Multiparticle Wannier states and Thouless pumping of interacting bosons

Abstract

The study of topological effects in physics is a hot area, and only recently researchers were able to address the important issues of topological properties of interacting quantum systems. But it is still a great challenge to describe multi-particle and interaction effects. Here, we introduce multi-particle Wannier states for interacting systems with co-translational symmetry. We reveal how the shift of multi-particle Wannier state relates to the multi-particle Chern number, and study the two-boson Thouless pumping in an interacting Rice-Mele model. In addition to the bound-state Thouless pumping in which two bosons move unidirectionally as a whole, we find topologically resonant tunneling in which two bosons move unidirectionally, one by the other, provided the neighboring-well potential bias matches the interaction energy. Our work creates a new paradigm for multi-particle topological effects and lays a cornerstone for detecting interacting topological states.

Topological invariant and cotranslational symmetry in strongly interacting multi-magnon systems

“…Our work studies the interacting two-body topological physics in a 2D quantum lattice model. During the submission/review procedure of this work (arXiv:1611.00205), several works have appeared on the interacting two-body topological physics in 1D quantum lattice models [37][38][39][40]. In [37], the authors explore the topological states of two interacting bosons in the Su-Schrieffer-Heeger (SSH) model.…”

“…In [39], the authors study the multihole topological states of interacting fermions in the SSH model. In [40], the authors explore the multi-particle Wannier states and the Thouless pumping of two interacting bosons in a Rice-Mele model. On the other hand, one may map a general 2D single-particle system onto a 1D two-particle system [41].…”

Topological quantum pump of strongly interacting fermions in coupled chains

“…Here R is the site around which the Wannier state is centred. Because there is full freedom in choosing the phase of each state y ñ | ( ) k m , it is possible to choose these phases in such a way to obtain maximally localized Wannier states [13]. Therefore, even for general l  it is meaningful to talk about local bound pairs.…”

“…can then be found by diagonalizing H(k). It is also possible to create the many body Wannier states [13]…”

“…With these versatile experimental setups it is in principle possible to tune the interactions between the particles, for example with Feshbach resonances or Rydberg atoms, which opens up the possibility to experimentally investigate topological quantum pumps with interacting particles. Because of this there is a renewed theoretical interest on the topic of topological quantum pumps, specifically focusing on the role of interactions [11][12][13][14][15][16][17].…”