Modern Physics Letters A

Integrable matrix product states of ABJM theory from projecting method

Nan Bai, Mao-Zhong Shao

Published May 3, 2025• 2 citations

Abstract

In this paper, we investigate the integrable boundary states in ABJM theory. We find an integrability condition for the two-site integrable matrix product state (MPS) similar to the KT-relation. We also construct a class of non-trivial MPSs from the projected K-matrices.

DOI: 10.1142/s0217732325500683

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Modern Physics Letters A

Integrable matrix product states of ABJM theory from projecting method

Nan Bai, Mao-Zhong Shao

Published May 3, 2025• 2 citations

Publisher

Abstract

DOI: 10.1142/s0217732325500683

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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.

Solving for the integrable boundary states of the ABJM spin chain from

KT

-relations

We study integrable boundary states of the alternating SU(4) spin chain arising in ABJM theory. Starting from the

KT

-relation, we directly solve the integrability constraints for states with

n

-site translational invariance. For odd and even

n

, these constraints are reduced respectively to state equations and operator equations for the elementary

n

-site block and the matrix

K(u)

. We analyze chiral and achiral cases for

n\leq4

. In the 1-site case we allow general operator-valued integrable pairs with an internal space, while in the remaining cases we focus on

c

-number solutions.

{m}^{5}

{m}^{3}

, where

m

is the matrix dimension, and $m\ensuremath{\simeq}100--1000$ in typical cases. We test the method on the

S=\frac{1}{2}

and

S=1

Heisenberg chains. It is also applicable to nontranslationally invariant cases. The method makes ground-state calculations with periodic boundary conditions about as efficient as traditional DMRG calculations for systems with open boundaries.