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UID:0-1065@lptms.universite-paris-saclay.fr
DTSTART;TZID=Europe/Paris:20251209T093000
DTEND;TZID=Europe/Paris:20251209T123000
DTSTAMP:20251204T090034Z
URL:http://www.lptms.universite-paris-saclay.fr/seminars/soutenance-de-the
 se-charbel-abetian/
SUMMARY:Soutenance de thèse : Charbel Abetian - Grand amphi\, bâtiment Pa
 scal n° 530 - 9 Déc 25 09:30
DESCRIPTION:Overlaps after a boundary quantum quench in the integrable XXZ 
 spin chain\n\nCharbel Abetian\n&nbsp\;\n\nThe aim of this thesis is to pro
 vide an exact analytical approach for computing overlaps between eigenstat
 es of the open XXZ chain before and after a boundary quench\, that is\, an
  abrupt change of one of the boundary magnetic fields. These overlaps cons
 titute a fundamental building block for the description of the out-of-equi
 librium dynamics of quantum systems and play a crucial role in understandi
 ng their post-quench evolution. We focus on the open XXZ spin-½ chain wit
 h parallel boundary magnetic fields in the massive antiferromagnetic regim
 e\, one of the simplest (non-trivially interacting) integrable models with
  non-periodic boundary conditions. This system can be interpreted as a qua
 ntum chain interacting with its environment through boundary degrees of fr
 eedom. The Quantum Inverse Scattering Method (QISM) and the Algebraic Beth
 e Ansatz (ABA) provide a strong theoretical framework for studying such qu
 antities. The goal of our analysis is to derive\, within this formalism\, 
 exact expressions for the overlaps in the thermodynamic limit. Using Slavn
 ov’s determinant formula for scalar products of Bethe states\, we first 
 derive a determinant representation for the overlaps between pre- and post
 -quench eigenstates. By employing what we refer to as the Gaudin extractio
 n method\, we show that we can extract from this (typically encountered) r
 atio of determinants\, a Cauchy-like determinant\, suitable for taking the
  thermodynamic limit. We show that the overlap between the gapped ground s
 tates (i.e.\, states whose Bethe root configurations contain no holes) bef
 ore and after the quench can be written in a product form\, valid up to ex
 ponentially small corrections in the system size. This allows us to obtain
  a closed analytical expression for the overlap in the infinite-size limit
 \, that depends only on the physical parameters of the model\, namely\, th
 e anisotropy parameter and the boundary magnetic fields. We further verify
  this formula through direct comparison with numerical diagonalization res
 ults. We extend this analysis to a broader class of (ground/excited) state
 s characterized by the presence of a finite number of holes in their Bethe
  root distributions. We show that the Gaudin extraction method yields once
  again a Cauchy-type structure\, now\, perturbed by a matrix of rank equal
  to the number of holes. In this case\, the overlap factorizes into a pref
 actor that can be written in a product form\, similar to the case of the g
 round state\, multiplied by a finite determinant whose size is equal to th
 e number of holes n. In the thermodynamic limit\, we obtain an explicit ex
 pression for the overlap that depends on the anisotropy\, the boundary mag
 netic fields\, and the hole positions. The results presented here lay the 
 groundwork for a broader analytical study of boundary-driven quenches in i
 ntegrable quantum systems through ABA techniques. \n\n&nbsp\;\n\nJury : P.
  Baseilhac\, O. Castro-Alvaredo\, J. De Nardis\, N. Kitanine (co-directeur
  de thèse)\, K. Kozlowski\, V. Pasquier\, V. Terras (directrice de thèse
 )
CATEGORIES:seminars
LOCATION:Grand amphi\, bâtiment Pascal n° 530\, rue André Rivière\, Ors
 ay\, 91405\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=rue André Rivière\, Orsay
 \, 91405\, France;X-APPLE-RADIUS=100;X-TITLE=Grand amphi\, bâtiment Pasca
 l n° 530:geo:0,0
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TZID:Europe/Paris
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DTSTART:20251026T020000
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