Chiral Integrable Boundary States of ABJM Spin Chain from Reflection Equations

TL;DR

The paper develops a systematic framework to construct chiral integrable boundary states as $2n$-site matrix product states in the ABJM spin chain using reflection equations and fusion, and derives exact overlap formulas for four-site cases that are governed by Gaudin-determinant structures with K-matrix dependent factors. It distinguishes SP- and SNP-type reflections, explores two-site and four-site constructions, and extends to dressed (bond-dimension>1) MPS and general $2n$-site generalizations, providing detailed norm and Gaudin-determinant analyses for parity-symmetric Bethe states. The work delivers explicit overlap formulas for symmetric and antisymmetric SNP K-matrices, and numerically analyzes chiral integrable subspaces for small system sizes, revealing a rich partially-explored structure and suggesting the existence of additional chiral states beyond current constructions. Overall, the study advances boundary integrability in ABJM by linking K-matrix reflection data to concrete, computable chiral MPS and their overlaps with Bethe eigenstates, with potential implications for quenches and defect CFT contexts.

Abstract

We develop a general framework for constructing $2n$-site chiral integrable matrix product states in Aharony-Bergman-Jafferis-Maldacena spin chain, based on reflection equations and the fusion procedure. For four-site chiral integrable product states, we propose their exact overlap formulas with Bethe states. We also investigate the chiral integrable subspaces numerically.

Figures (13)

• Figure 1: Two SP-type reflection $K$-matrices: (a) soliton to soliton reflection; (b) anti-soliton to anti-soliton reflection.
• Figure 2: Two SP-type reflections.
• Figure 3: Two SNP-type reflection $K$-matrices: (a) soliton to anti-soliton reflection; (b) anti-soliton to soliton reflection.
• Figure 4: Two SNP-type reflections.
• Figure 5: SP- and SNP-mixed reflection process.