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arXiv:2105.02229 · SciPost Physics

Thermalization and hydrodynamics of two-dimensional quantum field theories

Luca V. Delacrétaz, A. Liam Fitzpatrick, Emanuel Katz, Matthew T. Walters

Published Apr 7, 2022• 1 citation
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Abstract

We consider 2d QFTs as relevant deformations of CFTs in the thermodynamic limit. Using causality and KPZ universality, we place a lower bound on the timescale characterizing the onset of hydrodynamics. The bound is determined parametrically in terms of the temperature and the scale associated with the relevant deformation. This bound is typically much stronger than \frac{1}{T} 1 T , the expected quantum equilibration time. Subluminality of sound further allows us to define a thermodynamic C C -function, and constrain the sign of the T\bar T T T ‾ term in EFTs.

DOI
10.21468/scipostphys.12.4.119

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We consider 2d QFTs as relevant deformations of CFTs in the thermodynamic limit. Using causality and KPZ universality, we place a lower bound on the timescale characterizing the onset of hydrodynamics. The bound is determined parametrically in terms of the temperature and the scale associated with the relevant deformation. This bound is typically much stronger than \frac{1}{T} 1 T , the expected quantum equilibration time. Subluminality of sound further allows us to define a thermodynamic C C -function, and constrain the sign of the T\bar T T T ‾ term in EFTs.
We consider 2d QFTs as relevant deformations of CFTs in the thermodynamic limit. Using causality and KPZ universality, we place a lower bound on the timescale characterizing the onset of hydrodynamics. The bound is determined parametrically in terms of the temperature and the scale associated with the relevant deformation. This bound is typically much stronger than 1T\frac{1}{T}T1​, the expected quantum equilibration time. Subluminality of sound further allows us to define a thermodynamic CCC-function, and constrain the sign of the TTˉ\mathcal T\bar{\mathcal T}TTˉ term in EFTs.
We identify the universal mechanism behind the thermalization of (1+1)d QFTs at high and low temperatures. Viewing these theories as CFTs perturbed by relevant or irrelevant deformations, we show that conformal perturbation theory in the thermal state breaks down at late times allowing for the emergence of hydrodynamics. This breakdown occurs universally due to the unsuppressed exchange of stress tensors near the lightcone. Furthermore, for theories with central charge c→∞ c → ∞ we solve for the emergent hydrodynamic theory to all orders in the gradient expansion by arguing that all transport parameters appearing in two-point functions have universal expressions in terms of the scaling dimension \Delta Δ of the perturbation. The radius of convergence of the hydrodynamic dispersion relations provides an early time cutoff for hydrodynamics, which agrees with the time scale at which conformal perturbation theory breaks down.
The local equilibration time τeqτ_{\rm eq}τeq​ of quantum many-body systems is conjectured to be bounded below by the Planckian time ℏ/T\hbar /Tℏ/T. We formalize this conjecture by defining τeqτ_{\rm eq}τeq​ as the time scale at which a hydrodynamic description emerges for conserved densities. Drawing on analytic properties of real time thermal correlators, we establish a rigorous lower bound τeq≥αℏ/Tτ_{\rm eq} \geq α\hbar /Tτeq​≥αℏ/T on the onset of hydrodynamic behavior in a `regulated' thermal two-point function. The dimensionless coefficient ααα depends only on dimensionality and the type of hydrodynamic or diffusive behavior that emerges, and is independent of the thermalization mechanism or other microscopic details. This bound applies universally to local quantum many-body systems, with or without a quasiparticle description, including in the presence of inelastic scattering.
The late time physics of interacting QFTs at finite temperature is controlled by hydrodynamics. For CFTs this implies that heavy operators – which are generically expected to create thermal states – can be studied semiclassically. We show that hydrodynamics universally fixes the OPE coefficients C_{HH'L} C H H ′ L , on average, of all neutral light operators with two non-identical heavy ones, as a function of the scaling dimension and spin of the operators. These methods can be straightforwardly extended to CFTs with global symmetries, and generalize recent EFT results on large charge operators away from the case of minimal dimension at fixed charge. We also revisit certain aspects of late time thermal correlators in QFT and other diffusive systems.
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