Baxter operators with deformed symmetry

D. Chicherin; D. Karakhanyan; R. Kirschner; S. Derkachov

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Baxter operators with deformed symmetry

D. Chicherin, S. Derkachov, D. Karakhanyan, R. Kirschner

Mathematical Physics · Submitted 13 Nov 2012

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Baxter operators are constructed for quantum spin chains with deformed $s\ell_2$ symmetry.

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Baxter operators are constructed for quantum spin chains with deformed $s\ell_2$ symmetry. The parallel treatment of Yang-Baxter operators for the cases of undeformed, trigonometrically and elliptically deformed symmetries presented earlier and relying on the factorization regarding parameter permutations is extended to the global chain operators following the scheme worked out recently in the undeformed case.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Baxter operators are constructed for quantum spin chains with deformed $s\ell_2$ symmetry.	contribution 0.95	0.88	0.56	asserted 1.00
s1	The parallel treatment of Yang-Baxter operators for the cases of undeformed, trigonometrically and elliptically deformed symmetries presented earlier and relying on the factorization regarding parameter permutations is extended to the global chain operators following the scheme worked out recently in the undeformed case.	contribution 0.74	0.60	0.32	asserted 0.99

What kind of paper the classifier reports this is: theoretical result 0.86 · evidence from proof or derivation 0.99.

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Original abstract

Baxter operators are constructed for quantum spin chains with deformed $s\ell_2$ symmetry. The parallel treatment of Yang-Baxter operators for the cases of undeformed, trigonometrically and elliptically deformed symmetries presented earlier and relying on the factorization regarding parameter permutations is extended to the global chain operators following the scheme worked out recently in the undeformed case.

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5 arXiv papers cite this in 7 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 4 sentences without a confident label

Cites it as background 3 papers

Among other approaches to the derivation of the $TQ$-relations for the “deformed” case we would like to mention the approach based on the factorization of the Yang–Baxter operators, see [ref] and references therein, and the approach based on the concept of $q$-characters [ref] developed in the paper [ref] .

Quantum groups and functional relations for higher rank · Conclusions · 0.89
Other interesting connections are discussed in [ref] .

Comment on star-star relations in statistical mechanics and elliptic gamma-function identities · Introduction · 0.97
We refer the reader to [ref] and references therein for alternative approaches.

The non-compact XXZ spin chain as stochastic particle process · Conclusion · 0.98

What it cites · 24 sentences without a confident label

Builds on 1 paper

However, going beyond the review of [ref] , here we establish a useful relation between the two Baxter operators $Q_1$ and $Q_2$.

Baxter operators for arbitrary spin · Factorized Yang-Baxter operators and Baxter equation · 0.81

Uses the method or tool of 2 papers

follow the general strategy and are very similar as in [ref] .

Baxter operators for arbitrary spin · Factorized Yang-Baxter operators and Baxter equation · 0.86
Choosing this operator representation of the algebra generators one can obtain the factorized form for the $L$-operator [ref] [equation] where we denote matrices involving theta functions as follows [equation] and specify the relation between two sets of spectral parameters $(u_1,u_2)$ and $(u,ℓ)$ according to ([ref]) as [equation] All notations and properties of theta functions relevant for us are collected in Appendix [ref].

Intertwining operators for Sklyanin algebra and elliptic hypergeometric series · Elliptic $L$-operator and parameter permutation operators · 0.85

Compares with 5 papers

The relation of this to another approach worked out in [ref] has been investigated in detail [ref] .

A Shortcut to the Q-Operator · Introduction · 0.82
The relation of this to another approach worked out in [ref] has been investigated in detail [ref] .

Baxter operators for arbitrary spin II · Introduction · 0.82
One of the possible solutions of the this relation which is suitable for our purposes has the form[Here and below we adopt the notation $Γ(∓a ∓b)=Γ(a+b)Γ(-a+b)Γ(a-b)Γ(-a-b)$.] [ref] [equation] A similar expression appeared in [ref] with some additional exponentials and without the shift by $τ/2$.

Yang-Baxter equation, parameter permutations, and the elliptic beta integral · Elliptic $L$-operator and parameter permutation operators · 0.88

Cites as support 1 paper

Finally, the indicated operators $S^1, S^2, S^3$ respect Coxeter relations ([ref]), ([ref]) [ref] that is the direct consequence of the elliptic beta integral evaluation formula by V.

Yang-Baxter equation, parameter permutations, and the elliptic beta integral · Elliptic $L$-operator and parameter permutation operators · 0.97

Cites as background 9 papers

In Section 2 a summary of the relevant relations of [ref] is given formulating simultaneously the relations which hold uniformly in all three cases.

Baxter operators for arbitrary spin · Introduction · 0.91
They have been considered recently in [ref] and also in [ref] concerning the undeformed $sℓ_2$; the present study will not touch this case.

Baxter operators for arbitrary spin II · Factorized Yang-Baxter operators and Baxter equation · 0.93
They have been considered recently in [ref] and also in [ref] concerning the undeformed $sℓ_2$; the present study will not touch this case.

A Shortcut to the Q-Operator · Factorized Yang-Baxter operators and Baxter equation · 0.93

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