Emergence of generalized hydrodynamics in the non-local Luttinger model

Abstract

We propose the Luttinger model with finite-range interactions as a simple tractable example in 1+1 dimensions to analytically study the emergence of Euler-scale hydrodynamics in a quantum many-body system. This non-local Luttinger model is an exactly solvable quantum field theory somewhere between conformal and Bethe-ansatz integrable models. Applying the recent proposal of generalized hydrodynamics, we show that the model allows for fully explicit yet non-trivial solutions of the resulting Euler-scale hydrodynamic equations. Comparing with exact analytical non-equilibrium results valid at all time and length scales, we show perfect agreement at the Euler scale when the interactions are short range. A formal proof of the emergence of generalized hydrodynamics in the non-local Luttinger model is also given, and effects of long-range interactions are briefly discussed.

Generalized-hydrodynamic approach to inhomogeneous quenches: correlations, entanglement and quantum effects

“…where the initial state is composed by the junction of two different homogeneous pieces, have been extensively studied in the literature. Of particular interest have been the sudden junction of two half chains prepared at different temperatures [38,39, and at different chemical potentials (or fillings) [38,44,50,, but more general initial states have also been considered [38,[111][112][113][114][115][116][117], particularly in relation to studies on the entanglement growth (see section 4 for references). Here we will refer to inhomogeneous quenches of this kind as 'bipartitioning protocols'.…”

Inhomogeneous Conformal Field Theory Out of Equilibrium

“…This scaling involves replacing v(•), β(•), μ(•), and (x, t) by v(•/λ), β(•/λ), μ(•/λ), and (λx, λt), respectively, for some λ > 0 and taking the limit λ → ∞; cf. [66] where this was studied for the non-local Luttinger model. [Naturally, for our generalized light-cone coordinates, this scaling entails that x± are replaced by λx ± .]…”

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

“…where the initial state is composed by the junction of two different homogeneous pieces, have been extensively studied in the literature. Of particular interest have been the sudden junction of two half chains prepared at different temperatures [35,36, and at different chemical potentials (or fillings) [35,41,47,, but more general initial states have also been considered [35,[108][109][110][111][112][113][114], particularly in relation to studies on the entanglement growth (see Section IV for references). Here we will refer to inhomogeneous quenches of this kind as "bipartitioning protocols".…”