Density matrices for a chain of oscillators

Peschel, Ingo; Chung, Ming-Chiang

doi:10.1088/0305-4470/32/48/305

Cited by 82 publications

(138 citation statements)

References 21 publications

(37 reference statements)

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“…n is computed through the correlators q r q s and p r p s as explained in [35]. Notice that we have improved this check with respect to [23], indeed the data in Fig.…”

Section: A )mentioning

confidence: 79%

Entanglement entropy and negativity of disjoint intervals in CFT: some numerical extrapolations

Nobili¹,

Coser²,

Tonni³

2015

J. Stat. Mech.

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Abstract. The entanglement entropy and the logarithmic negativity can be computed in quantum field theory through a method based on the replica limit. Performing these analytic continuations in some cases is beyond our current knowledge, even for simple models. We employ a numerical method based on rational interpolations to extrapolate the entanglement entropy of two disjoint intervals for the conformal field theories given by the free compact boson and the Ising model. The case of three disjoint intervals is studied for the Ising model and the non compact free massless boson. For the latter model, the logarithmic negativity of two disjoint intervals has been also considered. Some of our findings have been checked against existing numerical results obtained from the corresponding lattice models.arXiv:1501.04311v1 [cond-mat.stat-mech]

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“…n is computed through the correlators q r q s and p r p s as explained in [35]. Notice that we have improved this check with respect to [23], indeed the data in Fig.…”

Section: A )mentioning

confidence: 79%

Entanglement entropy and negativity of disjoint intervals in CFT: some numerical extrapolations

Nobili¹,

Coser²,

Tonni³

2015

J. Stat. Mech.

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“…The reduced density matrix of a region A can be found by tracing out degrees of freedom outside region A. Then the entanglement entropy of the region A are [78][79][80],…”

Section: Numerical Analysismentioning

confidence: 99%

On the mutual information in conformal field theory

Chen

Hao

et al. 2017

J. High Energ. Phys.

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Abstract:In this work, we study the universal behaviors in the mutual information of two disjoint spheres in a conformal field theory (CFT). By using the operator product expansion of the spherical twist operator in terms of the conformal family, we show that the large distance expansion of the mutual information can be cast in terms of the conformal blocks. We develop the 1/n prescription to compute the coefficients before the conformal blocks. For a single conformal family, the leading nonvanishing contribution to the mutual information comes from the bilinear operators. We show that the coefficients of these operators take universal forms and such universal behavior persists in the bilinear operators with derivatives as well. Consequently the first few leading order contributions to the mutual information in CFT take universal forms. To illustrate our framework, we discuss the free scalars and free fermions in various dimensions. For the free scalars, we compute the mutual information to the next-to-leading order and find good agreement with the improved numerical lattice result. For the free fermion, we compute the leading order result, which is of universal form, and find the good match with the numerical study. Our formalism could be applied to any CFT potentially.

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“…In (A22) the constant b accounts for the dependence of , L on the microscopic cutoff (lattice spacing). The behavior (A22) has been proved analytically for the single-particle entanglement spectrum levels of free fermionic models 80,82 and conjectured for free bosonic models 81,[83][84][85] . Here we only propose it as a fitting function: the result of the fit is shown in Figure 9 as dash-dotted line, and it is in perfect agreement with the data.…”

Section: T2mentioning

confidence: 99%

Negativity spectrum of one-dimensional conformal field theories

2016

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The partial transpose ρ T 2 A of the reduced density matrix ρA is the key object to quantify the entanglement in mixed states, in particular through the presence of negative eigenvalues in its spectrum. Here we derive analytically the distribution of the eigenvalues of ρA , that we dub negativity spectrum, in the ground sate of gapless one-dimensional systems described by a Conformal Field Theory (CFT), focusing on the case of two adjacent intervals. We show that the negativity spectrum is universal and depends only on the central charge of the CFT, similarly to the entanglement spectrum. The precise form of the negativity spectrum depends on whether the two intervals are in a pure or mixed state, and in both cases, a dependence on the sign of the eigenvalues is found. This dependence is weak for bulk eigenvalues, whereas it is strong at the spectrum edges. We also investigate the scaling of the smallest (negative) and largest (positive) eigenvalues of ρ T 2 A . We check our results against DMRG simulations for the critical Ising and Heisenberg chains, and against exact results for the harmonic chain, finding good agreement for the spectrum, but showing that the smallest eigenvalue is affected by very large scaling corrections.

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Density matrices for a chain of oscillators

Cited by 82 publications

References 21 publications

Entanglement entropy and negativity of disjoint intervals in CFT: some numerical extrapolations

Entanglement entropy and negativity of disjoint intervals in CFT: some numerical extrapolations

On the mutual information in conformal field theory

Negativity spectrum of one-dimensional conformal field theories

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