Universal Wave-Function Overlap and Universal Topological Data from Generic Gapped Ground States.

Area of Science:

• Condensed Matter Physics
• Quantum Information Theory
• Topological Quantum Matter

Background:

• Topological orders characterize exotic phases of matter with unique properties.
• Existing methods like topological entanglement entropy have limitations in scope and efficiency.
• Characterizing topological orders in various dimensions and boundary conditions remains a challenge.

Purpose of the Study:

• To develop a universal method for extracting topological data from generic ground states of gapped quantum systems.
• To demonstrate that these extracted data can fully characterize topological orders, including those with gapped or gapless boundaries.
• To provide a more powerful and numerically efficient alternative to existing methods.

Main Methods:

• The proposed method utilizes wave-function overlaps of ground states.
• For (2+1)D nonchiral topological orders, the data form matrices S and T generating a projective representation of SL(2,Z).
• For higher dimensions with gapped boundaries, the data form a projective representation of the mapping class group MCG(M^d).

Main Results:

• Universal topological data are extracted from generic ground states of gapped systems in any dimension.
• These data fully characterize topological orders with gapped or gapless boundaries.
• The extracted quantities are protected to all orders in perturbation theory for 2D models.

Conclusions:

• Wave-function overlap provides a universal and powerful tool for topological quantum matter research.
• This method surpasses topological entanglement entropy in both power and numerical efficiency.
• The approach facilitates a deeper understanding and characterization of topological orders across different dimensions and boundary conditions.