Finite-Size Scaling Exponents of the Lipkin-Meshkov-Glick Model

TL;DR

This paper analyzes the critical behavior of the Lipkin-Meshkov-Glick model, calculating finite-size scaling exponents for various physical quantities and examining entanglement near the phase transition.

Contribution

It provides explicit calculations of finite-size scaling exponents using advanced techniques, offering new insights into the model's critical properties.

Findings

Finite-size scaling exponents for energy gap and ground state energy

Behavior of two-spin entanglement near phase transition

Quantitative analysis of magnetization and correlation functions

Abstract

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.