Thermodynamics of the S=12 maple-leaf Heisenberg antiferromagnet

The Heisenberg antiferromagnet on the maple-leaf lattice has recently gathered a great deal of attention. Competition between three nonequivalent bond interactions results in various ground-state quantum phases, with the exact dimer-product singlet ground state being among them. The thermodynamic properties of this model are much less understood. We used high-temperature expansion up to the 18th order to study the thermodynamics of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi>S</a:mi><a:mo>=</a:mo><a:mn>1</a:mn><a:mo>/</a:mo><a:mn>2</a:mn></a:mrow></a:math> Heisenberg model on the uniform maple-leaf lattice with the ground state exhibiting a six-sublattice <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:msup><b:mn>120</b:mn><b:mo>∘</b:mo></b:msup></b:math> long-range magnetic order. Padé approximants allow us to get reliable results up to the temperatures of about <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mi>T</c:mi><c:mo>≈</c:mo><c:mn>0.4</c:mn></c:mrow></c:math>. To study thermodynamics for arbitrary temperatures, we made the interpolation using the entropy method. Based on the analysis of close Padé approximants, we find ground-state energy <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:msub><d:mi>e</d:mi><d:mn>0</d:mn></d:msub><d:mo>=</d:mo><d:mo>−</d:mo><d:mn>0.53064</d:mn><d:mo>...</d:mo><d:mo>−</d:mo><d:mn>0.53023</d:mn></d:mrow></d:math> in good agreement with numerical results. The specific heat <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:mi>c</e:mi><e:mo>(</e:mo><e:mi>T</e:mi><e:mo>)</e:mo></e:mrow></e:math> has a typical maximum at rather low temperatures <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mrow><f:mi>T</f:mi><f:mo>≈</f:mo><f:mn>0.379</f:mn></f:mrow></f:math> and the uniform susceptibility <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mrow><g:mi>χ</g:mi><g:mo>(</g:mo><g:mi>T</g:mi><g:mo>)</g:mo></g:mrow></g:math> at <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:mrow><h:mi>T</h:mi><h:mo>≈</h:mo><h:mn>0.49</h:mn></h:mrow></h:math>. We also estimate the value of <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:mrow><i:mi>χ</i:mi><i:mo>(</i:mo><i:mi>T</i:mi><i:mo>)</i:mo></i:mrow></i:math> at zero temperature <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"><j:mrow><j:msub><j:mi>χ</j:mi><j:mn>0</j:mn></j:msub><j:mo>≈</j:mo><j:mn>0.05</j:mn><j:mo>...</j:mo><j:mn>0.06</j:mn></j:mrow></j:math>. The ground-state order manifests itself in the divergence of the so-called generalized Wilson ratio.