Quantum hydrodynamics from local thermal pure states

TL;DR

This paper introduces a pure state approach, called $ ext{l}$TPQ, for describing hydrodynamics in isolated quantum many-body systems, demonstrating convergence to local Gibbs states and validating thermodynamic laws.

Contribution

The paper develops the $ ext{l}$TPQ state framework, providing a new pure state formulation for quantum hydrodynamics that is both theoretically rigorous and numerically efficient.

Findings

Convergence of $ ext{l}$TPQ states to local Gibbs ensembles in large systems

Numerical validation of hydrodynamic relaxation obeying Fourier's law

Proof and numerical validation of the second law and fluctuation theorem

Abstract

We provide a pure state formulation for hydrodynamic dynamics of isolated quantum many-body systems. A pure state describing quantum systems in local thermal equilibrium is constructed, which we call a local thermal pure quantum ($\ell$TPQ) state. We show that the thermodynamic functional and the expectation values of local operators (including a real-time correlation function) calculated from the $\ell$TPQ state converge to those from a local Gibbs ensemble in the large fluid-cell limit. As a numerical demonstration, we investigate a one-dimensional spin chain and observe the hydrodynamic relaxation obeying the Fourier's law. We further prove the second law of thermodynamics and the quantum fluctuation theorem, which are also validated numerically. The $\ell$TPQ formulation gives a useful theoretical basis to describe the emergent hydrodynamic behavior of quantum many-body systems furnished with a numerical efficiency, being applicable to both the non-relativistic and relativistic regimes.