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Correlation spreading in quantum lattice models with variable-range interactions

Julien Despres 1
1 Laboratoire Charles Fabry / Gaz Quantiques
LCF - Laboratoire Charles Fabry
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 main motivation for this research topic was to shed new light on the conflicting results in the literature concerning the scaling law of the correlation edge, its lack of universality and the incompleteness of the existing physical pictures to fully characterize the propagation of quantum correlations. To do so, we have presented a general theoretical approach relying on a quasiparticle theory. 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 velocites of the quasiparticle dispersion relation of the post-quench Hamiltonian. For long-range interactions of the form 1/|R|^α, the correlation spreading is substantially different due to a possible divergence of group velocity when tuning the power-law exponent α. For a divergent group velocity, extit{ie.} 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. The previous theoretical predictions have been verified numerically using tensor network techniques within the case study of the short-range Bose-Hubbard chain and the long-range s=1/2 XY and transverse Ising chains.
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Julien Despres. Correlation spreading in quantum lattice models with variable-range interactions. Optics [physics.optics]. Université Paris Saclay (COmUE), 2019. English. ⟨NNT : 2019SACLO018⟩. ⟨tel-02921450⟩

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