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.
Highlights
Recent years have witnessed new advances in the application of hydrodynamics to study 1+1dimensional quantum many-body systems out of equilibrium
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
Applying the recent proposal of generalized hydrodynamics, we show that the model allows for fully explicit yet non-trivial solutions of the resulting Eulerscale hydrodynamic equations
Summary
Recent years have witnessed new advances in the application of hydrodynamics to study 1+1dimensional quantum (and classical) many-body systems out of equilibrium. (The latter generalize the usual constant thermodynamic variables that correspond to equilibrium states.) This is an example of an inhomogeneous quantum quench Such non-equilibrium results in the NLL model can be computed by exact analytical means [31, 32], which allows for direct analytical comparisons between those and the GHD results that we will derive here. The corresponding Euler-scale GHD results describe expectations within fluid cells that are in local equilibrium Such states ρβ(x,t) are given by a suitably chosen generalized Gibbs ensemble consisting of conserved charges Q = Given the initial state ρμ(⋅) above, it will follow from our general results that the only non-constant fields in β(x, t) are μ±(x, t) = μ(x ∓ v(0)t) conjugate to the conserved U(1) charges for right- and left-moving excitations For this case, we will show that the GHD results for the particle density and the charge current are.
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