2014/06/30 by J. Sirker, J Sirker, M. Maiti +5
Materials Science · Physics and Astronomy · #Boundary (topology) #Chain (unit) #Eigenvalues and eigenvectors #Entropy (arrow of time) #Hamiltonian (control theory) #Organic and Molecular Conductors Research #Phase transition #Quantum entanglement #Quantum many-body systems #Quantum phase transition #Renormalization group #Topological Materials and Phenomena #cond-mat.stat-mech #cond-mat.str-el #quant-ph
paper · pdf · doi:10.1088/1742-5468/2014/10/p10032
published as J. Stat. Mech. P10032 (2014) · References added
arxiv created 2014/07/03 · openalex publication_date 2014/10/21 · arxiv updated 2014/10/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We present a detailed study of the fidelity, the entanglement entropy, and the entanglement spectrum, for a dimerized chain of spinless fermions---a simplified Su-Schrieffer-Heeger (SSH) model---with open boundary conditions which is a well-known example for a model supporting a symmetry protected topological (SPT) phase. In the non-interacting case the Hamiltonian matrix is tridiagonal and the eigenvalues and -vectors can be given explicitly as a function of a single parameter which is known analytically for odd chain lengths and can be determined numerically in the even length case. From a scaling analysis of these data for essentially semi-infinite chains we obtain the fidelity susceptibility and show that it contains a boundary contribution which is different in the topologically ordered than in the topologically trivial phase. For the entanglement spectrum and entropy we confirm predictions from massive field theory for a block in the middle of an infinite chain but also consider blocks containing the edge of the chain. For the latter case we show that in the SPT phase additional entanglement---as compared to the trivial phase---is present which is localized at the boundary. Finally, we extend our study to the dimerized chain with a nearest-neighbour interaction using exact diagonalization, Arnoldi, and density-matrix renormalization group methods and show that a phase transition into a topologically trivial charge-density wave phase occurs.