Abstract
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.
Highlights
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
We have considered high energy zero-entropy states for the anisotropic Heisenberg spin chain defined by a double-Fermi sea quantum-number configuration
Our focus was on dynamical correlations computed by summing over relevant matrix elements of particle-hole excitations at finite system size, the matrix elements being given by algebraic Bethe Ansatz
Summary
The ground states and low-lying excitations of one-dimensional many-body quantum systems often display interesting features associated to the Tomonaga-Luttinger liquid universality class [1, 2], notable examples being one-dimensional quantum gases and spin chains. The zero-entropy nature of the states we consider here translates into a quasicondensate momentum distribution with sharp peaks at finite momenta similar to the ones observed in cold atoms after domain-wall melting of a one-dimensional Mott insulator [24] At present it is not clear whether a connection exists between the steady state for this quantum quench and the split-Fermi-sea states we consider. The static spin-spin correlations are subsequently studied from both the matrix element summation approach from algebraic Bethe Ansatz and the multi-component Tomonaga-Luttinger predictions supported by parameter fitting from integrability, which show surprisingly good correspondence for both the long-range asymptotics and short distances.
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