56 research outputs found
Topological invariants for interacting systems: from twisted boundary condition to center-of-mass momentum
Beyond the well-known topological band theory for single-particle systems, it
is a great challenge to characterize the topological nature of interacting
multi-particle quantum systems. Here, we uncover the relation between
topological invariants defined through the twist boundary condition (TBC) and
the center-of-mass (c.m.) momentum state in multi-particle systems. We find
that the Berry phase defined through TBC can be equivalently obtained from the
multi-particle Wilson loop formulated by c.m. momentum states. As the Chern
number can be written as the winding of the Berry phase, we consequently prove
the equivalence of Chern numbers obtained via TBC and c.m. momentum state
approaches. As a proof-of-principle example, we study topological properties of
the Aubry-Andr{\'e}-Harper (AAH) model. Our numerical results show that the TBC
approach and c.m. approach are well consistent with each other for both
many-body case and few-body case. Our work lays a concrete foundation and
provides new insights for exploring multi-particle topological states.Comment: 17 pages, 7 figure
Shortcuts to adiabatic Thouless pumping
Thouless pumping, the quantized transport of particles in a cyclic adiabatic
evolution, faces a challenge: slow driving may exceed the coherent time, while
fast driving may break quantization. To address this dilemma, we propose to
speed up Thouless pumping using shortcuts to adiabaticity. By using
counterdiabatic theory, we analytically derive the controlled Hamiltonian for
implementing dispersion-suppressed Thouless pumping beyond the adiabatic
regime. Compared to traditional Thouless pumping methods, our fast topological
pumping approach offers remarkable advantages. Firstly, it enables a
substantial reduction of pumping time up to 11 orders of magnitude faster than
the traditional approach. Secondly, our method effectively suppresses
wavepacket diffusion, further enhancing its efficiency. Furthermore, we
demonstrate the resilience of our protocol against moderate noise levels. Our
study offers a practical and efficient method for achieving fast topological
pumping beyond the adiabatic regime.Comment: Comments and suggestions are welcom
- …