Fuji Yohei, Pollmann Frank, Oshikawa Masaki
Institute for Solid State Physics, University of Tokyo, Kashiwa 277-8581, Japan.
Max-Planck-Institut für Physik komplexer Systeme, D-01187 Dresden, Germany.
Phys Rev Lett. 2015 May 1;114(17):177204. doi: 10.1103/PhysRevLett.114.177204.
The ground state of the S=1 antiferromagnetic Heisenberg chain belongs to the Haldane phase--a well-known example of the symmetry-protected topological phase. A staggered field applied to the S=1 antiferromagnetic chain breaks all the symmetries that protect the Haldane phase as a topological phase, reducing it to a trivial phase. That is, the Haldane phase is then connected adiabatically to an antiferromagnetic product state. Nevertheless, as long as the symmetry under site-centered inversion combined with a spin rotation is preserved, the phase is still distinct from another trivial phase. We demonstrate the existence of such distinct symmetry-protected trivial phases using a field-theoretical approach and numerical calculations. Furthermore, a general proof and a nonlocal order parameter are given in terms of a matrix-product state formulation.
S = 1反铁磁海森堡链的基态属于霍尔丹相——对称保护拓扑相的一个著名例子。施加到S = 1反铁磁链上的交错场打破了所有将霍尔丹相作为拓扑相进行保护的对称性，使其退化为平凡相。也就是说，霍尔丹相随后通过绝热过程连接到一个反铁磁积态。然而，只要以格点中心反演并结合自旋旋转的对称性得以保留，该相仍然与另一个平凡相不同。我们用场论方法和数值计算证明了这种独特的对称保护平凡相的存在。此外，还根据矩阵乘积态公式给出了一个一般性证明和一个非局域序参量。
