Topological entanglement negativity in Chern-Simons theories

Wen, Xueda; Chang, Po-Yao; Ryu, Shinsei

doi:10.1007/jhep09(2016)012

Cited by 66 publications

(63 citation statements)

References 74 publications

(102 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The (logarithmic) entanglement negativity is a measure of quantum entanglement, which can be applied to mixed states. In the quantum field theory context, for example, it has been computed and discussed for (1+1)d CFTs and (2+1)d topological quantum field theories [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31].…”

mentioning

confidence: 99%

Entanglement negativity and minimal entanglement wedge cross sections in holographic theories

2019

Self Cite

View full text Add to dashboard Cite

We calculate logarithmic negativity, a quantum entanglement measure for mixed quantum states, in quantum error-correcting codes and find it to equal the minimal cross sectional area of the entanglement wedge in holographic codes with a quantum correction term equal to the logarithmic negativity between the bulk degrees of freedom on either side of the entanglement wedge cross section. This leads us to conjecture a holographic dual for logarithmic negativity that is related to the area of a cosmic brane with tension in the entanglement wedge plus a quantum correction term. This is closely related to (though distinct from) the holographic proposal for entanglement of purification. We check this relation for various configurations of subregions in AdS 3/CFT 2. These are disjoint intervals at zero temperature, as well as a single interval and adjacent intervals at finite temperature. We also find this prescription to effectively characterize the thermofield double state. We discuss how a deformation of a spherical entangling region complicates calculations and speculate how to generalize to a covariant description.

show abstract

mentioning

confidence: 99%

Entanglement negativity and minimal entanglement wedge cross sections in holographic theories

2019

Self Cite

View full text Add to dashboard Cite

show abstract

“…Note added: In a forthcoming paper, 46 the entanglement negativity in Chern-Simons theories is studied based on the replica trick and sugery method. The results agree with the edge theory approach in this work for all the cases under study.…”

Section: Discussionmentioning

confidence: 99%

Edge theory approach to topological entanglement entropy, mutual information, and entanglement negativity in Chern-Simons theories

2016

Self Cite

View full text Add to dashboard Cite

We develop an approach based on edge theories to calculate the entanglement entropy and related quantities in (2+1)-dimensional topologically ordered phases. Our approach is complementary to, e.g., the existing methods using replica trick and Witten's method of surgery, and applies to a generic spatial manifold of genus g, which can be bipartitioned in an arbitrary way. The effects of fusion and braiding of Wilson lines can be also straightforwardly studied within our framework. By considering a generic superposition of states with different Wilson line configurations, through an interference effect, we can detect, by the entanglement entropy, the topological data of Chern-Simons theories, e.g., the R-symbols, monodromy and topological spins of quasiparticles. Furthermore, by using our method, we calculate other entanglement/correlation measures such as the mutual information and the entanglement negativity. In particular, it is found that the entanglement negativity of two adjacent non-contractible regions on a torus provides a simple way to distinguish Abelian and non-Abelian topological orders. CONTENTS

show abstract

“…Harmonic oscillator chains were studied using the covariance matrix technique [23][24][25][26][27][28] and quantum spin chains were studied using the density matrix renormalization group [29][30][31][32][33] and exactly [34,35]. The topologically ordered phases were also investigated for the (2+1) dimensional Chern-Simons theories [36,37] and for the toric code where exact calculations are applicable [38,39]. A particularly important progress was due to a systematic approach developed for conformal field theories (CFTs) [40,41].…”

Section: Introductionmentioning

confidence: 99%

Partial time-reversal transformation and entanglement negativity in fermionic systems

2017

Self Cite

View full text Add to dashboard Cite

The partial transpose of density matrices in many-body quantum systems, in which one takes the transpose only for a subsystem of the full Hilbert space, has been recognized as a useful tool to diagnose quantum entanglement. It can be used, for example, to define the (logarithmic) negativity. For fermionic systems, it has been known that the partial transpose of Gaussian fermionic density matrices is not Gaussian. In this work, we propose to use partial time-reversal transformation to define (an analogue of) the entanglement negativity and related quantities. We demonstrate, for the symmetry-protected topological phase realized in the Kitaev chain, the conventional definition of the partial transpose (and hence the entanglement negativity) fails to capture the formation of the edge Majorana fermions, while the partial time-reversal computes the quantum dimension of the Majorana fermions. Furthermore, we show that the partial time-reversal of fermionic density matrices are Gaussian and can be computed efficiently. Various results (both numerical and analytical) for the entanglement negativity using the partial-time reversal are presented for (1+1)-dimensional conformal field theories, and also for fermionic disordered systems (random single phases).

show abstract

Topological entanglement negativity in Chern-Simons theories

Cited by 66 publications

References 74 publications

Entanglement negativity and minimal entanglement wedge cross sections in holographic theories

Entanglement negativity and minimal entanglement wedge cross sections in holographic theories

Edge theory approach to topological entanglement entropy, mutual information, and entanglement negativity in Chern-Simons theories

Partial time-reversal transformation and entanglement negativity in fermionic systems

Contact Info

Product

Resources

About