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

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

URL: http://arxiv.org/abs/2211.07494v2
Date: Thu, 15 Dec 2022 01:12:31 GMT
Title: Topological invariants for interacting systems: from twisted boundary condition to center-of-mass momentum
Authors: Ling Lin, Yongguan Ke and Chaohong Lee
Abstract summary: 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. 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.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
Abstract: 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.

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