Gaussian many-body states: Tachyonic Quenches and Conformal Blocks
Author
Montes Valencia, SebastiánEntity
UAM. Departamento de Física TeóricaDate
2018-04-13Subjects
Campos, Teoría de (Física) - Tesis doctorales; Función de onda - Tesis doctorales; Superconductores - Tesis doctorales; FísicaNote
Tesis doctoral inédita leída en la Universidad Autónoma de Madrid, Facultad de Ciencias, Departamento de Física Teórica. Fecha de lectura: 13-04-2018Esta obra está bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.
Abstract
This thesis is divided into two independent parts:
• Part I is based on Reference [1]. We present a characterization of a bosonic field
theory driven by a free (Gaussian) tachyonic Hamiltonian. This regime is motivated
using a theory describing two coupled bosonic fields. Relevant physical quantities
such as simple correlators, entanglement entropies, and the mutual information of
disconnected subregions are computed. We show that the causal structure resembles
a critical (massless) quench. Because of the inherent instability of the driving
Hamiltonian, an exponential growth ends up dominating the dynamics in a very
characteristic way. This is related to the fact that the low-frequency modes do not
equilibrate, but rather become exponentially occupied. Some applications and extensions
to other physical systems are outlined.
• Part II is based in References [2, 3]. We present a characterization of the manybody
lattice wave functions obtained from the conformal blocks (CBs) of the Ising
conformal field theory (CFT). The formalism is interpreted as a matrix product
state using continuous ancillary degrees of freedom. We provide analytic and numerical
evidence that the resulting states can be written as BCS states. We give
a complete proof that the translationally invariant 1D configurations have a BCS
form and we find suitable parent Hamiltonians. We find interesting relations to the
Kramers-Wannier (KW) duality and the Temperley-Lieb-Jones algebra. In particular,
we prove that the ground state of the finite-size critical Ising transverse field
(ITF) Hamiltonian can be obtained exactly with this construction. Finally, we study
2D configurations using an operator product expansion (OPE) approximation. We
associate these states to the weak pairing phase of the p+ip superconductor via the
scaling of the pairing function and the entanglement spectrum.
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