Regensburg 2007 – wissenschaftliches Programm

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TT: Fachverband Tiefe Temperaturen

TT 20: Correlated Electrons - Poster Session

TT 20.72: Poster

Mittwoch, 28. März 2007, 14:00–17:45, Poster A

Auxiliary Fermions and The Popov–Fedotov-Trick: Application to The Phase Diagram of The Bi-Layer Heisenberg Model — •Johannes Reuther, Jan Brinckmann, and Peter Woelfle — Institut f. Theorie der Kondensierten Materie, Universität Karlsruhe

We consider the antiferromagnetic spin-1/2 quantum Heisenberg model for two coupled planes. Each plane consists of spins on a two-dimensional square lattice with a nearest-neighbor coupling J>0, while the planes are connected by another antiferromagnetic coupling J_⊥. As is well known, for J_⊥= 0 the decoupled planes feature a Néel-like groundstate, while for very large J_⊥ the formation of local spin singlets (valence-bond state) is evident.

We use the auxiliary-fermion formulation of spin operators in conjunction with a method proposed by Popov and Fedotov. The latter enables us to take exactly into account the auxiliary-particle constraint (i.e., the projection onto the physical Hilbert space).

The ground-state phase diagram of the model is calculated, using a simple diagrammatic approximation for the fermion’s self energy. We find a Néel state at small J_⊥ and a continuous transition into a valence-bond state (VBS) if J_⊥ is increased beyond a critical value. The VBS is characterized by short-range correlations and gapped spin excitations. At the transition point the gap vanishes continuously, and the spin-1 spectrum becomes the magnon dispersion of the Néel state.

The magnetization and the evolution of the spin-excitation spectra as function of J_⊥ are compared to the literature.