Jan Thorben Schneider soutiendra publiquement ses travaux de thèse le 30 septembre 2022 à 15h00 au CPHT dans la salle de conférence Louis Michel.
Titre de la thèse : Far-from-equilibrium dynamics and entanglement in long-range quantum systems
Directeur de thèse : Laurent Sanchez-Palencia
Membres du jury de thèse
Grégoire Misguich, CEA Saclay, Rapporteur
Marco Schirò, Collège de France, Rapporteur
Karyn Le Hur, École Polytechnique, Examinatrice
Leonardo MazzaUniversité Paris-Saclay, Examinateur
Laurent Sanchez-Palenci, École polytechnique, Directeur de thèse
In this thesis, we study the effects of long-range interactions on out-of-equilibrium and in-equilibrium features of lattice spin models by employing complementary analytical calculations and state-of-the-art tensor-network simulations while particularly focusing on the central and unique quantum feature of entanglement.
First, in the long-range transverse-field Ising model, we show the emergence of a weak form of causality characterised by non-universal dynamical exponents. On the one hand, local magnetisation and correlations have an emergent sub-ballistic causal cone while the marked features in the interior of it propagate super-ballistic or ballistic, respectively. On the other hand, the emergent causal cone for all entanglement entropies is shown to be ballistic irrespective of the interaction range and the interior is without marked features. Second, we determine the equilibrium quantum phase diagram of the long-range XXZ model in terms of the anisotropic coupling and the long-range interaction exponent through studying a representation of the spectrum of the reduced density matrix following a half-chain bipartition, the so-called entanglement spectrum.
We show it exhibits a remarkable self-similarity within the critical phase where the system is described by a Luttinger liquid while the self-similarity extends to the geometric entanglement and the Luttinger parameter.
The transition away from a Luttinger liquid is consistent with the breakdown of self-similarity and a renormalisation group analysis. The synergetic combination of the two latter allows us to locate the corresponding phase transitions which we corroborate by numerical simulations.
Furthermore, we show the entanglement Hamiltonian, the Hermitian operator whose spectrum is the entanglement spectrum, follows the form of the Bisognano--Wichmann theorem in large regions of the phases which include the short-range limit, while such a form can be excluded in the phase where genuinely long-ranged effects are relevant.
Our results shed new light through the lens of quantum entanglement on the out-of-equilibrium as well as ground state features of long-range interacting spin chains and pave the way for further experimental and theoretical studies.