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

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{é}-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.

17 pages, 7 figures

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• Topological phases of commensurate or incommensurate non-Hermitian Su-Schrieffer-Heeger lattices
• Calculations of Chern number: equivalence of real-space and twisted-boundary-condition formulae
• Topological pumping induced by spatiotemporal modulation of interaction
• Quantum Walk on Orbit Spaces
• Inter-species topological phases via a dynamical gauge field
• Efficient Berry Phase Calculation via Adaptive Variational Quantum Computing Approach
• Nonperturbative signatures of fractons in the twisted multiflavor Schwinger Model
• Topological bound states in a lattice of rings with nearest-neighbour interactions