ENCORE: An extended contractor renormalization algorithm.

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics
• Computational Physics

Background:

• Contractor renormalization (CORE) is a real-space renormalization-group technique.
• The original CORE method decomposes lattices into blocks, with effective degrees of freedom as tensor products.
• This limits its applicability to specific model types.

Purpose of the Study:

• To extend the Contractor renormalization (CORE) method.
• To enable derivation of effective models beyond simple tensor product Hilbert spaces.
• To facilitate the search for microscopic models emulating exotic low-energy phenomena.

Main Methods:

• Generalization of the Contractor renormalization (CORE) method.
• Development of a framework to derive effective models with arbitrary Hilbert spaces.
• Application to microscopic models for emulation of exotic quantum systems.

Main Results:

• An extended CORE method capable of deriving effective models with non-tensor product Hilbert spaces.
• Demonstration of the method's suitability for emulating complex low-energy models.
• Guidance for the design of novel quantum devices.

Conclusions:

• The generalized CORE method significantly expands the scope of renormalization-group techniques.
• This advancement is crucial for understanding and designing systems exhibiting exotic quantum behaviors.
• The method provides a powerful tool for theoretical physics and experimental quantum device development.