Work

Fusion of low-entanglement excitations in 2D toric code

Year: 2025

Type: article

Abstract: On top of a D D -dimensional gapped bulk state, Low Entanglement Excitations (LEE) on d( d ( < D ) -dimensional sub-manifolds can have extensive energy but preserves the entanglement area law of the ground state. Due to their multi-dimensional nature, the LEEs embody a higher-category structure in quantum systems. They are the ground state of a modified Hamiltonian and hence capture the notions of ‘defects’ of generalized symmetries. In previous works, we studied the low-entanglement excitations in a trivial phase as well as those in invertible phases. We find that LEEs in these phases have the same structure as lower-dimensional gapped phases and their defects within. In this paper, we study the LEEs inside non-invertible topological phases. We focus on the simple example of \mathbb{Z}_2 ℤ 2 toric code and discuss how the fusion result of 1d LEEs with 0d morphisms can depend on both the choice of fusion circuit and the ordering of the fused defects.

Source: SciPost Physics

DOI: 10.21468/scipostphys.18.3.106

Authors: Jingyu Zhao, Xie Chen

Institutions: Tsinghua University, California Institute of Technology

Language: English

Topic: Quantum many-body systems

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: diamond

Funders: Simons Foundation, California Institute of Technology, Walter Burke Institute for Theoretical Physics, Institute for Quantum Information and Matter, California Institute of Technology

Awards: G115469955, G5745281885