatz solution of the Hubbard model in the infinite coupling limit.

Frank Göhmann, Shuichi Murakami

We develop a general scheme for the use of Fermi operators within the framework of integrable systems. This enables us to read off a fermionic Hamiltonian from a given solution of the Yang-Baxter equation and to express the corresponding L -matrix and the generators of symmetries in terms of Fermi operators. We illustrate our approach through a number of examples. Our main example is the algebraic Bethe ansatz solution of the Hubbard model in the infinite coupling limit.

David A. Coker

Rinat Kedem

Y. Avishai, J. Richert

The feasibility of using Monte Carlo methods in finite fermion systems has been investigated. The basic tool is a (recently suggested) functional integral representation of $Z=\mathrm{tr}[\mathrm{exp}(\ensuremath{-}\ensuremath{\beta}II)]$ using real coherent states of Slater determinants. Conditions for using the discretized ($N$-point lattice) version as a starting point for Monte Carlo integrations are studied. The limit of large $\ensuremath{\beta}$ is achieved only with large $\ensuremath{\surd}N$. For a two-fermion system numerical calculations of the ground-state energy agree farily well with the exact value.