Topological entanglement properties of disconnected partitions in the Su-Schrieffer-Heeger model

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.

Error-correction properties of an interacting topological insulator

“…In the following, we assume that the system has been measured in the error basis, yielding a classical string of errors. As the topological phases of the SSH model are SPT phases [22], we need to ensure that the error correction circuit cannot perform operations that violate these symmetries [9]. For example, performing an operation that corrects a single |+ error directly to the |− state would be a violation of the chiral symmetry.…”

Topological quantum interference in a pumped Su-Schrieffer-Heeger lattice

“…Evaluating S D using the free fermion techniques of [44] as outlined in Ref. 43, yields the behavior in Fig. 2(a) for our chain with 2N = 40 sites.…”

“…To characterize the finite size analog of the bulk topological phase transition we employ here the disconnected entanglement entropy S D introduced in [42,43]. S D is defined in terms of both connected and disconnected entanglement entropies of different segments of the system, in order to cancel out all area and volume law contributions to the bipartite entanglement entropy.…”

“…For the finite SSH chain in the topological phase, with both periodic and open boundary conditions at large chain length, S D is equal to 2 log 2 as a result of the entanglement of the localized edge states across the full extent of the chain. With open boundary conditions, S D is equal to zero only in the trivial gapped phase, with a smooth transition between the two phases that becomes increasingly abrupt as the chain size increases [43]. Evaluating S D using the free fermion techniques of [44] as outlined in Ref.…”

Quantum dot coupled to topological insulators: The role of edge states

“…Apart from the original polymer system, the SSH model was realized experimentally and the topological edge states were detected in more controllable settings such as cold atoms [20][21][22][23], electronic states in artificial atomic lattices [24] or superlattices [25], mechanical chains [26], and photonic systems [27][28][29]. Among theoretically predicted signatures of the topological edge states are effects in the entanglement entropy [30], in the decoherence of a coupled qubit [31], and in transport and noise characteristics in non-equilibrium settings where a current is driven through an SSH chain [32][33][34][35][36]. However, to the best of our knowledge, the archetypal mesoscopic setup of a quantum dot coupled to leads has not yet been studied if the latter are modeled as SSH chains.…”