Continuous unitary transformations and finite-size scaling exponents in the Lipkin-Meshkov-Glick model

TL;DR

This paper combines Holstein-Primakoff representation and continuous unitary transformations to analytically compute finite-size scaling exponents and ground state properties in the Lipkin-Meshkov-Glick model, supported by numerical validation.

Contribution

It introduces an analytical method to determine finite-size corrections in the LMG model using continuous unitary transformations, enhancing understanding of its scaling behavior.

Findings

Analytical expressions for ground state energy corrections

Validation of the approach with numerical calculations for large systems

Insights into entanglement properties and concurrence in the thermodynamic limit

Abstract

We analyze the finite-size scaling exponents in the Lipkin-Meshkov-Glick model by means of the Holstein-Primakoff representation of the spin operators and the continuous unitary transformations method. This combination allows us to compute analytically leading corrections to the ground state energy, the gap, the magnetization, and the two-spin correlation functions. We also present numerical calculations for large system size which confirm the validity of this approach. Finally, we use these results to discuss the entanglement properties of the ground state focusing on the (rescaled) concurrence that we compute in the thermodynamical limit.