A Q-Operator for Open Spin Chains I: Baxter's TQ Relations

Research output: Contribution to journalArticle

Abstract

We construct a Q-operator for the open XXZ Heisenberg quantum spin chain with diagonal boundary conditions and give a rigorous derivation of Baxter's TQ relation. Key roles in the theory are played by a particular infinite-dimensional solution of the reflection equation and by short exact sequences of intertwiners of the standard Borel subalgebras of Uq(sl2ˆ). The resulting Bethe equations are the same as those arising from Sklyanin's algebraic Bethe ansatz.
Original languageEnglish
Number of pages39
JournalJournal of Physics A: Mathematical and General
Publication statusSubmitted - 29 Jan 2020

Fingerprint

operators
derivation
boundary conditions

Cite this

@article{f19c1340ab8d48849c0bf07e6b87100c,
title = "A Q-Operator for Open Spin Chains I: Baxter's TQ Relations",
abstract = "We construct a Q-operator for the open XXZ Heisenberg quantum spin chain with diagonal boundary conditions and give a rigorous derivation of Baxter's TQ relation. Key roles in the theory are played by a particular infinite-dimensional solution of the reflection equation and by short exact sequences of intertwiners of the standard Borel subalgebras of Uq(sl2ˆ). The resulting Bethe equations are the same as those arising from Sklyanin's algebraic Bethe ansatz.",
author = "Weston, {Robert Andrew} and Bart Vlaar",
year = "2020",
month = "1",
day = "29",
language = "English",
journal = "Journal of Physics A: Mathematical and General",
issn = "0305-4470",
publisher = "IOP Publishing",

}

TY - JOUR

T1 - A Q-Operator for Open Spin Chains I: Baxter's TQ Relations

AU - Weston, Robert Andrew

AU - Vlaar, Bart

PY - 2020/1/29

Y1 - 2020/1/29

N2 - We construct a Q-operator for the open XXZ Heisenberg quantum spin chain with diagonal boundary conditions and give a rigorous derivation of Baxter's TQ relation. Key roles in the theory are played by a particular infinite-dimensional solution of the reflection equation and by short exact sequences of intertwiners of the standard Borel subalgebras of Uq(sl2ˆ). The resulting Bethe equations are the same as those arising from Sklyanin's algebraic Bethe ansatz.

AB - We construct a Q-operator for the open XXZ Heisenberg quantum spin chain with diagonal boundary conditions and give a rigorous derivation of Baxter's TQ relation. Key roles in the theory are played by a particular infinite-dimensional solution of the reflection equation and by short exact sequences of intertwiners of the standard Borel subalgebras of Uq(sl2ˆ). The resulting Bethe equations are the same as those arising from Sklyanin's algebraic Bethe ansatz.

M3 - Article

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

SN - 0305-4470

ER -