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The complexity of the XYZ spin 1/2 chain captures the most generic anisotropic magnetic interaction in a one-dimensional system. It constitutes a reference system to better understand quantum magnetism and related phenomena. Starting from this spin chain, defined on a discrete lattice, we will study its sector with an odd number of sites to analyze frustration and its implications. The standard Bethe ansatz procedure cannot be applied to the XYZ chain with an odd number of sites, and the adapted technique shows how static systems may require very convoluted approaches. In the continuum limit, the XYZ chain maps onto the famous sine-Gordon model, but this mapping is non-trivial. Studying the frustrated boundary condition sector of the chain will allow for the examination of the field theory model, especially the behavior of topological excitations, known for their robustness. In contrast, a much more intuitive approach emerges for studying the dynamics of a system of hard-core bosons in one dimension. Such bosonic particles, in the impenetrability limit, are reduced to free fermions and are thus connected to spin chains. In the described project, these bosons are confined in a box, then released and subjected to ballistic transport. For these systems, Generalised Hydrodynamics techniques find fertile ground and are clear and effective. They show that an interesting phenomenon arises due to the dynamics: at finite temperatures, in the static case, the system is known to present exponentially decaying density-density correlations. After the quench—removing the wall and allowing the system to evolve—these correlations exhibit algebraic decay, a typical feature of the ground state. A deep numerical counterpart is provided to study the robustness of this emergence, as well as the suitability of Quantum Generalised Hydrodynamics for the regimes involved.

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Damiano De Angelis, LPTM - Cergy Paris
SR 0.01
Contact: Matteo Rizzi & Xhek Turkeshi