Dimensional modulation of spontaneous magnetic order in quasi-two-dimensional quantum antiferromagnets

TL;DR

This paper explores how magnetic order in quantum antiferromagnets changes as the system's dimensionality decreases from three to two, revealing that the Neel temperature remains finite even in two dimensions, with the order parameter being smoothly suppressed.

Contribution

It provides a comprehensive theoretical analysis of the dimensional modulation of magnetic order, combining multiple methods to show the persistence of finite Neel temperature in low-dimensional systems.

Findings

Neel temperature remains finite in the two-dimensional limit.

Order parameter is smoothly suppressed with decreasing dimensionality.

Multiple independent methods agree on the dimensional modulation behavior.

Abstract

Spontaneous symmetry breaking is deeply related to dimensionality of system. The Neel order going with spontaneous breaking of $U(1)$ symmetry is safely allowed at any temperature for three-dimensional systems but allowed only at zero temperature for purely two-dimensional systems. We closely investigate how smoothly the ordering process of the three-dimensional system is modulated into that of the two-dimensional one with reduction of dimensionality, considering spatially anisotropic quantum antiferromagnets. We first show that the N\'eel temperature is kept finite even in the two-dimensional limit although the N\'eel order is greatly suppressed for low-dimensionality. This feature of the N\'eel temperature is highly nontrivial, which dictates how the order parameter is squashed under the reduction of dimensionality. Next we investigate this dimensional modulation of the order parameter. We develop our argument taking as example a coupled spin-ladder system relevant for experimental studies. The ordering process is investigated multidirectionally using theoretical techniques of a mean-field method combined with analytical (exact solutions of quantum field theories) or numerial (density-matrix renormalization-group) method, a variational method, a renormalization-group study, linear spin-wave theory, and quantum Monte-Carlo simulation. We show that these methods independent of each other lead to the same conclusion about the dimensional modulation.