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arXiv:2409.09112 · SciPost Physics

Universal thermalization dynamics in (1+1)d QFTs

Richard A. Davison, Luca V. Delacrétaz

Published Jun 4, 2025• 1 citation
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Abstract

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.

DOI
10.21468/scipostphys.18.6.177

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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.
Hydrodynamics provides a universal description of interacting quantum field theories at sufficiently long times and wavelengths, but breaks down at scales dependent on microscopic details of the theory.In the vicinity of a quantum critical point, it is expected that some aspects of the dynamics are universal and dictated by properties of the critical point.We use gauge-gravity duality to investigate the breakdown of diffusive hydrodynamics in two low-temperature states dual to black holes with AdS 2 horizons, which exhibit quantum critical dynamics with an emergent scaling symmetry in time.We find that the breakdown is characterized by a collision between the diffusive pole of the retarded Green's function with a pole associated to the AdS 2 region of the geometry, such that the local equilibration time is set by infrared properties of the theory.The absolute values of the frequency and wave vector at the collision (ω eq and k eq ) provide a natural characterization of all the low-temperature diffusivities D of the states via D ¼ ω eq =k 2 eq , where ω eq ¼ 2πΔT is set by the temperature T and the scaling dimension Δ of an operator of the infrared quantum critical theory.We confirm that these relations are also satisfied in a Sachdev-Ye-Kitaev chain model in the limit of strong interactions.Our work paves the way toward a deeper understanding of transport in quantum critical phases.
In this paper, we consider the energy and momentum transport in (1+11+11+1)-dimension conformal field theories (CFTs) that are deformed by an irrelevant operator TT‾T\overline{T}TT, using the integrability based generalized hydrodynamics, and holography. The two complementary methods allow us to study the energy and momentum transport after the in-homogeneous quench, derive the exact nonequilibrium steady states, and calculate the Drude weights. Our analysis reveals that all of these quantities satisfy universal formulae regardless of the underlying CFT, thereby generalizing the universal formulas for these quantities in pure CFTs. We also compute the exact momentum diffusion constant using the integrability-based method and confirm that it agrees with the conformal perturbation. These fundamental physical insights have important consequences for our understanding of the TT‾T\overline{T}TT-deformed CFTs. First of all, they provide the first check of the TT‾T\overline{T}TT-deformed AdS3/CFT2{\mathrm{AdS}}_{3}/{\mathrm{CFT}}_{2}AdS3​/CFT2​ correspondence from the dynamical standpoint. And second, we are able to identify a remarkable connection between the TT‾T\overline{T}TT-deformed CFTs and reversible cellular automata.
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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<!--HTML-->Nonintegrable QFTs are expected to thermalize and exhibit emergence of hydrodynamics and chaos. In weakly coupled QFTs, kinetic theory captures local thermalization; such a versatile tool is absent away from the perturbative regime. I will present analytical and numerical results using nonperturbative methods to study thermalization at strong coupling. I will show how requiring causality in the thermal state leads to strong analytic constraints on the thermodynamics and out of equilibrium properties of any relativistic 1+1d QFT. I will then discuss Lightcone Conformal Truncation (LCT) as a powerful numerical tool to study thermalization of QFTs. Applied to ϕ4\phi^4ϕ4 theory in 1+1d, LCT reveals eigenstate thermalization and onset of random matrix universality at any nonzero coupling. Finally, I will discuss prospects for observing the emergence of hydrodynamics in QFTs using Hamiltonian truncation.
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.