Correlation Spreading in Quantum Lattice Models with Variable-Range Interactions

TL;DR

This thesis investigates how quantum correlations spread in lattice models with variable-range interactions after a quench, revealing universal structures and differing propagation behaviors depending on interaction range and system gap.

Contribution

It introduces a quasiparticle-based theoretical framework that describes correlation spreading in both short- and long-range quantum lattice models, uncovering universal features of the causality cone.

Findings

Correlation edge propagates slower than ballistic.

Local extrema propagate faster than ballistic in long-range interactions.

Universal algebraic structure of the causality cone in the quasi-local regime.

Abstract

In this thesis, we have investigated the spreading of quantum correlations in isolated lattice models with short- or long-range interactions driven far from equilibrium via sudden global quenches. A general theoretical approach relying on a quasiparticle theory is presented. The latter has permitted to unveil a generic expression for the equal-time connected correlation functions valid both for short-range and long-range interacting particle and spin lattice models on a hypercubic lattice. Relying on stationary phase arguments, we have shown that its causality cone displays a universal twofold structure consisting of a correlation edge and a series of local extrema defining the outer and inner structure of the space-time correlations. For short-range interactions, the motion of each structure is ballistic and the associated spreading velocities are related to the group and phase velocities of the quasiparticle dispersion relation of the post-quench Hamiltonian. For long-range interactions of the form $1/|R|^{\alpha}$, the correlation spreading is substantially different due to a possible divergence of group velocity when tuning the power-law exponent $\alpha$. For a divergent group velocity, i.e. the quasi-local regime, we have presented evidence of a universal algebraic structure for the causality cone. While, the correlation edge motion has been found to be always slower than ballistic, the local extrema propagate faster than ballistically and ballistically for gapless and gapped quantum systems respectively. For the local regime implying a well-defined group velocity, we have recovered similar scaling laws and spreading velocities than the short-range case for the causality cone of correlations.