Abstract
We study the excited state Rényi entropy and subsystem Schatten distance in the two-dimensional free massless non-compact bosonic field theory, which is a conformal field theory. The discretization of the free non-compact bosonic theory gives the harmonic chain with local couplings. We consider the field theory excited states that correspond to the harmonic chain states with excitations of more than one quasiparticle, which we call multi-particle states. This extends the previous work by the same authors to more general excited states. In the field theory we obtain the exact Rényi entropy and subsystem Schatten distance for several low-lying states. We obtain short interval expansion of the Rényi entropy and subsystem Schatten distance for general excited states, which display different universal scaling behaviors in the gapless and extremely gapped limits of the non-compact bosonic theory. In the locally coupled harmonic chain we calculate numerically the excited state Rényi entropy and subsystem Schatten distance using the wave function method. We find excellent matches of the analytical results in the field theory and numerical results in the gapless limit of the harmonic chain. We also make some preliminary investigations of the Rényi entropy and the subsystem Schatten distance in the extremely gapped limit of the harmonic chain.
Highlights
Free massless non-compact bosonic theoryWe first present some useful details of the quasiprimary operators and their multi-point correlation functions in the 2D free massless non-compact bosonic field theory
When the Rényi entropy SA(n,G) of the ground state |G is known, one can use FA(n,X) to denote the excited state Rényi entropy
We study the excited state Rényi entropy and subsystem Schatten distance in the two-dimensional free massless non-compact bosonic field theory, which is a conformal field theory
Summary
We first present some useful details of the quasiprimary operators and their multi-point correlation functions in the 2D free massless non-compact bosonic field theory. One can find review of the basics of the 2D free massless bosonic theory in [71, 72]. The results are well-known, while at higher conformal weights we need to derive them following the basic rules. The excited states in the CFT are constructed by applying the quasiprimary operators and their derivatives on the ground state. We calculate the products of the excited state RDMs that are the basic ingredients to calculate the Rényi entropy and the Schatten distance
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