Topological Green's Function Zeros in an Exactly Solved Model and Beyond.

Area of Science:

• Condensed Matter Physics
• Quantum Information Science
• High-Energy Physics

Background:

• Topological electronic band structures and strong interparticle interactions are key for designing entangled many-body systems.
• Fractionalized topological insulators represent a promising class of such systems.

Purpose of the Study:

• To investigate an exactly integrable model of a fractionalized topological insulator.
• To analyze the role of topological bands of zeros in the fermionic Green's function.
• To understand their effect on topological invariants and transport properties.

Main Methods:

• Utilizing controlled perturbation theory around an exactly integrable limit.
• Analyzing the fermionic Green's function for topological bands of zeros.
• Examining the system's behavior near a Higgs transition signaling fractionalization breakdown.

Main Results:

• Demonstrated the existence of topological bands of zeros in the fermionic Green's function.
• Showed these bands affect the topological invariant but not quantized transport response.
• Observed a finite "lifetime" for topological bands of zeros before fractionalization breakdown.
• Identified edge states and edge zeros at domain walls between different system phases.

Conclusions:

• The studied model serves as a platform for controlled investigations of Green's function zeros phenomenology.
• The underlying lattice gauge theory highlights interdisciplinary connections between condensed matter, high-energy physics, and quantum information.
• This work advances the understanding of topological phenomena in strongly correlated systems.