Symmetry Protected Topological Order by Folding a One-Dimensional Spin-1/2 Chain

2015/02/26 by Pejman Jouzdani, Jouzdani, Pejman
Computer Science · #Cellular Automata and Applications #FOS: Physical sciences #Strongly Correlated Electrons (cond-mat.str-el) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1502.07678

openalex publication_date 2015/02/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We present a toy model with a Hamiltonian H⁽²⁾_T on a folded one-dimensional spin chain. The non-trivial ground states of H⁽²⁾_T are separated by a gap from the excited states. By analyzing the symmetries in the model, we find that the topological order is protected by a ℤ₂ global symmetry. However, by using perturbation series and excluding thermal effects, we show that the ℤ₂ symmetry is stable in comparison to a standard nearest-neighbor Ising model with a Hamiltonian H_I. We find that H⁽²⁾_T is a member of a family of Hamiltonians that are adiabatically connected to H_I. Furthermore, the generalizations of this class of Hamiltonians, their adiabatic connection to H_I, and the relation to quantum error-correcting codes are discussed. Finally, we show the correspondence between the two ground states of H⁽²⁾_T and the unpaired Majorana modes, and provide numerical examples.

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