Journal
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
Volume -, Issue -, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1742-5468/2014/10/P10032
Keywords
solvable lattice models; topology and combinatorics; density matrix renormalization group calculations; entanglement in extended quantum systems (theory)
Categories
Funding
- DFG via the collaborative research center SFB/TR 49
- Graduate School of Excellence MAINZ
- Natural Sciences and Engineering Council (NSERC) of Canada
- Regional Computing Center at the University of Kaiserslautern
- AHRP
- Compute Canada
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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.
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