Theory of a spherical quantum rotors model: low--temperature regime and finite-size scaling

TL;DR

This paper develops a rigorous finite-size scaling analysis of a spherical quantum rotors model, which effectively describes low-temperature quantum antiferromagnets, exploring critical behavior across various dimensions and geometries.

Contribution

It introduces a comprehensive finite-size scaling framework for the spherical quantum rotors model in arbitrary dimensions and geometries, emphasizing the two-dimensional case.

Findings

Finite-size effects are rigorously analyzed at quantum critical points.

Susceptibility and equations of state are derived using classical special functions.

The model provides insights into quantum critical phenomena similar to classical models.

Abstract

The quantum rotors model can be regarded as an effective model for the low-temperature behavior of the quantum Heisenberg antiferromagnets. Here, we consider a $d$-dimensional model in the spherical approximation confined to a general geometry of the form $L^{d-d'}\times\infty^{d'}\times L_{\tau}^{z}$ ( $L$-linear space size and $L_{\tau}$-temporal size) and subjected to periodic boundary conditions. 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 $0\leq d'\leq d$ a detailed analysis, in terms of the special functions of classical mathematics, for the susceptibility and the equation of state is given. Particular attention is paid to the two-dimensional case.