General finite-size effects for zero-entropy states in one-dimensional quantum integrable models

Abstract

Abstract. We present a general derivation of the spectrum of excitations for gapless states of zero entropy density in Bethe ansatz solvable models. Our formalism is valid for an arbitrary choice of bare energy function which is relevant to situations where the Hamiltonian for time evolution differs from the Hamiltonian in a (generalized) Gibbs ensemble, i.e. out of equilibrium. The energy of particle and hole excitations, as measured with the time-evolution Hamiltonian, is shown to include additional contributions stemming from the shifts of the Fermi points that may now have finite energy. The finite-size effects are also derived and the connection with conformal field theory discussed. The critical exponents can still be obtained from the finite-size spectrum, however the velocity occurring here differs from the one in the constant Casimir term. The derivation highlights the importance of the phase shifts at the Fermi points for the critical exponents of asymptotes of correlations. We generalize certain results known for the ground state and discuss the relation to the dressed charge (matrix). Finally, we discuss the finite-size corrections in the presence of an additional particle or hole which are important for dynamical correlation functions.

The effect of atom losses on the distribution of rapidities in the one-dimensional Bose gas

“…These are very challenging tasks. A simpler problem, which might serve as a good starting point for further analytical developments, would be to compute the functional F at low temperature using an effective Luttinger liquid approach, or more generally in states close to zero-entropy states where this approach can be generalized [81,82,[82][83][84].…”

Generalized-Hydrodynamic approach to Inhomogeneous Quenches: Correlations, Entanglement and Quantum Effects

“…Locally, they look like split Fermi seas [269][270][271], labelled by a finite number of Fermi points {k a } a=1,••• ,2Q . Importantly, since entropy is conserved at the hydrodynamic level, these states remain zero-entropy states under GHD evolution.…”

“…where ρ t,x,t (λ) and η x,t (λ) are defined in terms of ρ x,t (λ) in ( 63) and ( 64) respectively (we suppressed the index n assuming no bound states). To proceed one replaces (126) with the general GHD equation for ϑ x,t (λ) in the presence of external potentials [265], and considers the class of zero-entropy states of the interacting system [269][270][271], now labelled by a finite number of "Fermi rapidities" {λ a } a=1,••• ,2Q . The associated filling function ϑ x,t (λ) takes again the form of a characteristic function, and small fluctuations can be seen as deformations of the Fermi rapidities {λ a }.…”

Quantum Generalized Hydrodynamics of the Tonks-Girardeau gas: density fluctuations and entanglement entropy

“…The zero-entropy states are fully specified by the contour Γ t . Moreover, locally (around a given x), they take the form of split Fermi seas [49][50][51][52],…”

“…Analogous split Fermi seas can be defined also in the interacting case [49][50][51][52]. For such states, GHD, namely Eq.…”