2014/03/12 by John Cardy · 7 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Conformal field theory #Conformal map #Density matrix #Geometry #Ground state #Inverse #Mathematical analysis #Mathematical physics #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum many-body systems #Quantum mechanics #cond-mat.stat-mech #hep-th
paper · pdf · doi:10.1103/physrevlett.112.220401
published as Phys. Rev. Lett. 112, 220401 (2014) · 5 pages, 3 figures
arxiv created 2014/03/12 · openalex publication_date 2014/06/05 · arxiv updated 2014/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We consider a quantum quench in a finite system of length L described by a 1+1-dimensional conformal field theory (CFT), of central charge c, from a state with finite energy density corresponding to an inverse temperature \ensuremathβ\ensuremath≪L. For times t such that \ensuremathℓ/2<t<(L\ensuremath-\ensuremathℓ)/2 the reduced density matrix of a subsystem of length \ensuremathℓ is exponentially close to a thermal density matrix. We compute exactly the overlap F of the state at time t with the initial state and show that in general it is exponentially suppressed at large L/\ensuremathβ. However, for minimal models with c<1 (more generally, rational CFTs), at times which are integer multiples of L/2 (for periodic boundary conditions, L for open boundary conditions) there are (in general, partial) revivals at which F is O(1), leading to an eventual complete revival with F=1. There is also interesting structure at all rational values of t/L, related to properties of the CFT under modular transformations. At early times t\ensuremath≪(L\ensuremathβ)1/2 there is a universal decay F\ensuremath∼exp(\ensuremath-(\ensuremathπc/3)Lt2/\ensuremathβ(\ensuremathβ2+4t2)). The effect of an irrelevant nonintegrable perturbation of the CFT is to progressively broaden each revival at t=nL/2 by an amount O(n1/2).