Mapping Topological to Conformal Field Theories through strange Correlators

Area of Science:

• Condensed Matter Physics
• Quantum Field Theory
• Topological Phases of Matter

Background:

• Strange correlators are defined for symmetry-protected phases.
• Topological phases of matter exhibit unique properties beyond symmetry protection.
• String-net states provide a framework for realizing topological phases.

Purpose of the Study:

• To extend the concept of strange correlators to topological phases of matter.
• To investigate the nature of partition functions and symmetries in these extended systems.
• To connect lattice models to conformal field theory and tensor network methods.

Main Methods:

• Calculating the inner product between string-net ground states and product states.
• Analyzing the symmetries of transfer matrices derived from string-net states.
• Applying strange correlator concepts to topological sectors of string nets.
• Calculating conformal field theory spectra for specific string net models (Fibonacci, Ising).

Main Results:

• The resulting partition functions are either critical or symmetry broken.
• Nonlocal matrix product operator symmetries are identified as lattice remnants of topological conformal defects.
• Conformal boundary conditions are linked to topological sectors via strange correlators.
• Tensor network renormalization methods are shown to approximate coarse-grained strange correlators.

Conclusions:

• The strange correlator framework successfully extends to topological phases.
• This extension provides insights into critical/symmetry-broken properties and their field theory descriptions.
• The study bridges lattice models, topological order, and conformal field theory through a unified approach.