Exact Fractionalized Ground States in an Extended Spin-1 Kitaev Chain

Area of Science:

• Condensed Matter Physics
• Quantum Many-Body Systems
• Spin Chains

Background:

• The Affleck-Kennedy-Lieb-Tasaki (AKLT) model provides a framework for exactly solvable spin chains.
• Kitaev-like models are crucial for understanding exotic quantum phases.
• Spin-1 chains exhibit complex behaviors relevant to magnetism and quantum computation.

Purpose of the Study:

• To present exact solutions for a spin-1 chain with Kitaev-like couplings.
• To explore an expanded Kitaev model incorporating bilinear and biquadratic terms.
• To investigate the nature of ground-state degeneracy and fractionalized excitations.

Main Methods:

• Reformulating the Hamiltonian as a sum of projection operators at an exactly solvable point.
• Projecting the component of spin along the bond direction, differing from the AKLT model's approach.
• Expressing ground states concisely using matrix product states.

Main Results:

• Achieved exact solutions for the spin-1 Kitaev-like model.
• Demonstrated exponential ground-state degeneracy through fractionalized spin-1/2 objects.
• Constructed a phase diagram by varying bilinear and biquadratic term strengths.

Conclusions:

• The fractionalized states offer a qualitative understanding of the spin-1 Kitaev model.
• Approximate forms for ground states and low-lying excitations were derived.
• This work provides insights into novel quantum phases in spin systems.