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UID:0-758@lptms.universite-paris-saclay.fr
DTSTART:20201214T140000Z
DTEND:20201214T170000Z
DTSTAMP:20201120T140621Z
URL:http://www.lptms.universite-paris-saclay.fr/seminars/soutenance-de-the
 se-hao-pei/
SUMMARY:Soutenance de thèse: Hao Pei - LPTMS (100% online seminar) - 14 D
 éc 20 14:00
DESCRIPTION:Separation of Variables and Correlation Functions of Quantum In
 tegrable Systems\npar\n\nHao Pei\nOnline defense - Zoom Meeting ID: 971 06
 60 6090 - Password: 379764\nJury:\n\nChristian Hagendorf\, Université c
 atholique de Louvain\, examinateur\n\nNikolai Kitanine\, Université de B
 ourgogne\, examinateur\n\nKarol Kozlowski\, CNRS\, ENS de Lyon\, rapport
 eur\n\nVincent Pasquier\, CEA Saclay\, Université Paris Saclay\, examina
 teur\n\nEric Ragoucy\, CNRS\, Université Savoie Mont Blanc\, rapporteur
 \n\nVéronique Terras\, Université Paris-Saclay\, directrice de thèse\n
 \nResumé:\nThe aim of this thesis is to develop an approach for computing
  correlation functions of quantum integrable lattice models within the qua
 ntum version of the Separation of Variables (SoV) method. SoV is a powerfu
 l method which applies to a wide range of quantum integrable models with v
 arious boundary conditions. Yet\, the problem of computing correlation fun
 ctions within this framework is still widely open. Here\, we more precisel
 y consider two simple models solvable by SoV: the XXX and XXZ Heisenberg c
 hains of spins 1/2\, with anti-periodic boundary conditions\, or more gene
 rally quasi-periodic boundary conditions with a non-diagonal twist. We fir
 st 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 mode
 l. We explain how to obtain convenient determinant representations for the
 se scalar products. We also explain how to generalize these determinant re
 presentations 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 pa
 rticular interest for the computation of correlation functions since all c
 orrelation functions can be obtained as a sum over form factors. Finally\,
  we consider more general elementary building blocks for the correlation f
 unctions\, and explain how to recover\, in the thermodynamic limit of the 
 model\, the multiple integral representations that were previously obtaine
 d from the consideration of the periodic models by algebraic Bethe Ansatz.
 \n&nbsp\;
CATEGORIES:seminars
LOCATION:LPTMS (100% online seminar)\, LPTMS - Bâtiment Pascal n° 530 rue
  André Rivière - Université Paris-Saclay\, Orsay\, 91405\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=LPTMS - Bâtiment Pascal n
 ° 530 rue André Rivière - Université Paris-Saclay\, Orsay\, 91405\, Fr
 ance;X-APPLE-RADIUS=100;X-TITLE=LPTMS (100% online seminar):geo:0,0
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