论文标题
双线性Majorana表示旋转大小的旋转操作员$ S> 1/2 $
Bilinear Majorana representations for spin operators with spin magnitudes $S>1/2$
论文作者
论文摘要
我们根据SU（2）的真实不可约的矩阵表示，对旋转式运算符的双线性主要表示分类进行了分类。我们确定了两种类型的表示形式：虽然可以将第一种类型直接映射到Spin-$ s $运算符的标准复杂的Fermionic表示上，但第二种类型实现了旋转幅度$ s = s（s+1）/4 $，使用$ s \ in \ Mathbb {n} $，并且可以通过fermions来表现出\ Mathbb {n} $，并且可以被认为是特别有效的。我们表明，对于$ s = 1 $和$ s = 2 $，第二种类型的重现已知的旋转-1/2 $和spin- $ 3/2 $ majoraana表示，我们证明这些是唯一不引入任何非物理旋转扇区的双线性Majorana表示。虽然对于$ s> 2 $，但不可避免的额外的非物理旋转空间比对于更标准的复杂的费米子表示，并且携带相对较小的自旋振幅的数量少。我们将Majorana表示形式应用于可溶解的小型自旋簇，并确认其低能特性不受非物理自旋扇区的影响，从而使我们的表示对基于辅助粒子的方法有用。
We present a classification of bilinear Majorana representations for spin-$S$ operators, based on the real irreducible matrix representations of SU(2). We identify two types of such representations: While the first type can be straightforwardly mapped onto standard complex fermionic representations of spin-$S$ operators, the second type realizes spin amplitudes $S=s(s+1)/4$ with $s\in\mathbb{N}$ and can be considered particularly efficient in representing spins via fermions. We show that for $s=1$ and $s=2$ this second type reproduces known spin-$1/2$ and spin-$3/2$ Majorana representations and we prove that these are the only bilinear Majorana representations that do not introduce any unphysical spin sectors. While for $s>2$, additional unphysical spin spaces are unavoidable they are less numerous than for more standard complex fermionic representations and carry comparatively small spin amplitudes. We apply our Majorana representations to exactly solvable small spin clusters and confirm that their low energy properties remain unaffected by unphysical spin sectors, making our representations useful for auxiliary-particle based methods.
