PIRSA:15010125

Video URL

https://pirsa.org/15010125

Haldane-like antiferromagnetic spin chain in the large anisotropy limit

Paranjape, M. (2015). Haldane-like antiferromagnetic spin chain in the large anisotropy limit. Perimeter Institute for Theoretical Physics. https://pirsa.org/15010125

Paranjape, Manu. Haldane-like antiferromagnetic spin chain in the large anisotropy limit. Perimeter Institute for Theoretical Physics, Jan. 20, 2015, https://pirsa.org/15010125 

          @misc{ scivideos_PIRSA:15010125,
            doi = {10.48660/15010125},
            url = {https://pirsa.org/15010125},
            author = {Paranjape, Manu},
            keywords = {Quantum Matter},
            language = {en},
            title = {Haldane-like antiferromagnetic spin chain in the large anisotropy limit},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2015},
            month = {jan},
            note = {PIRSA:15010125 see, \url{https://scivideos.org/index.php/pirsa/15010125}}
          }

Manu Paranjape Université de Montréal

Talk numberPIRSA:15010125
DOI10.48660/15010125
Source RepositoryPIRSA
Collection
Talk Type Scientific Series
Subject

Abstract

We consider the one dimensional, periodic spin chain with $N$ sites, similar to the one studied by Haldane \cite{hal}, however in the opposite limit of very large anisotropy and small nearest neighbour, anti-ferromagnetic exchange coupling between the spins, which are of large magnitude $s$.  For a  chain with an even number of sites we show that actually the ground state is non degenerate and given by a superposition of the two Néel states, due to quantum spin tunnelling.  With an odd number of sites, the Néel state must necessarily contain a soliton. The position of the soliton is arbitrary thus the  ground state is $N$-fold degenerate.  This set of  states reorganizes into a band. We show that this occurs at order $2s$ in perturbation theory.  The ground state is non-degenerate for integer spin, but degenerate for half-odd integer spin as is required by Kramer's theorem \cite{kram}. arXiv:1404.6706 , Phys.Lett. A378 (2014) 3066-3069; arXiv:1304.3734 Phys.Rev. B88 (2013) 22, 220403