Rényi entropy at large energy density in 2D CFT

Guo, Wu; Lin, Feng Li; Zhang, Jiaju

doi:10.1007/jhep08(2019)010

Cited by 4 publications

(5 citation statements)

References 60 publications

(175 reference statements)

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“…One potential application of these results is to investigate the thermalization of subsystems in a finite total system, like that in [81] for thermalization of subsystems in an infinite total system after a global quantum quench [82][83][84]. Another possible application is the distinguishability of the black hole microstates and other states in gravity and holographic CFTs [85][86][87][88][89].…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Rényi entropy and subsystem distances in finite size and thermal states in critical XY chains

Arias¹,

Zhang²

2020

J. Stat. Mech.

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We study the Rényi entropy and subsystem distances on one interval for the finite size and thermal states in the critical XY chains, focusing on the critical Ising chain and XX chain with zero transverse field. We construct numerically the reduced density matrices and calculate the von Neumann entropy, Rényi entropy, subsystem trace distance, Schatten two-distance, and relative entropy. As the continuum limit of the critical Ising chain and XX chain with zero field are, respectively, the two-dimensional free massless Majorana and Dirac fermion theories, which are conformal field theories, we compare the spin chain numerical results with the analytical results in conformal field theories and find perfect matches in the continuum limit.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Rényi entropy and subsystem distances in finite size and thermal states in critical XY chains

Arias¹,

Zhang²

2020

J. Stat. Mech.

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“…However, for large subsystem there exists many probes to distinguish them. One of them is the Rényi entropy [34,35]. Here we can also use the Rényi entropy to distinguish ρ A,m from ρ A .…”

Section: Indistinguishability Of ρ Am From ρ Amentioning

confidence: 99%

Entanglement spectrum of geometric states

Guo

2021

J. High Energ. Phys.

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The reduced density matrix of a given subsystem, denoted by ρA, contains the information on subregion duality in a holographic theory. We may extract the information by using the spectrum (eigenvalue) of the matrix, called entanglement spectrum in this paper. We evaluate the density of eigenstates, one-point and two-point correlation functions in the microcanonical ensemble state ρA,m associated with an eigenvalue λ for some examples, including a single interval and two intervals in vacuum state of 2D CFTs. We find there exists a microcanonical ensemble state with λ0 which can be seen as an approximate state of ρA. The parameter λ0 is obtained in the two examples. For a general geometric state, the approximate microcanonical ensemble state also exists. The parameter λ0 is associated with the entanglement entropy of A and Rényi entropy in the limit n → ∞. As an application of the above conclusion we reform the equality case of the Araki-Lieb inequality of the entanglement entropies of two intervals in vacuum state of 2D CFTs as conditions of Holevo information. We show the constraints on the eigenstates. Finally, we point out some unsolved problems and their significance on understanding the geometric states.

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“…The reduced density matrix of subsystem 1 or 2 is the microcanonical ensemble state with energy E. It has been shown the microcanonical ensemble state is almost undistinguishable from the canonical one for short interval if λ = β [27]. But for medium interval or long interval, one can find some probes to distinguish these two ensemble, such as Rényi entropy [31,32]. The two-point correlator with…”

Section: Jhep08(2020)125mentioning

confidence: 99%

“…But their difference will appear if the measurements are performed in a larger subregion. One may use the Rényi entropy as a probe to detect their difference [31,32]. In [52] the author construct a modified state of…”

Section: Jhep08(2020)125mentioning

confidence: 99%

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Correlations in geometric states

Guo

2020

J. High Energ. Phys.

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In this paper we explore the correlations in the geometric states. Here the geometric state means the state in CFTs that can be effectively described by classical geometry in the bulk in the semi-classical limit G → 0. By using the upper bound of Holevo information we show the convex combination of geometric states cannot be a geometric state. To understand the duality between thermofield double state and eternal black hle, we construct several correlated states of two CFTs. In all the examples we show their correlations are too weak to produce the a connected spacetime. Then we review the measure named quantum discord and use it to characterize the classical and quantum correlations in quantum field theories. Finally, we discuss the correlations between two intervals A and B with distance d in the vacuum state of 2D CFTs with large central charge c. The feature is the phase transition of the mutual information I (ρAB). We analyse the quasi-product state of ρAB for large d. By using the Koashi-Winter relation of tripartite states the quantum and classical correlations between A and B can expressed as Holevo information, which provides a new understanding of the correlations as accessible information.

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Rényi entropy at large energy density in 2D CFT

Cited by 4 publications

References 60 publications

Rényi entropy and subsystem distances in finite size and thermal states in critical XY chains

Rényi entropy and subsystem distances in finite size and thermal states in critical XY chains

Entanglement spectrum of geometric states

Correlations in geometric states

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