Problems with using separated variables for computing expectation values for higher ranks

Abstract

We consider the simplest classical integrable model corresponding to a non-hyperelliptic spectral curve. We show that a certain complicated integral occurs when computing the average of observables in this model. This integral does not factorise. Since similar problems should also exist in the quantum case, we think that a serious question arises of how to deal with these integrals.

15 pages, acknowledgement added

References in corpus (3)

• Hidden Grassmann Structure in the XXZ Model II: Creation Operators
• Hidden Grassmann structure in the XXZ model
• Hidden Grassmann Structure in the XXZ Model III: Introducing Matsubara direction

Cited by in corpus (15)

• Current operators in integrable models: A review
• On quantum separation of variables
• Separation of variables and scalar products at any rank
• Complete spectrum of quantum integrable lattice models associated to Y(gl(n)) by separation of variables
• On Scalar Products in Higher Rank Quantum Separation of Variables
• On quantum separation of variables beyond fundamental representations
• Complete spectrum of quantum integrable lattice models associated to ${\mathcal{U}}_q(\widehat{g{l}_n})$ by separation of variables
• Separation of variables bases for integrable $g{l}_{\mathcal{M}|\mathcal{N}}$ and Hubbard models
• On the calculation of the correlation functions of the ${\mathfrak{sl}}_3$-model by means of the reduced qKZ equation
• Correlation functions by Separation of Variables: the XXX spin chain
• Correlation functions for open XXZ spin 1/2 quantum chains with unparallel boundary magnetic fields
• All correlation functions of the open XXX spin 1/2 quantum chains for unparallel boundary magnetic fields with one constraint
• On correlation functions for the open XXZ chain with non-longitudinal boundary fields : the case with a constraint
• Separation of variables for higher rank integrable models: review of recent progress
• On correlation functions in models related to the Temperley-Lieb algebra