Spin Permutation at Work in the BCS Hamiltonian

B. A. Men', P. T. Varshavskii

Hans-Thomas Elze

The dynamics-from-permutations of classical Ising spins are studied for a chain of four spins. We obtain the Hamiltonian operator which is equivalent to the unitary permutation matrix that encodes assumed pairwise exchange interactions. It is shown how this can be summarized by an exact terminating Baker–Campbell–Hausdorff formula, which relates the Hamiltonian to a product of exponentiated two-spin exchange permutations. We briefly comment upon physical motivation and implications of this study.

J. D. Fan, Y. M. Malozovsky

Vladyslav O. Cheranovskii

王安民, 朱仁贵

我们扩大 BCS paring 模型与同等地，到 generalone 维的 spin-1/2 海森堡的 spaced 层次当模特儿。海森堡的二著名对称当模特儿，即 permutational 和纺纱倒置对称，不再存在。然而，当一起连接这二操作时，我们发现在它的潜水艇空间 n 和 Fock 空间的潜水艇空间 L- n 之间的精力光谱的新对称。一个严密证明被介绍。

Hong-Hao Tu

We propose a class of projected BCS wave functions and derive their parent spin Hamiltonians. These wave functions can be formulated as infinite matrix product states constructed by chiral correlators of Majorana fermions. In one dimension, the spin Hamiltonians can be viewed as SO($n$) generalizations of Haldane-Shastry models. We numerically compute the spin-spin correlation functions and R\'enyi entropies for $n=5$ and 6. Together with the results for $n=3$ and 4, we conclude that these states are critical and their low-energy effective theory is the SO($n$)${}_{1}$ Wess-Zumino-Witten model. In two dimensions, we show that the projected BCS states are chiral spin liquids, which support non-Abelian anyons for odd $n$ and Abelian anyons for even $n$.