On determinant representations of scalar products and form factors in the SoV approach: the XXX case

Abstract

In the present article we study the form factors of quantum integrable lattice models solvable by the separation of variables (SoV) method. It was recently shown that these models admit universal determinant representations for the scalar products of the so-called separate states (a class which includes in particular all the eigenstates of the transfer matrix). These results permit to obtain simple expressions for the matrix elements of local operators (form factors). However, these representations have been obtained up to now only for the completely inhomogeneous versions of the lattice models considered. In this article we give a simple algebraic procedure to rewrite the scalar products (and hence the form factors) for the SoV related models as Izergin or Slavnov type determinants. This new form leads to simple expressions for the form factors in the homogeneous and thermodynamic limits. To make the presentation of our method clear, we have chosen to explain it first for the simple case of the $XXX$ Heisenberg chain with anti-periodic boundary conditions. We would nevertheless like to stress that the approach presented in this article applies as well to a wide range of models solved in the SoV framework.

46 pages

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Cited by in corpus (28)

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• On quantum separation of variables
• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra I
• The hexagon in the mirror: the three-point function in the SoV representation
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• Complete spectrum of quantum integrable lattice models associated to Y(gl(n)) by separation of variables
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• Separation of variables for rational gl(n) spin chains in any compact representation, via fusion, embedding morphism and Backlund flow
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• Correlation functions by Separation of Variables: the XXX spin chain
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• Spin-$s$ Rational $Q$-system
• Thermodynamic limit of the two-spinon form factors for the zero field XXX chain
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• Separation of variables for higher rank integrable models: review of recent progress
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