Hannover 2013 – scientific programme

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A: Fachverband Atomphysik

A 35: Ultra-cold atoms, ions and BEC VII (with Q)

A 35.7: Talk

Thursday, March 21, 2013, 15:30–15:45, B 305

Quasi-particle excitation spectra of general quantum lattice systems via the 1/Z expansion — •Patrick Navez, Konstantin Krutitsky, Friedemann Queisser, and Ralf Schützhold — Fakultät für Physik, Universität Duisburg-Essen, Duisburg, Germany

We investigate general quantum lattice systems such as the Bose and Fermi Hubbard models or the Heisenberg spin model using the 1/Z expansion method [1,2] where Z is the coordination number. This method provides a general framework for deriving linearized equations of motion for quasi-particle excitation operators, which yield the excitation spectra, for example. Their solutions determine the one-site reduced density matrix and the two-sites reduced correlation density matrix, which are given in terms of bilinear expectation values of the quasi-particle excitation operators (displaying the quantum fluctuations). We illustrate the powerfulness of these general concepts for several examples such as particle-hole operators in the Mott phase of the Bose and Fermi Hubbard models (which lower the ground state energy by virtual tunneling) or the Heisenberg model (where virtual magnon excitations of opposite spin reduce antiferromagnetism) and compare our findings with the results found in the literature.

1. P. Navez, R. Schützhold, Phys. Rev. A 82, 063603 (2010)
2. F. Queisser, K. Krutitsky, P. Navez, R. Schützhold, arXiv:1203.2164