2016/06/30 by Rogier Vlijm, R. Vlijm, I. S. Eliëns +3 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Anderson impurity model #Ansatz #Bethe ansatz #Density matrix #Ground state #Magnon #Observable #Quantum #Quantum Information and Cryptography #Quantum many-body systems #Scaling #Spin (aerodynamics) #cond-mat.str-el
paper · pdf · doi:10.21468/scipostphys.1.1.008
published as SciPost Phys. 1, 008 (2016) · 30 pages, 12 figures; v2: minor revisions; Submitted to SciPost Physics
openalex created_date 2016/07/22 · arxiv created 2016/09/06 · openalex publication_date 2016/10/25 · arxiv updated 2017/01/10 · openalex updated_date 2026/08/05
Pumping a finite energy density into a quantum system typically leads to ‘melted’ states characterized by exponentially-decaying correlations, as is the case for finite-temperature equilibrium situations. An important exception to this rule are states which, while being at high energy, maintain a low entropy. Such states can interestingly still display features of quantum criticality, especially in one dimension. Here, we consider high-energy states in anisotropic Heisenberg quantum spin chains obtained by splitting the ground state’s magnon Fermi sea into separate pieces. Using methods based on integrability, we provide a detailed study of static and dynamical spin-spin correlations. These carry distinctive signatures of the Fermi sea splittings, which would be observable in eventual experimental realizations. Going further, we employ a multi-component Tomonaga-Luttinger model in order to predict the asymptotics of static correlations. For this effective field theory, we fix all universal exponents from energetics, and all non-universal correlation prefactors using finite-size scaling of matrix elements. The correlations obtained directly from integrability and those emerging from the Luttinger field theory description are shown to be in extremely good correspondence, as expected, for the large distance asymptotics, but surprisingly also for the short distance behavior. Finally, we discuss the description of dynamical correlations from a mobile impurity model, and clarify the relation of the effective field theory parameters to the Bethe Ansatz solution.