Entanglement constant for conformal families

Caputa, Paweł; Véliz-Osorio, Álvaro

doi:10.1103/physrevd.92.065010

Cited by 49 publications

(55 citation statements)

References 34 publications

(62 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…While proceeding with this project, we noticed a recent papers [40] appearing in arXiv, which has overlap with our discussion in the sections 2.3 and 2.4.…”

Section: Jhep10(2015)173mentioning

confidence: 77%

Entanglement entropy for descendent local operators in 2D CFTs

Chen

Guo

et al. 2015

J. High Energ. Phys.

View full text Add to dashboard Cite

We mainly study the Rényi entropy and entanglement entropy of the states locally excited by the descendent operators in two dimensional conformal field theories (CFTs). In rational CFTs, we prove that the increase of entanglement entropy and Rényi entropy for a class of descendent operators, which are generated by L (−)L(−) onto the primary operator, always coincide with the logarithmic of quantum dimension of the corresponding primary operator. That means the Rényi entropy and entanglement entropy for these descendent operators are the same as the ones of their corresponding primary operator. For 2D rational CFTs with a boundary, we confirm that the Rényi entropy always coincides with the logarithmic of quantum dimension of the primary operator during some periods of the evolution. Furthermore, we consider more general descendent operators generated by d {n i }{n j } ( i L −n i jL −n j ) on the primary operator. For these operators, the entanglement entropy and Rényi entropy get additional corrections, as the mixing of holomorphic and anti-holomorphic Virasoro generators enhance the entanglement. Finally, we employ perturbative CFT techniques to evaluate the Rényi entropy of the excited operators in deformed CFT. The Rényi and entanglement entropies are increased, and get contributions not only from local excited operators but also from global deformation of the theory.

show abstract

“…While proceeding with this project, we noticed a recent papers [40] appearing in arXiv, which has overlap with our discussion in the sections 2.3 and 2.4.…”

Section: Jhep10(2015)173mentioning

confidence: 77%

Entanglement entropy for descendent local operators in 2D CFTs

Chen

Guo

et al. 2015

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…In this paper, we consider the subsystem trace distance in latter category of quenches: at an initial time t = 0, a local operator is inserted somewhere in the ground state of the theory, and then the system is let evolve without further disturbance. The time evolution of entanglement and Rényi entropies, as well as of local operators, has been intensively studied in the literature [10][11][12][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. The main goal of this paper is to investigate the distance between the RDMs at different times after a local operator quench.…”

Section: Introductionmentioning

confidence: 99%

Subsystem distance after a local operator quench

Zhang

Calabrese

2020

J. High Energ. Phys.

View full text Add to dashboard Cite

We investigate the time evolution of the subsystem trace distance and Schatten distances after local operator quenches in two-dimensional conformal field theory (CFT) and in one-dimensional quantum spin chains. We focus on the case of a subsystem being an interval embedded in the infinite line. The initial state is prepared by inserting a local operator in the ground state of the theory. We only consider the cases in which the inserted local operator is a primary field or a sum of several primaries. While a nonchiral primary operator can excite both left-moving and rightmoving quasiparticles, a holomorphic primary operator only excites a right-moving quasiparticle and an anti-holomorphic primary operator only excites a left-moving one. The reduced density matrix (RDM) of an interval hosting a quasiparticle is orthogonal to the RDM of the interval without any quasiparticles. Moreover, the RDMs of two intervals hosting quasiparticles at different positions are also orthogonal to each other. We calculate numerically the entanglement entropy, Rényi entropy, trace distance, and Schatten distances in time-dependent states excited by different local operators in the critical Ising and XX spin chains. These results match the CFT predictions in the proper limit.

show abstract

“…[7] for entanglement in a related class of globally excited states. In 2d CFT this analysis can be preformed analytically and Rényi entropies detect an increase in entanglement equal to the logarithm of the quantum dimension of the conformal family [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Quantum dimensions from local operator excitations in the Ising model

Caputa

Rams

2017

J. Phys. A: Math. Theor.

Self Cite

View full text Add to dashboard Cite

We compare the time evolution of entanglement measures after local operator excitation in the critical Ising model with predictions from conformal field theory. For the spin operator and its descendants we find that Rényi entropies of a block of spins increase by a constant that matches the logarithm of the quantum dimension of the conformal family. However, for the energy operator we find a small constant contribution that differs from the conformal field theory answer equal to zero. We argue that the mismatch is caused by the subtleties in the identification between the local operators in conformal field theory and their lattice counterpart. Our results indicate that evolution of entanglement measures in locally excited states not only constraints this identification, but also can be used to extract non-trivial data about the conformal field theory that governs the critical point. We generalize our analysis to the Ising model away from the critical point, states with multiple local excitations, as well as the evolution of the relative entropy after local operator excitation and discuss universal features that emerge from numerics.

show abstract

Entanglement constant for conformal families

Cited by 49 publications

References 34 publications

Entanglement entropy for descendent local operators in 2D CFTs

Entanglement entropy for descendent local operators in 2D CFTs

Subsystem distance after a local operator quench

Quantum dimensions from local operator excitations in the Ising model

Contact Info

Product

Resources

About