Soutenance de thèse: Sebastian GRIJALVA

Boundary effects in Quantum Spin Chains and Finite-Size Effects in the Toroidal Correlated Percolation model


Sebastian Grijalva


Christian Hagendorf, Université catholique de Louvain, examinateur

Jacopo De Nardis, ENS, invité

Nikolai Kitanine, Institut de Mathématiques de Bourgogne, examinateur

Karol Kozlowski, ENS de Lyon, rapporteur

Vincent Pasquier, IPhT, examinateur

Pierre Pujol, Université Paul Sabatier, rapporteur

Raoul Santachiara, LPTMS, Université Paris Saclay, co-directeur de thèse

Véronique Terras, LPTMS, Université Paris Saclay, directrice de thèse



This thesis is divided in two parts: The first one presents a 2D statistical model of correlated percolation on a toroidal lattice. We present a protocol to construct long-range correlated surfaces based on fractional Gaussian surfaces and then we relate the level sets to a family of correlated percolation models. The emerging clusters are then numerically studied, and we test their conformal symmetry by verifying that their finite-size corrections follow the predictions of Conformal Field Theory. We also provide numerical details to produce the results.
The second part studies the quantum integrable XXZ spin-1/2 chain with open boundary conditions for even and odd number of sites. We concentrate in the anti-ferromagnetic regime and use the Algebraic Bethe Ansatz to determine the ground state configurations that arise in terms of the boundary fields. We find the conditions of existence of quasi-degenerate ground states separated by a gap to the rest of the spectrum. We calculate the boundary magnetization at zero temperature and find that it depends on the field at the opposite edge even in the semi-infinite chain limit. We finally calculate the time auto- correlation function at the boundary and show that in the even-size case it is finite for the long-time limit as a result of the quasi-degeneracy.

ZOOM Meeting ID: 962 2604 2868
Password: 708393

Date/Time : 15/10/2020 - 14:30 - 17:30

Location : Grand amphi, bâtiment Pascal n° 530

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