26th March 2019: Ph.D. Offer – Université de Lorraine

Numerical study of the critical point of random quantum spin models in high dimensions.

Laboratoire de Physique et Chimie Theoriques (http://lpct.univ-lorraine.fr/)
Ph.D. adviser: Christophe Chatelain,
Faculte des Sciences et Technologies, Boulevard des aiguillettes, F-54506 Vandoeuvre les Nancy, France
e-mail : christophe.chatelain@univ-lorraine.fr, Phone : +33

Topic :
The context of this Ph.D. is in the field of Statistical Physics, and more precisely Critical Phenomena, i.e. the study of the singularities of thermodynamical quantities in
the neighborhood of a phase transition. From the point of view of Statistical Physics, the influence of disorder on the critical properties of classical systems is usually considered as
well understood. According to the behavior of speci fic heat at the transition temperature, the introduction of disorder in the couplings of the Hamiltonian will modify or not the
critical behavior. First-order phase transitions are softened by disorder and can even become continuous for a strong enough disorder. In dimension d = 2, an in finitesimal
amount of disorder is sufficient to make the transition continuous. Lattice spin models (Ising, Potts models) were intensively studied in the last decades in the presence of
disorder, mostly by Monte Carlo simulations. Quantum Phase Transitions are not driven by thermal fluctuations as classical phase transitions but by quantum fluctuations. The paradigmatic model is the quantum Ising chain in a transverse field. It was shown analytically that the introduction of disorder leads to a drastic change of critical behavior. The quantum fluctuations are overwhelmed by disorder fluctuations. Interestingly, several other one-dimensional spin models (Potts, Ashkin-Teller) were observed to have the same critical behavior in presence of disorder. The case of higher dimensions (d  2) could present surprises. Up to now, only the quantum Ising model in a transverse field has been studied numerically in dimension d  2. The aim of this thesis is therefore to extend the real-space renormalization procedure applied to the Ising model to other models and to implement it numerically to study the critical behavior.
The Ph.D. candidate is expected to have a good knowledge of Statistical Physics, to master a programming language and to be highly motivated. This Ph.D. will be funded
by the University of Lorraine for a duration of 36 months, starting from October 1st 2019. The Ph.D. student will be integrated to the "Laboratoire de Physique et Chimie
Theoriques" in a research group in Statistical Physics. He will have access to computer facilities to perform his calculations and will have opportunities to attend congresses,
conferences and topical schools.