Low-temperature regimes and finite-size scaling in a quantum spherical model

TL;DR

This paper investigates the finite-size scaling and low-temperature behavior of a quantum spherical model in various geometries, providing rigorous analysis near quantum critical points and emphasizing the two-dimensional case.

Contribution

It offers a detailed finite-size scaling analysis of a quantum spherical model across different dimensions and geometries, highlighting its relevance for quantum critical phenomena.

Findings

Finite-size effects are rigorously characterized for dimensions 1<d<3.

Critical behavior near zero-temperature quantum critical points is analyzed.

Special functions are used to describe free energy, susceptibility, and equations of state.

Abstract

A $d$--dimensional quantum model in the spherical approximation confined to a general geometry of the form $L^{d-d^{\prime}} \times\infty^{d^{\prime}}\times L_{\tau}^{z}$ ($L$--linear space size and $L_{\tau}$--temporal size) and subjected to periodic boundary conditions is considered. Because of its close relation with the quantum rotors model it can be regarded as an effective model for studying the low-temperature behavior of the quantum Heisenberg antiferromagnets. Due to the remarkable opportunity it offers for rigorous study of finite-size effects at arbitrary dimensionality this model may play the same role in quantum critical phenomena as the popular Berlin-Kac spherical model in classical critical phenomena. Close to the zero-temperature quantum critical point, the ideas of finite-size scaling are utilized to the fullest extent for studying the critical behavior of the model. For different dimensions $1<d<3$ and $0\leq d^{\prime}\leq d$ a detailed analysis, in terms of the special functions of classical mathematics, for the free energy, the susceptibility and the equation of state is given. Particular attention is paid to the two-dimensional case.