Matrix-Product State Skeletons in Onsager-Integrable Quantum Chains.

Area of Science:

• Condensed Matter Physics
• Quantum Many-Body Theory
• Quantum Information Science

Background:

• Matrix-product states (MPS) are crucial for describing ground states in certain quantum many-body systems.
• Previous studies established dense MPS skeletons in free-fermion models, enabling analytic ground state approximations.
• Understanding MPS skeletons in interacting systems is vital for advancing quantum simulations and condensed matter theory.

Purpose of the Study:

• To investigate and expose the MPS skeleton in interacting spin chains, specifically the N-state Onsager-integrable chiral clock families.
• To determine if MPS can represent eigenstates beyond ground states in these interacting systems.
• To explore the applicability of these findings to other interacting models and the disorder parameter.

Main Methods:

• Construction of specific MPS for N-state Onsager-integrable chiral clock models.
• Analysis of MPS properties within gapped regions surrounding fixed-point Hamiltonians.
• Identification of MPS as eigenstates in both gapped and non-gapped spectral regions.

Main Results:

• A dense MPS skeleton was constructed in the gapped regions of the chiral clock models.
• These MPS represent ground states in specific spectral sectors outside the gapped regions.
• New MPS eigenstates corresponding to low-lying excited states were identified, extending previous work.
• A closed-form expression for the disorder parameter in interacting models was derived.

Conclusions:

• The study successfully extends the concept of MPS skeletons to interacting quantum systems.
• The constructed MPS provide valuable tools for analyzing both ground and excited states in these models.
• The findings highlight the general applicability of methods based on the Onsager algebra, transcending specific model representations.