56 research outputs found

    Topological invariants for interacting systems: from twisted boundary condition to center-of-mass momentum

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    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

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    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
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