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arXiv 1209.4399cond-mat.str-el
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接近反铁磁Neel序的三维对称性保护拓扑相

Three dimensional Symmetry Protected Topological Phase close to Antiferromagnetic Neel order

Cenke Xu

摘要:

一维自旋为1的链的Halcantine相是一种对称性保护的拓扑相,可用非线性西格玛模型(NLSM)描述,在Theta = 2 Pi处引入了一个Theta项.本文研究了SU(2N)反铁磁自旋系统的三维SPT相,系统的每一格点都具有自共轭表象。该系统的自旋有序Neel相具有一个基态流形M = U(2 N)/[U(N)xU(N)],该系统可用一个由流形M定义的NLSM来描述.由于同伦群Pi 4 [M] = Z(N > 1),这个NLSM自然可以有一个θ项。我们将论证当Theta = 2 Pi时,此NLSM描述SPT相位。这个SPT相位受到SU(2N)自旋对称性或其子群SU(N)xSU(N)xZ 2的保护,而不假设任何其他离散对称性。我们还将在一个三维晶格上构造一个SU(2N)自旋态,并证明该态的长波物理性质可以用上述的NLSM(θ = 2 Pi)精确描述。

英文摘要:

It is well-known that the Haldane phase of one-dimensional spin-1 chain is a symmetry protected topological (SPT) phase, which is described by a nonlinear Sigma model (NLSM) with a Theta-term at Theta = 2Pi. In this work we study a three dimensional SPT phase of SU(2N) antiferromagnetic spin system with a self-conjugate representation on every site. The spin ordered Neel phase of this system has a ground state manifold M = U(2N)/[U(N)xU(N)], and this system is described by a NLSM defined with manifold M. Since the homotopy group Pi4[M] = Z for N > 1, this NLSM can naturally have a Theta-term. We will argue that when Theta = 2Pi this NLSM describes a SPT phase. This SPT phase is protected by the SU(2N) spin symmetry, or its subgroup SU(N)xSU(N)xZ2, without assuming any other discrete symmetry. We will also construct a trial SU(2N) spin state on a 3d lattice, we argue that the long wavelength physics of this state is precisely described by the aforementioned NLSM with Theta = 2Pi.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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