Exact renormalization in quantum spin chains

TL;DR

This paper presents an exact real-space renormalization group method to identify solvable quantum spin chains and their ground states, providing a comprehensive list of solutions for SU(2) symmetric chains with spins up to 4 and some with spin 5.

Contribution

It introduces a novel exact renormalization approach for quantum spin chains, classifies solutions into fixed point and non-fixed point classes, and explicitly enumerates solutions for spins up to 4 and some with spin 5.

Findings

Classified solutions into fixed point and non-fixed point categories.

Provided a complete list of exact solutions for SU(2) symmetric chains with S≤4.

Identified ground states as matrix product states or partially ferromagnetic states.

Abstract

We introduce a real-space exact renormalization group method to find exactly solvable quantum spin chains and their ground states. This method allows us to provide a complete list for exact solutions within SU(2) symmetric quantum spin chains with $S\leq 4$ and nearest-neighbor interactions, as well as examples with S=5. We obtain two classes of solutions: One of them converges to the fixed points of renormalization group and the ground states are matrix product states. Another one does not have renormalization fixed points and the ground states are partially ferromagnetic states.