Topological quantum paramagnet in a quantum spin ladder

Abstract

It has recently been found that bosonic excitations of ordered media, such as phonons or spinons, can exhibit topologically nontrivial band structures. Of particular interest are magnon and triplon excitations in quantum magnets, as they can easily be manipulated by an applied field. Here we study triplon excitations in an S=1/2 quantum spin ladder and show that they exhibit nontrivial topology, even in the quantum-disordered paramagnetic phase. Our analysis reveals that the paramagnetic phase actually consists of two separate regions with topologically distinct triplon excitations. We demonstrate that the topological transition between these two regions can be tuned by an external magnetic field. The winding number that characterizes the topology of the triplons is derived and evaluated. By the bulk-boundary correspondence, we find that the non-zero winding number implies the presence of localized triplon end states. Experimental signatures and possible physical realizations of the topological paramagnetic phase are discussed.The last decade has witnessed tremendous progress in understanding and classifying topological band structures of fermions [1][2][3][4]. Soon after the discovery of fermionic topological insulators [5,6], it was recognized that bosonic excitations of ordered media can as well exhibit topologically nontrivial bands [7][8][9][10][11]. Such bosonic topological bands have been observed not long ago for photons in dielectric superlattices [12]. Theoretical proposals of topological states in polaritonic systems have been made [13][14][15], some of which have been observed experimentally [16]. Besides these examples, bosonic band structures are also realized by elementary excitations of quantum spin systems, e.g., by magnons in (anti)ferromagnets or by triplons in dimerized quantum magnets.The study of these collective spin excitations is enjoying growing interest, due to potential applications for magnonic devices and spintronics [17]. Because magnetic excitations are charge neutral, they are weakly interacting, and therefore exhibit good coherence and support nearly dissipationless spin transport. Moreover, the properties of spin excitations are easily tunable by magnetic fields of moderate strength, as the magnetic interaction scale is in most cases relatively small. Of particular interest are magnetic excitations with nontrivial band structure topology, since they exhibit protected magnon or triplon edges states. This was recently studied for triplons in the ordered phase of the Shastry-Sutherland model [9,18,19] and for magnons in an ordered pyrochlore antiferromagnet [20] as well as in an ordered honeycomb ferromagnet [21]. However, the development of a comprehensive topological band theory for magnetic excitations is still in its infancy. Specifically, it has remained unclear whether topological spin excitations can exist also in quantum disordered paramagnets.In this paper, we address this question by considering, as a prototypical example, the paramagnetic phase of an S=1/2 quantum spin ...

Nontrivial Triplon Topology and Triplon Liquid in Kitaev-Heisenberg-type Excitonic Magnets

“…At weaker superexchange, where the ground state is dominated by the J tot = 0 state of the ion, excitations are found to be topologically nontrivial as soon as orbital anisotropies become relevant. Topologically nontrivial triplon bands have been proposed [24] and found to agree with neutron scattering data [44] for SrCu 2 (BO 3 ) 2 , whose ground state consists of singlets on dimers; the discussion has since been extended to other geometries [25,32,36]. Topological triplon states in these dimer systems rely on DM interactions, which we found to compete with symmetric anisotropic exchange in the present onsite-singlet systems.…”

Topological magnon bands for magnonics

“…Long-range ordered magnets display magnons (or spin waves) 14 , valence-bond crystals mostly feature triplons 15 , whereas quantum spin liquids may display fractional excitations 16 , for instance, spinons 17 . For triplons, topological behavior, i.e., non-zero Chern numbers 18 , has been predicted 19,20 and verified 21 in Shastry-Sutherland lattices and in spin ladders 22 . For ferromagnetically ordered systems, topological magnons have been theoretically suggested in kagome lattices 23,24 , pyrochlore lattices 25 , and in honeycomb lattices 26,27 .…”

Absence of localized edge modes in spite of a non-trivial Zak phase in BiCu2PO6

“…Otherwise, the abrupt change of discrete topological invariants cannot be accounted for. These so-called edge states should exist at the ends of strips with a finite discrete Zak phase or a finite winding number [32,51,52] in the bulk. Hence, we are looking for localized edge states at the ends of finite strips of the minimal model for BiCu 2 PO 6 .…”

“…In the main text, we focused on the Zak phase because it is based on a Berry phase and can be defined for any one-dimensional system regardless of symmetries. But there is another often considered topological invariant in one-dimensional systems, namely the winding number [32,51,52,75].…”