Dpto. Fisica Aplicada I, E.T.S. Ingenieria de Bilbao, Universidad del Pais Vasco (UPV/EHU), Alda. Urquijo s/n, 48013 Bilbao, Spain. Dpto. Fisica Aplicada I, E.U. Ingenieria de Vitoria, Universidad del Pais Vasco (UPV/EHU), C/Nieves Cano 12, 01006 Vitoria, Spain.
J Phys Condens Matter. 2014 Apr 2;26(13):136002. doi: 10.1088/0953-8984/26/13/136002. Epub 2014 Mar 13.
A simple phenomenological real-space renormalization group method for quantum Heisenberg spins with nearest and next nearest neighbour interactions on a pyrochlore lattice is presented. Assuming a scaling law for the order parameter of two clusters of different sizes, a set of coupled equations that gives the fixed points of the renormalization group transformation and, thus, the critical temperatures and ordered phases of the system is found. The particular case of spins 1/2 is studied in detail. Furthermore, to simplify the mathematical details, from all the possible phases arising from the renormalization group transformation, only those phases in which the magnetic lattice is commensurate with a subdivision of the crystal lattice into four interlocked face-centred cubic sublattices are considered. These correspond to a quantum spin liquid, ferromagnetic order, or non-collinear order in which the total magnetic moment of a tetrahedral unit is zero. The corresponding phase diagram is constructed and the differences with respect to the classical model are analysed. It is found that this method reproduces fairly well the phase diagram of the pyrochlore lattice under the aforementioned constraints.
提出了一种简单的用于研究最近邻和次近邻相互作用的量子海森堡自旋在钙钛矿晶格上的经验实空间重整化群方法。假设两个不同大小的团簇的序参量具有标度律，我们找到了一组耦合方程，这些方程给出了重整化群变换的不动点，从而给出了系统的临界温度和有序相。详细研究了自旋为 1/2 的特殊情况。此外，为了简化数学细节，从重整化群变换产生的所有可能相中，仅考虑那些磁晶格与将晶格细分为四个相互锁的面心立方子晶格的相。这些对应于量子自旋液体、铁磁序或非共线序，其中四面体单元的总磁矩为零。构建了相应的相图，并分析了与经典模型的差异。结果发现，在上述约束条件下，该方法相当准确地再现了钙钛矿晶格的相图。
