Topological polarons, quasiparticle invariants, and their detection in one-dimensional symmetry-protected phases

Abstract

In the presence of symmetries, one-dimensional quantum systems can exhibit topological order, which in many cases can be characterized by a quantized value of the many-body geometric Zak or Berry phase. We establish that this topological Zak phase is directly related to the Zak phase of an elementary quasiparticle excitation in the system. By considering various systems, we establish this connection for a number of different interacting phases including: the Su-Schrieffer-Heeger model, p-wave topological superconductors, and the Haldane chain. Crucially, in contrast to the bulk many-body Zak phase associated with the ground state of such systems, the topological invariant associated with quasiparticle excitations (above this ground-state) exhibit a more natural route for direct experimental detection. To this end, we build upon recent work [Nature Communications 7, 11994 (2016)] and demonstrate that mobile quantum impurities can be used, in combination with Ramsey interferometry and Bloch oscillations, to directly measure these quasiparticle topological invariants. Finally, a concrete experimental realization of our protocol for dimerized Mott insulators in ultracold atomic systems is discussed and analyzed.

Topological magnon insulator and quantized pumps from strongly-interacting bosons in optical superlattices

“…Importantly, our topological magnonic models are compatible with recent optical-lattice experiments on magnon physics [22,33]. In this sense, our proposal provides a promising platform for exploring bosonic excitations with topological properties [26]. Finally, we note that topological two-magnon bound states have been analyzed in the context of Chern-insulator models [30,31]; it would be interesting to study the properties of such bound states in symmetry-protected one-dimensional models, such as the magnonic SSH model explored in this work.…”

“…In this way, we show that the single-particle topological properties of the underlying SSH model are transferred to the bosonic magnonic excitations. Such a transfer of topological band properties to interacting-particle settings is reminiscent of that discussed in [23,24], in the context of topological doublons, and in [25,26] in the context of topological polarons; see also [27][28][29][30][31][32] on interplays between topological properties and magnons.…”

Bound states in two-dimensional Fermi systems with quadratic band touching

“…From Eqs. (24) and (25), we see that the degeneracy point happens along the directions where sin(2ϕ q0 ) = sgn(g ⊥ ), i.e., for angles ϕ q0 = π 4 , 5π 4 for g ⊥ > 0 and ϕ q0 = 3π 4 , 7π 4 for g ⊥ < 0. The value of q 0 is determined by the conditions ple, we do find a bound state below the two-particle continuum.…”

Topological transport of mobile impurities

“…A worthwhile goal for future study is the extension to the strong-coupling limit, in particular the analysis of impuritymajority bound state formation. These bound states may have a rather rich physics: They could inherit the topological characteristics of the majority particles [14,15], have opposite chirality as found for the Haldane model in the two-body limit [49], or even be topological when the single-particle states are trivial [50][51][52].…”

“…* dpimenov@umn.edu This goal has been approached in a few recent theoretical works, mainly from two perspectives: Either interaction effects are strong such that an impurity-majority bound state is formed [14][15][16][17], and the impurity inherits the topological quantum numbers of the majority, or, alternatively, one can study the problem in weak coupling [18], as previously done by some of us, with the majority forming a Chern insulator. This perturbative approach is well controlled and does not require additional regularization.…”