Numerical study of constrained many body systems. – (Bhupen DABHOLKAR/ LPT / Thèse). – 11/06/2024, 14H

Soutenance de thèse

Bhupen DABHOLKAR, LPT, Salle de Conférence FeRMI 3R4

Abstract :
This thesis presents computational studies of three different models of many-body physics with direct or indirect constraints. The presence of constraints in complex many-body systems calls for non-trivial
numerical algorithms to study them. The first two models which have a direct form of local constraint are the Rokhsar-Kivelson Quantum Dimer model (QDM) and a classical statistical mechanics model of non-intersecting loops with attractive interactions, both on the square lattice. The investigations of such constrained models have found a recent resurgence with their direct realizations on Rydberg atom arrays quantum simulators. The study of the classical model uses a Monte Carlo directed loop algorithm while the QDM calls for a novel Quantum Monte Carlo scheme based on the framework of Stochastic Series Expansions called the Sweeping Cluster Algorithm (SCA). We present a modification of the SCA in order to render simulations fully ergodic at finite temperature. For both models, our numerical studies show the existence of a critical phase separated by a phase transition at finite temperature to an ordered phase of dimers or loops which spontaneously breaks certain lattice symmetries. We show that for the case where the interaction is attractive this phase transition is of
Kosterlitz-Thouless type and can be understood by constructing a coarse-grained field theory through a height mapping. The finite temperature phase diagram of the QDM presents an unusual re-entrance
behavior in the critical phase. The final part of this thesis deals with the role of non-abelian symmetries in the thermalization process of quantum many-body systems. We study the high-energy eigenstates of a SU(3) symmetric spin chain in presence of disorder. While the model does not directly have constraints, we perform exact diagonalization in a constrained basis of Young tableau making use of the full SU(3) symmetry of the model. By looking at the commonly used probes for thermalization (spectral statistics, distribution of local observables and scaling of entanglement entropy), we show that the model exhibits a non-ergodic regime over a broad range of system sizes for strong enough disorder, contrasting with the rapid thermalization observed at weak disorder.