Boundary Fidelity and Entanglement in the symmetry protected topological phase of the SSH model

Abstract

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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References in corpus (31)

• Entanglement spectrum of a topological phase in one dimension
• Calculation of reduced density matrices from correlation functions
• Topological phases of fermions in one dimension
• Ground state overlap and quantum phase transitions
• Topological Origin of Zero-Energy Edge States in Particle-Hole Symmetric Systems
• Topological Phases of One-Dimensional Fermions: An Entanglement Point of View
• Quantum critical scaling of the geometric tensors
• Quantum Spin Chain, Toeplitz Determinants and Fisher-Hartwig Conjecture
• Form factors of branch-point twist fields in quantum integrable models and entanglement entropy
• Boundary effects in the critical scaling of entanglement entropy in 1D systems
• Density-Matrix Spectra of Solvable Fermionic Systems
• Parity effects in the scaling of block entanglement in gapless spin chains
• Uhlmann Phase as a Topological Measure for One-Dimensional Fermion Systems
• Entanglement entropy and the Berry phase in solid states
• On the definition of a unique effective temperature for non-equilibrium critical systems
• Fidelity susceptibility and long-range correlation in the Kitaev honeycomb model
• Topological invariants and interacting one-dimensional fermionic systems
• Quantum fidelity in the thermodynamic limit
• Universal parity effects in the entanglement entropy of XX chains with open boundary conditions
• Symmetry protected topological phases in non-interacting fermion systems
• Fidelity analysis of topological quantum phase transitions
• Boundary-locality and perturbative structure of entanglement spectra in gapped systems
• Finite temperature fidelity susceptibility for one-dimensional quantum systems
• Lightcone renormalization and quantum quenches in one-dimensional Hubbard models
• Estimating Quasi-long-range Order via Renyi Entropies
• Thermally activated Peierls dimerization in ferromagnetic spin chains
• Temperature driven crossover phenomena in the correlation lengths of the one-dimensional t-J model
• Critical properties and Rényi entropies of the spin-3/2 XXZ chain
• The 1/2-XXZ spin-chain at finite magnetic field: Crossover phenomena driven by temperature
• Universal corrections to the entanglement entropy in gapped quantum spin chains: a numerical study
• Entanglement measures and the quantum to classical mapping

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• A Dynamical Bulk-Boundary Correspondence in Two Dimensional Topological Matter
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