Soutenance de thèse: Hao Pei

Separation of Variables and Correlation Functions of Quantum Integrable Systems

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Hao Pei

Online defense – Zoom Meeting ID: 971 0660 6090 – Password: 379764

Jury:

Christian Hagendorf, Université catholique de Louvain, examinateur

Nikolai Kitanine, Université de Bourgogne, examinateur

Karol Kozlowski, CNRS, ENS de Lyon, rapporteur

Vincent Pasquier, CEA Saclay, Université Paris Saclay, examinateur

Eric Ragoucy, CNRS, Université Savoie Mont Blanc, rapporteur

Véronique Terras, Université Paris-Saclay, directrice de thèse

Resumé:

The aim of this thesis is to develop an approach for computing correlation functions of quantum integrable lattice models within the quantum version of the Separation of Variables (SoV) method. SoV is a powerful method which applies to a wide range of quantum integrable models with various boundary conditions. Yet, the problem of computing correlation functions within this framework is still widely open. Here, we more precisely consider two simple models solvable by SoV: the XXX and XXZ Heisenberg chains of spins 1/2, with anti-periodic boundary conditions, or more generally quasi-periodic boundary conditions with a non-diagonal twist. We first review their solution by SoV, which present some similarities but also crucial differences. Then we study the scalar products of separate states, a class of states that notably contains all the eigenstates of the model. We explain how to obtain convenient determinant representations for these scalar products. We also explain how to generalize these determinant representations in the case of form factors, i.e. of matrix elements of the local operators in the basis of eigenstates. These form factors are of particular interest for the computation of correlation functions since all correlation functions can be obtained as a sum over form factors. Finally, we consider more general elementary building blocks for the correlation functions, and explain how to recover, in the thermodynamic limit of the model, the multiple integral representations that were previously obtained from the consideration of the periodic models by algebraic Bethe Ansatz.

 


Date/Time : 14/12/2020 - 14:00 - 17:00

Location : LPTMS (100% online seminar)

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