Quantum Quench in Conformal Field Theory from a General Short ...

ggi.fi.infn.it

Quantum Quench in Conformal Field Theory from a General Short ...

Is this a Generalised Gibbs Ensemble?

in GGE an equal-time correlation function should have the

form

[

〈Φ(x 1 , t)Φ(x 2 , t)〉 = tr e −βH e − ∑ ]

p βpHp Φ(x 1 )Φ(x 2 )

where {H, H p } are an infinite set of commuting conserved

charges.

in CFT a minimal set are H p = ∫ [:T(x, t) p : + :T(x, t) p :]dx for

p = 2, 3, . . .

in terms of Virasoro operators


H p ∝ :L n1 L n2 · · · L np : +c.c.

n 1 +···+n p=0

the normal ordering implies that n 1 ≤ n 2 ≤ · · · ≤ n p , so

H p ∝ L p 0 + terms with n p ≥ 1 + c.c.

so acting on a primary operator H p ∝ ∆ p Φ

Quantum Quench in Conformal Field Theory

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