SciPost Phys. 1, 008 (2016) ·
published 25 October 2016

· pdf
Pumping a finite energy density into a quantum system typically leads to
`melted' states characterized by exponentiallydecaying correlations, as is the
case for finitetemperature 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 highenergy 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 spinspin
correlations. These carry distinctive signatures of the Fermi sea splittings,
which would be observable in eventual experimental realizations. Going further,
we employ a multicomponent TomonagaLuttinger model in order to predict the
asymptotics of static correlations. For this effective field theory, we fix all
universal exponents from energetics, and all nonuniversal correlation
prefactors using finitesize 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.