The Baxter Q-operator for the graded SL(2|1) spin chain

Andrei Belitsky, S. É Derkachov, G. P. Korchemsky, A. N. Manashov

Research output: Contribution to journalArticle

28 Citations (Scopus)

Abstract

We study an integrable non-compact superspin chain model that emerged in recent studies of the dilatation operator in the super-Yang-Mills theory. It was found that the latter can be mapped into a homogeneous Heisenberg magnet with the quantum space in all sites corresponding to infinite dimensional representations of the SL(2|1) group. We extend the method of the Baxter Q-operator to spin chains with supergroup symmetry and apply it to determine the eigenspectrum of the model. Our analysis relies on a factorization property of the -operators acting on the tensor product of two generic infinite dimensional SL(2|1) representations. It allows us to factorize an arbitrary transfer matrix into a product of three 'elementary' transfer matrices which we identify as Baxter Q-operators. We establish functional relations between transfer matrices and use them to derive the T-Q relations for the Q-operators. The proposed construction can be generalized to integrable models based on supergroups of higher rank and, as distinct from the Bethe ansatz, it is not sensitive to the existence of the pseudovacuum state in the quantum space of the model.

Original languageEnglish (US)
Article numberP01005
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number1
DOIs
StatePublished - Jan 1 2007

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Spin Chains
operators
Transfer Matrix
Operator
Elementary matrix
Factorise
Integrable Models
Dilatation
Bethe Ansatz
Yang-Mills Theory
products
Yang-Mills theory
factorization
Tensor Product
Factorization
magnets
Model
tensors
Model-based
Distinct

Keywords

  • Integrable spin chains (vertex models)
  • Quantum integrability (Bethe ansatz)

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistical and Nonlinear Physics

Cite this

The Baxter Q-operator for the graded SL(2|1) spin chain. / Belitsky, Andrei; Derkachov, S. É; Korchemsky, G. P.; Manashov, A. N.

In: Journal of Statistical Mechanics: Theory and Experiment, No. 1, P01005, 01.01.2007.

Research output: Contribution to journalArticle

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