Finite-Time Universality in Nonequilibrium CFT

Abstract

Recently, remarkably simple exact results were presented about the dynamics of heat transport in the local Luttinger model for nonequilibrium initial states defined by position-dependent temperature profiles. We present mathematical details on how these results were obtained. We also give an alternative derivation using only algebraic relations involving the energy-momentum tensor which hold true in any unitary conformal field theory (CFT). This establishes a simple universal correspondence between initial temperature profiles and the resulting heat-wave propagation in CFT. We extend these results to larger classes of nonequilibrium states. It is proposed that such universal CFT relations provide benchmarks to identify nonuniversal properties of nonequilibrium dynamics in other models.

Conformal field theory on top of a breathing one-dimensional gas of hard core bosons

“…The problem we will treat is the one of a gas of hard-core bosons, also known as the Tonks-Girardeau gas, in a time-dependent harmonic potential V (x, t). This problem is well-known to be exactly solvable [34][35][36], and our goal is to use it to illustrate our approach, which extends recent works by others and by ourselves and our collaborators [1,[37][38][39][40][41][42][43][44][45][46][47][48][49][50][51]. We will see that we recover some known results about equal-time correlations, and we uncover new ones, including results for correlation functions at different time.…”

“…Refs. [1,[37][38][39][40][41][42][43][44][45][46][47][48][49][50][51]), by considering a truly dynamical situation: a breathing gas of hard core bosons at zero temperature. In particular, we have found new formulas for the 1/N ∼ ħ h → 0 asymptotics of 2n-point functions of boson creation/annihilation operators, and also for fermionic observables for which we provided numerical checks.…”

“…Importantly, we need to fix the prefactor of that leading term in Eq. (43). Since Ψ † is homogeneous to a length to the power −1/2, while the vertex operator : e − i 2 (ϕ − −ϕ + ) : has scaling dimension 1/4, we see by dimensional analysis that the prefactor must scale as ρ(x, t) 1/4 , because the inverse density ρ −1 is the only local length scale in the problem.…”

Emergence of generalized hydrodynamics in the non-local Luttinger model

“…Comparing the results above with the CFT ones in [34], we see that those in (35) are the same as in CFT and universal in the sense that they do not depend on the exact details of the NLL interactions: They only depend on the interaction strengths. The same is true for the first terms in (34).…”

“…Comparing the results above with the CFT ones in [34], we see that those in (35) are the same as in CFT and universal in the sense that they do not depend on the exact details of the NLL interactions: They only depend on the interaction strengths. The same is true for the first terms in (34). However, the second terms in (34) are clearly different from the corresponding CFT results and non-universal in the sense that they do depend on all details of the interactions, including the spatial dependence.…”