The delocalization or scrambling of quantum information has emerged as a central ingredient in the understanding of thermalization in isolated quantum manybody systems. Recently, significant progress has been made analytically by modeling nonintegrable systems as periodically driven systems, lacking a Hamiltonian picture, while honest Hamiltonian dynamics are frequently limited to small system sizes due to computational constraints. In this paper, we address this by investigating the role of conservation laws (including energy conservation) in the thermalization process from an informationtheoretic perspective. For general nonintegrable models, we use the equilibrium approximation to show that the maximal amount of information is scrambled (as measured by the tripartite mutual information of the timeevolution operator) at late times even when a system conserves energy. In contrast, we explicate how when a system has additional symmetries that lead to degeneracies in the spectrum, the amount of information scrambled must decrease. This general theory is exemplified in case studies of holographic conformal field theories (CFTs) and the SachdevYeKitaev (SYK) model. Due to the large Virasoro symmetry in 1+1D CFTs, we argue that, in a sense, these holographic theories are not maximally chaotic, which is explicitly seen by the nonsaturation of the second Rényi tripartite mutual information. The roles of particlehole and U(1) symmetries in the SYK model are milder due to the degeneracies being only twofold, which we confirm explicitly at both large and smallN. We reinterpret the operator entanglement in terms of the growth of local operators, connecting our results with the information scrambling described by outoftimeordered correlators, identifying the mechanism for suppressed scrambling from the Heisenberg perspective.
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Topological gauging and double current deformations
A bstract We study solvable deformations of twodimensional quantum field theories driven by a bilinear operator constructed from a pair of conserved U(1) currents J a . We propose a quantum formulation of these deformations, based on the gauging of the corresponding symmetries in a path integral. This formalism leads to an exact dressing of the S matrix of the system, similarly as what happens in the case of a $$ \textrm{T}\overline{\textrm{T}} $$ T T ¯ deformation. For conformal theories the deformations under study are expected to be exactly marginal. Still, a peculiar situation might arise when the conserved currents J a are not welldefined local operators in the original theory. A simple example of this kind of system is provided by rotation currents in a theory of multiple free, massless, noncompact bosons. We verify that, somewhat unexpectedly, such a theory is indeed still conformal after deformation and that it coincides with a TsT transformation of the original system. We then extend our formalism to the case in which the conserved currents are nonAbelian and point out its connection with Deformed Tdual Models and homogeneous YangBaxter deformations. In this case as well the deformation is based on a gauging of the symmetries involved and it turns out to be nontrivial only if the symmetry group admits a nontrivial central extension. Finally we apply what we learned by relating the $$ \textrm{T}\overline{\textrm{T}} $$ T T ¯ deformation to the central extension of the twodimensional Poincaré algebra.
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 Award ID(s):
 2210349
 NSFPAR ID:
 10428757
 Date Published:
 Journal Name:
 Journal of High Energy Physics
 Volume:
 2023
 Issue:
 5
 ISSN:
 10298479
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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