Topological Disorder Parameter
Bin-Bin Chen, Hong-Hao Tu, Zi Yang Meng, Meng Cheng

TL;DR
This paper introduces the topological disorder parameter (TDP), a new invariant for characterizing gapped quantum phases with symmetry, linking it to quantum dimensions and entanglement properties, and demonstrating its effectiveness through lattice models.
Contribution
The paper defines the TDP as a novel topological invariant, relates it to quantum dimensions and entanglement entropy, and applies it to various lattice models to detect topological order.
Findings
TDP scales as exp(-αl+γ) with γ related to quantum dimensions.
TDP reduces to topological Rényi entropy in certain symmetry cases.
Numerical and analytical results confirm TDP as a robust topological order detector.
Abstract
We introduce a many-body topological invariant, called the topological disorder parameter (TDP), to characterize gapped quantum phases with global internal symmetry in (2+1)d. TDP is defined as the constant correction that appears in the ground state expectation value of a partial symmetry transformation applied to a connected spatial region , the absolute value of which scales generically as where is the perimeter of and is the TDP. Motivated by a topological quantum field theory interpretation of the operator, we show that can be related to the quantum dimension of the symmetry defect, and provide a general formula for when the entanglement Hamiltonian of the topological phase can be described by a (1+1)d conformal field theory (CFT). A special case of TDP is equivalent to the topological R\'enyi entanglement entropy…
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