Gaussian many-body states: Tachyonic quenches and conformal blocks

Resumen

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.