Eur. Phys. J. B (2018) 91: 69
https://doi.org/10.1140/epjb/e2018-80707-7

Regular Article

Criticality of the low-frequency conductivity for the bilayer quantum Heisenberg model

Department of Physics, Faculty of Science, Okayama University, Okayama 700-8530, Japan

^a e-mail: nisiyama@psun.phys.okayama-u.ac.jp

Received: 17 December 2017
Received in final form: 4 February 2018
Published online: 16 April 2018

Abstract

The criticality of the low-frequency conductivity for the bilayer quantum Heisenberg model was investigated numerically. The dynamical conductivity (associated with the O(3) symmetry) displays the inductor σ(ω) = (iωL)⁻¹ and capacitor iωC behaviors for the ordered and disordered phases, respectively. Both constants, C and L, have the same scaling dimension as that of the reciprocal paramagnetic gap Δ⁻¹. Then, there arose a question to fix the set of critical amplitude ratios among them. So far, the O(2) case has been investigated in the context of the boson-vortex duality. In this paper, we employ the exact diagonalization method, which enables us to calculate the paramagnetic gap Δ directly. Thereby, the set of critical amplitude ratios as to C, L and Δ are estimated with the finite-size-scaling analysis for the cluster with N ≤ 34 spins.