Abstract:Bound states of two interacting particles moving on a lattice can exhibit remarkable features that are not captured by the underlying single-particle picture. Inspired by this phenomenon, we introduce a novel framework by which genuine interaction-induced geometric and topological effects can be realized in quantum-engineered systems. Our approach builds on the design of effective lattices for the center-of-mass motion of two-body bound states (doublons), which can be created through long-range interactions. T… Show more
“…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].…”
We study the Hall response of topologically trivial mobile impurities (Fermi polarons) interacting weakly with majority fermions forming a Chern-insulator background. This setting involves a rich interplay between the genuine many-body character of the polaron problem and the topological nature of the surrounding cloud. When the majority fermions are accelerated by an external field, a transverse impurity current can be induced. To quantify this polaronic Hall effect, we compute the drag transconductivity, employing controlled diagrammatic perturbation theory in the impurity-fermion interaction. We show that the impurity Hall drag is not simply proportional to the Chern number characterizing the topological transport of the insulator on its own-it also depends continuously on particle-hole breaking terms, to which the Chern number is insensitive. However, when the insulator is tuned across a topological phase transition, a sharp jump of the impurity Hall drag results, for which we derive an analytical expression. We describe how to experimentally detect the polaronic Hall drag and its characteristic jump, setting the emphasis on the circular dichroism displayed by the impurity's absorption rate.
“…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].…”
We study the Hall response of topologically trivial mobile impurities (Fermi polarons) interacting weakly with majority fermions forming a Chern-insulator background. This setting involves a rich interplay between the genuine many-body character of the polaron problem and the topological nature of the surrounding cloud. When the majority fermions are accelerated by an external field, a transverse impurity current can be induced. To quantify this polaronic Hall effect, we compute the drag transconductivity, employing controlled diagrammatic perturbation theory in the impurity-fermion interaction. We show that the impurity Hall drag is not simply proportional to the Chern number characterizing the topological transport of the insulator on its own-it also depends continuously on particle-hole breaking terms, to which the Chern number is insensitive. However, when the insulator is tuned across a topological phase transition, a sharp jump of the impurity Hall drag results, for which we derive an analytical expression. We describe how to experimentally detect the polaronic Hall drag and its characteristic jump, setting the emphasis on the circular dichroism displayed by the impurity's absorption rate.
“…By mapping the subspaces of lowest-energy two-boson states into single-particle models, we show that the system has a topologically nontrivial phase. In contrast with other realizations of two-body topological states [13,[29][30][31][32][33][34][35][36][37][38][39][40][41], in this case the topological character is controlled through effective two-boson tunneling amplitudes that depend on the interaction strength. In a diamond chain with open boundaries, this topological phase is benchmarked by the presence of robust in-gap states localized at the edges, which are in turn composed of bound pairs of bosons, each occupying a localized single-particle eigenstate.…”
Section: Introductionmentioning
confidence: 86%
“…These two-body states, which are stable even for repulsive interactions due to the finite bandwidth of the singleparticle kinetic energy [9], have been observed [10][11][12][13] and extensively analyzed [14][15][16][17][18][19][20][21][22][23][24][25] in optical lattices, and have also been emulated in photonic systems [26,27] and in topolectrical circuits [28]. Motivated in part by these advances, several recent works have focused on the topological properties of two-body states [13,[29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44], with the long-term aim of paving the path to a better comprehension of topological phases in a full many-body interacting scenario. A distinctive advantage that these small-sized systems offer is that it is often possible to map the problem of two interacting particles in a lattice into a single-particle model defined in a different lattice, the topological characterization of which can then be performed with well-established techniques [31][32][33]36,40,…”
Section: Introductionmentioning
confidence: 99%
“…Motivated in part by these advances, several recent works have focused on the topological properties of two-body states [13,[29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44], with the long-term aim of paving the path to a better comprehension of topological phases in a full many-body interacting scenario. A distinctive advantage that these small-sized systems offer is that it is often possible to map the problem of two interacting particles in a lattice into a single-particle model defined in a different lattice, the topological characterization of which can then be performed with well-established techniques [31][32][33]36,40,41].…”
In flat-band systems, destructive interference leads to the localization of noninteracting particles and forbids their motion through the lattice. However, in the presence of interactions the overlap between neighboring single-particle localized eigenstates may enable the propagation of bound pairs of particles. In this work, we show how these interaction-induced hoppings can be tuned to obtain a variety of two-body topological states. In particular, we consider two interacting bosons loaded into the orbital angular momentum l = 1 states of a diamond-chain lattice, wherein an effective π flux may yield a completely flat single-particle energy landscape. In the weakly interacting limit, we derive effective single-particle models for the two-boson quasiparticles which provide an intuitive picture of how the topological states arise. By means of exact diagonalization calculations, we benchmark these states and we show that they are also present for strong interactions and away from the strict flat-band limit. Furthermore, we identify a set of doubly localized two-boson flat-band states that give rise to a special instance of Aharonov-Bohm cages for arbitrary interactions.
“…Furthermore, as the first step towards understanding topological many-body systems, one may judiciously focus on the simplest nontrivial subspace with interactions, that of only two excitations. Indeed, the two-excitation sector already provides some hallmarks of multi-excitation physics, such as bound two-particle states and novel bands in the quasiparticle bandstructure 23 – 27 . Figure 1 Sketches of dimerized chains of oscillators, each of resonance frequency , and represented by yellow and pink disks.…”
We investigate theoretically the Bose–Hubbard version of the celebrated Su-Schrieffer-Heeger topological model, which essentially describes a one-dimensional dimerized array of coupled oscillators with on-site interactions. We study the physics arising from the whole gamut of possible dimerizations of the chain, including both the weakly and the strongly dimerized limiting cases. Focusing on two-excitation subspace, we systematically uncover and characterize the different types of states which may emerge due to the competition between the inter-oscillator couplings, the intrinsic topology of the lattice, and the strength of the on-site interactions. In particular, we discuss the formation of scattering bands full of extended states, bound bands full of two-particle pairs (including so-called ‘doublons’, when the pair occupies the same lattice site), and different flavors of topological edge states. The features we describe may be realized in a plethora of systems, including nanoscale architectures such as photonic cavities, optical lattices and qubits, and provide perspectives for topological two-particle and many-body physics.
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