Abstract
We present an open-source Matlab framework, titled iFluid, for simulating the dynamics of integrable models using the theory of generalized hydrodynamics (GHD). The framework provides an intuitive interface, enabling users to define and solve problems in a few lines of code. Moreover, iFluid can be extended to encompass any integrable model, and the algorithms for solving the GHD equations can be fully customized. We demonstrate how to use iFluid by solving the dynamics of three distinct systems: (i) The quantum Newton's cradle of the Lieb-Liniger model, (ii) a gradual field release in the XXZ-chain, and (iii) a partitioning protocol in the relativistic sinh-Gordon model.
Highlights
The only model-specific parameters that enter the calculations is the scattering phase, Θ(λ), encoding the interactions of the quasiparticles and the oneparticle eigenvalues, hj(λ). These quantities can be obtained for a given model through the thermodynamic Bethe ansatz, and once plugged into the hydrodynamical equations the full framework of generalized hydrodynamics (GHD) can be applied to the problem
We have demonstrated that iFluid enables the user to perform state of the art GHD calculations in only a few lines of code
We have shown that iFluid can be extended to encompass a large number of integrable models and numerical solvers
Summary
In recent decades great experimental advances in the field of ultracold atoms have enable the preparation and manipulation of one-dimensional many-body quantum system far from equilibrium [1,2,3,4,5,6,7,8,9]. The GHD details how the flow of an infinite set of charges of an integrable model is given by the semiclassical propagation of a phase-space density of a quasiparticle collection. Eq (9) is a simple Eulerian fluid equation, which describes the flow of the infinite set of conserved charges through a single expression It is the main equation of GHD along with its root density-based counterpart. The only model-specific parameters that enter the calculations is the scattering phase, Θ(λ), encoding the interactions of the quasiparticles and the oneparticle eigenvalues, hj(λ) These quantities can be obtained for a given model through the thermodynamic Bethe ansatz, and once plugged into the hydrodynamical equations the full framework of GHD can be applied to the problem. The discretized equations are found in Appendix B, while further information regarding the iFluidTensor is written in the documentation [47]
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