Berlin 2015 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 33: Critical Phenomena and Phase Transitions

DY 33.7: Talk

Wednesday, March 18, 2015, 16:45–17:00, BH-N 334

Quantum phase transitions in networks of Lipkin–Meshkov–Glick models — •Aleksandr Sorokin, Victor Bastidas, and Tobias Brandes — Technische Universität Berlin, Berlin, Germany

The Lipkin–Meshkov–Glick (LMG) model describes an ensemble of all-to-all–coupled two-level systems with anisotropic interactions, exhibiting quantum phase transitions. In this contribution we show that coupling of several LMG systems with the overall Hamiltonian

gives rise to phases with different collective behaviour. Namely, the weak-coupling regime corresponds to the paramagnetic phase when the local field dominates the dynamics, but the local anisotropy leads to the existence of an exponentially degenerate ground state. In the strong-coupling regime, the ground state is twofold degenerate and possesses long-range magnetic ordering.

The calculations were performed in the mean-field (MF) approximation but taking into account quantum fluctuations around the MF solution. Within this approach analytical expressions for the ground-state and excitation energies as well as correlation functions in different phases were obtained for a network with the ring topology.

For details see [AV Sorokin, VM Bastidas and T Brandes, Phys. Rev. E 90, 042141 (2014)]