Investigation of ground state correlations in an extended Lipkin-Meshkov-Glick model

Robert Gilmore, D.H. Feng

Robert Gilmore, D.H. Feng

Ching-Yee Leung, Wing Chi Yu, Ho-Man Kwok +2 more

In this paper, we study the scaling behavior of the ground-state logarithmic fidelity in the Lipkin–Meshkov–Glick (LMG) model. We find that the logarithmic fidelity shows a different scaling behavior in different phases of the model. It is an extensive quantity in the model's symmetry-broken phase while it behaves intensively in the polarized phase. Moreover, we also find that the logarithmic fidelity shows a singular behavior around the vicinity of the critical point and the critical exponent of the correlation length is also obtained numerically.

A.I. Vdovin, Aleksej Nikolaevich Storozhenko

Stoyan Mishev, M. Savova

Abstract In this paper we approximate the wave function of the Lipkin-Meshkov-Glick (LMG) model by a simple feed-forward neural network. By using the NetKet toolkit we obtain the ground state energies of LMG systems with different interaction strengths and find out that they are very close to the exact values.

Sébastien Dusuel, Julien Vidal

We study the ground state properties of the critical Lipkin-Meshkov-Glick model. Using the Holstein-Primakoff boson representation, and the continuous unitary transformation technique, we compute explicitly the finite-size scaling exponents for the energy gap, the ground state energy, the magnetization, and the spin-spin correlation functions. Finally, we discuss the behavior of the two-spin entanglement in the vicinity of the phase transition.