A bound on thermal relativistic correlators at large spacelike momenta

Self Cite

A macroscopic version of Einstein-Podolsky-Rosen entanglement is obtained by quenching a quadratic coupling between two O(N ) vector models. A quench of the mixed vacuum produces an excited entangled state, reminiscent of purified thermal equilibrium, whose properties can be studied analytically in the free limit of the individual field theories.The decoupling of different wavelength modes in free field theory prevents true thermalisation but a more subtle difference is that the density operator obtained by a partial trace does not commute with the post-quench Hamiltonian. Generalized thermal behaviour is obtained at late times, in the limit of weak initial mixing or a smooth but rapid quench. More surprisingly, late-time correlation functions of composite operators in the post-quench free field theory share interesting properties with correlators in strongly coupled systems. We propose a holographic interpretation of our result.

Section: Discussionsupporting

confidence: 73%

Section: Introductionmentioning

confidence: 91%

Quenched coupling, entangled equilibria, and correlated composite operators: a tale of two O(N) models

Banerjee¹,

Engelsöy²,

Larana-Aragon³

et al. 2019

Self Cite

“…A motivation behind the operator thermalisation hypothesis, and one of its strengths, is that it can be used to study surprising similarities between ordinary interacting systems and free or integrable systems [6,10,11,13]. While pure exponential decay occurs in free systems in contrast to naive expectations, it is generally masked by leading power law decay for d > 2, as well as multiplied by inverse powers of time.…”

Section: Jhep09(2020)103mentioning

confidence: 99%

“…Such operators can in fact interact with the thermal bath and as such exhibit a range of phenomena that are usually attributed to their interacting counterparts. For instance, their correlation functions can exhibit exponential decay at late times [10] and JHEP09(2020)103 their spectral densities have support in the deeply off-shell regime [10,11], reminiscent of collision-less Landau damping [12].…”

Section: Introductionmentioning

confidence: 99%

Operator thermalisation in d > 2: Huygens or resurgence

Engelsöy

Larana-Aragon

Sundborg

et al. 2020

Correlation functions of most composite operators decay exponentially with time at non-zero temperature, even in free field theories. This insight was recently codified in an OTH (operator thermalisation hypothesis). We reconsider an early example, with large N free fields subjected to a singlet constraint. This study in dimensions d > 2 motivates technical modifications of the original OTH to allow for generalised free fields. Furthermore, Huygens’ principle, valid for wave equations only in even dimensions, leads to differences in thermalisation. It works straightforwardly when Huygens’ principle applies, but thermalisation is more elusive if it does not apply. Instead, in odd dimensions we find a link to resurgence theory by noting that exponential relaxation is analogous to non- perturbative corrections to an asymptotic perturbation expansion. Without applying the power of resurgence technology we still find support for thermalisation in odd dimensions, although these arguments are incomplete.

“…The states |n of the CFT are forced to satisfy the condition E n ≥ |P n |, but this does not necessarily force ρ(k, ω) to be zero if |k| > |ω|. An intuitive explanation [7] is that in the thermal background φ can create a particle with some energy E and momentum k and destroy another one with a similar energy but opposite momentum. This excitation will have a small energy but possibly large momentum.…”

Section: Introductionmentioning

confidence: 99%

Thermal CFTs in momentum space

Manenti

2020

We study some aspects of conformal field theories at finite temperature in momentum space. We provide a formula for the Fourier transform of a thermal conformal block and study its analytic properties. In particular we show that the Fourier transform vanishes when the conformal dimension and spin are those of a "double twist" operator ∆ = 2∆ φ + ℓ + 2n. By analytically continuing to Lorentzian signature we show that the spectral density at high spatial momenta has support on the spectrum condition |ω| > |k|. This leads to a series of sum rules. Finally, we explicitly match the thermal block expansion with the momentum space Green's function at finite temperature in several examples. 14 6.