### 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 language | English (US) |
---|---|

Article number | P01005 |

Journal | Journal of Statistical Mechanics: Theory and Experiment |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2007 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Statistics and Probability
- Statistical and Nonlinear Physics

### Cite this

*Journal of Statistical Mechanics: Theory and Experiment*, (1), [P01005]. https://doi.org/10.1088/1742-5468/2007/01/P01005

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

Research output: Contribution to journal › Article

*Journal of Statistical Mechanics: Theory and Experiment*, no. 1, P01005. https://doi.org/10.1088/1742-5468/2007/01/P01005

}

TY - JOUR

T1 - The Baxter Q-operator for the graded SL(2|1) spin chain

AU - Belitsky, Andrei

AU - Derkachov, S. É

AU - Korchemsky, G. P.

AU - Manashov, A. N.

PY - 2007/1/1

Y1 - 2007/1/1

N2 - 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.

AB - 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.

KW - Integrable spin chains (vertex models)

KW - Quantum integrability (Bethe ansatz)

UR - http://www.scopus.com/inward/record.url?scp=37649032939&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=37649032939&partnerID=8YFLogxK

U2 - 10.1088/1742-5468/2007/01/P01005

DO - 10.1088/1742-5468/2007/01/P01005

M3 - Article

AN - SCOPUS:37649032939

JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

SN - 1742-5468

IS - 1

M1 - P01005

ER -