Thermalization and hydrodynamics of two-dimensional quantum field theories

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 \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.

arXiv:2105.02229SciPost PhysicsApr 7, 20221 citation

Universal thermalization dynamics in (1+1)d QFTs

Richard A. Davison, Luca V. Delacrétaz

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.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.

arXiv:2409.09112SciPost PhysicsJun 4, 20251 citation

Planckian bound on the local equilibration time

Marvin Qi, Alexey Milekhin, Luca V. Delacrétaz

The local equilibration time $τ_{\rm eq}$ of quantum many-body systems is conjectured to be bounded below by the Planckian time $\hbar /T$ . We formalize this conjecture by defining $τ_{\rm eq}$ 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 $τ_{\rm eq} \geq α\hbar /T$ on the onset of hydrodynamic behavior in a `regulated' thermal two-point function. The dimensionless coefficient $α$ 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 local equilibration time $τ_{\rm eq}$ of quantum many-body systems is conjectured to be bounded below by the Planckian time $\hbar /T$. We formalize this conjecture by defining $τ_{\rm eq}$ 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 $τ_{\rm eq} \geq α\hbar /T$ on the onset of hydrodynamic behavior in a `regulated' thermal two-point function. The dimensionless coefficient $α$ 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.

arXiv:2602.17638Feb 19, 20260 citations

Heavy operators and hydrodynamic tails

Luca V. Delacrétaz

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.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.

arXiv:2006.01139SciPost PhysicsSep 8, 202068 citations

Nonperturbative Methods in Quantum Field Theory

Luca V. Delacrétaz

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 $\phi^4$ 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.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 $\phi^4$ 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.

Jan 1, 20220 citations

Universal spectrum of 2d conformal field theory in the large c limit

Thomas Hartman, Christoph A. Keller, Bogdan Stoica

Two-dimensional conformal field theories exhibit a universal free energy in the high temperature limit T → ∞, and a universal spectrum in the Cardy regime, Δ → ∞. We show that a much stronger form of universality holds in theories with a large central charge c and a sparse light spectrum. In these theories, the free energy is universal at all values of the temperature, and the microscopic spectrum matches the Cardy entropy for all $\Delta \ge \frac{c}{6}$ . The same is true of three-dimensional quantum gravity; therefore our results provide simple necessary and sufficient criteria for 2d CFTs to behave holographically in terms of the leading spectrum and thermodynamics. We also discuss several applications to CFT and gravity, including operator dimension bounds derived from the modular bootstrap, universality in symmetric orbifolds, and the role of non-universal ‘enigma’ saddlepoints in the thermodynamics of 3d gravity.Two-dimensional conformal field theories exhibit a universal free energy in the high temperature limit T → ∞, and a universal spectrum in the Cardy regime, Δ → ∞. We show that a much stronger form of universality holds in theories with a large central charge c and a sparse light spectrum. In these theories, the free energy is universal at all values of the temperature, and the microscopic spectrum matches the Cardy entropy for all $$ \Delta \ge \frac{c}{6} $$ . The same is true of three-dimensional quantum gravity; therefore our results provide simple necessary and sufficient criteria for 2d CFTs to behave holographically in terms of the leading spectrum and thermodynamics. We also discuss several applications to CFT and gravity, including operator dimension bounds derived from the modular bootstrap, universality in symmetric orbifolds, and the role of non-universal ‘enigma’ saddlepoints in the thermodynamics of 3d gravity.

arXiv:1405.5137Journal of High Energy PhysicsSep 1, 2014396 citations

\frac{1}{T}

, the expected quantum equilibration time. Subluminality of sound further allows us to define a thermodynamic

C

-function, and constrain the sign of the

\mathcal T\bar{\mathcal T}

term in EFTs.

The local equilibration time

τ_{\rm eq}

of quantum many-body systems is conjectured to be bounded below by the Planckian time

\hbar /T

. We formalize this conjecture by defining

τ_{\rm eq}

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

τ_{\rm eq} \geq α\hbar /T

on the onset of hydrodynamic behavior in a `regulated' thermal two-point function. The dimensionless coefficient

α

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.

\phi^4

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.

\Delta \ge \frac{c}{6}

. The same is true of three-dimensional quantum gravity; therefore our results provide simple necessary and sufficient criteria for 2d CFTs to behave holographically in terms of the leading spectrum and thermodynamics. We also discuss several applications to CFT and gravity, including operator dimension bounds derived from the modular bootstrap, universality in symmetric orbifolds, and the role of non-universal ‘enigma’ saddlepoints in the thermodynamics of 3d gravity.