Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 9 (2013), 076, 15 pages      arXiv:1206.3364      https://doi.org/10.3842/SIGMA.2013.076

Ground-State Analysis for an Exactly Solvable Coupled-Spin Hamiltonian

Eduardo Mattei a and Jon Links b
a) Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, Rio de Janeiro, Brazil
b) School of Mathematics and Physics, The University of Queensland, 4072, Australia

Received July 23, 2013, in final form November 22, 2013; Published online November 30, 2013

Abstract
We introduce a Hamiltonian for two interacting su(2) spins. We use a mean-field analysis and exact Bethe ansatz results to investigate the ground-state properties of the system in the classical limit, defined as the limit of infinite spin (or highest weight). Complementary insights are provided through investigation of the energy gap, ground-state fidelity, and ground-state entanglement, which are numerically computed for particular parameter values. Despite the simplicity of the model, a rich array of ground-state features are uncovered. Finally, we discuss how this model may be seen as an analogue of the exactly solvable p+ip pairing Hamiltonian.

Key words: mean-field analysis; Bethe ansatz; quantum phase transition.

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