The numerical value for a universal quantity of a two-dimensional dimerized quantum antiferromagnet Fu-Jiun Jiang

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The numerical value for a universal quantity of a two-dimensional dimerized quantum

antiferromagnet

Fu-Jiun Jiang∗

Department of Physics, National Taiwan Normal University, 88, Sec.4, Ting-Chou Rd., Taipei 116, Taiwan

The numerical value of a universal quantity associated with the quantum critical regime, namely

χuc2/T , for a two-dimensional (2D) dimerized spin-1/2 antiferromagnet is calculated using the

quantum Monte Carlo simulations (QMC). Here χu,c, and Tare the uniform susceptibility, the

spin-wave velocity, and the temperature, respectively. By simulating large lattices at moderately

low temperatures, we ﬁnd χuc2/T ∼0.32. Our estimation of χuc2/T deviates from the related

analytic prediction but agrees with recent numerical calculations of other 2D dimerized spin-1/2

antiferromagnets.

I. INTRODUCTION

Spatial dimension two is special because of the famous

Mermin–Wagner theorem [1]. Speciﬁcally, continuous

symmetry cannot be broken spontaneously (at ﬁnite tem-

perature T) in spatial dimension two. As a result, for

two-dimensional (2D) quantum antiferromagnets, as T

rises from zero temperature, one encounters a crossover

instead of a phase transition to a unique phase called the

quantum critical regime (QCR).

Using the relevant ﬁeld theory, properties of QCR are

investigated [2]. In particular, several universal quanti-

ties are proposed. Among these quantities, we are es-

pecially interested in χuc2/T due to the recently found

discrepancy between the analytic prediction and the nu-

merical calculations. Here χuand care the uniform sus-

ceptibility and the spin-wave velocity, respectively.

Analytically, it is predicted that the numerical value

of χuc2/T is given by (around) 0.27185. Although this

prediction was conﬁrmed by earlier Monte Carlo stud-

ies [2, 3], recent investigations of 2D dimerized bilayer

and plaquette spin-1/2 Heisenberg models conclude that

χuc2/T ∼0.32(0.33) [4, 5]. Because of this discrepancy,

it will be interesting to conduct a further examination on

the numerical value of χuc2/T .

In this study, we perform large-scale Monte Carlo simu-

lations to determine the χuc2/T of a 2D dimerized quan-

tum antiferromagnetic Heisenberg model. By simulating

lattices as large as L= 512 (Lis the linear system size),

we obtain χuc2/T ∼0.32 which matches quantitatively

with recent outcomes claimed in Refs. [4, 5]. Our re-

sult suggests that a reﬁnement of analytic calculation is

needed.

The rest of the paper is organized as follows. After the

introduction, the model and the measured observables

are described in Sec. II. We then present the obtained

results in Sec. III. In particular, the numerical evidence

to support χuc2/T ∼0.32 is demonstrated. We conclude

our investigation in Sec. VI.

∗fjjiang@ntnu.edu.tw

FIG. 1: The herringbone model considered in this study. The

thick and thin bonds represent the coulplings of strength J0

and J, respectively

II. THE CONSIDERED MODEL AND

OBSERVABLE

The Hamiltonian of the considered 2D spin-1

2dimer-

ized herringbone Heisenberg model takes the following

expression

H=X

hiji

Si·~

Sj+X

hi0j0i

J0~

Si0·~

Sj0,(1)

where Jand J0are the antiferromagnetic couplings con-

necting nearest neighbor spins hijiand hi0j0i, respec-

tively, and ~

Siis the spin-1

2operator at site i. A cartoon

representation of the studied model is depicted in ﬁg. 1.

Jis set to 1 in our investigation. As the magnitude of

J0increases, a phase transition will occur for a partic-

ular value of J0> J. This special point J0/J in the

parameter space is denoted by (J0/J)cand is found to

be (J0/J)c= 2.4981(2) in the literature [6]. The investi-

gation presented in this study is conducted at the critical

point (J0/J)c.

To examine the universal quantity χuc2/T of QCR,

the uniform susceptibility χuand the spin-wave velocity

care measured. On a ﬁnite lattice of linear size L, the

uniform susceptibility χuis deﬁned by

χu=β

L2* X

i!2+.(2)

The quantity βappearing above is the inverse tempera-

ture. The spin-wave velocity cfor the investigated model

is calculated through the temporal and spatial winding

numbers squared (hW2

tiand hW2

iiwith i∈ {1,2}).

arXiv:2210.14471v1 [cond-mat.str-el] 26 Oct 2022

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Thenumericalvalueforauniversalquantityofatwo-dimensionaldimerizedquantumantiferromagnetFu-JiunJiangDepartmentofPhysics,NationalTaiwanNormalUniversity,88,Sec.4,Ting-ChouRd.,Taipei116,TaiwanThenumericalvalueofauniversalquantityassociatedwiththequantumcriticalregime,namelyuc2=T,foratwo-dimensional(2D...

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The numerical value for a universal quantity of a two-dimensional dimerized quantum antiferromagnet Fu-Jiun Jiang

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