Abstract
We study the disconnected entanglement entropy, S^\mathrm{D}SD, of the Su-Schrieffer-Heeger model. S^\mathrm{D}SD is a combination of both connected and disconnected bipartite entanglement entropies that removes all area and volume law contributions and is thus only sensitive to the non-local entanglement stored within the ground state manifold. Using analytical and numerical computations, we show that S^\mathrm{D}SD behaves like a topological invariant, i.e., it is quantized to either 00 or 2\log(2)2log(2) in the topologically trivial and non-trivial phases, respectively. These results also hold in the presence of symmetry-preserving disorder. At the second-order phase transition separating the two phases, S^\mathrm{D}SD displays a finite-size scaling behavior akin to those of conventional order parameters, that allows us to compute entanglement critical exponents. To corroborate the topological origin of the quantized values of S^\mathrm{D}SD, we show how the latter remain quantized after applying unitary time evolution in the form of a quantum quench, a characteristic feature of topological invariants associated with particle-hole symmetry.
Highlights
To corroborate the topological origin of the quantized values of SD, we show how the latter remain quantized after applying unitary time evolution in the form of a quantum quench, a characteristic feature of topological invariants associated with particle-hole symmetry
We provide here the two arguments explaining why topological invariants associated with particle-hole symmetry (PHS) are invariant to symmetry-preserving quenches that are presented in Ref. [40]
We have shown how entanglement entropies distinguish topological and non-topological insulating phases in the Su-Schrieffer-Heeger one-dimensional model with open boundary conditions
Summary
When a phase is topological, its ground state(s) displays robust entanglement properties. This paper aims at characterizing the properties of SD for the case of one-dimensional topological insulators, focusing on a simple, yet paradigmatic example: the Su-Schrieffer-Heeger model [33, 34] (SSH) This model of spinless fermions displays a topologically trivial phase and an SPTP with two edge modes. SD remains quantized on average in the presence of disorder Such a scaling behavior and critical exponents are different with respect to the Kitaev wire [31] (the only other occurrence of such an analysis for fermionic systems to our knowledge) and to bosonic cluster models realized as instances of random unitary circuits
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