arXiv:1907.08508 · Journal of High Energy Physics

An inverse mass expansion for the mutual information in free scalar QFT at finite temperature

Dimitrios Katsinis, Georgios Pastras

Published Feb 1, 2020• 6 citations

Abstract

Abstract We study the entanglement entropy and the mutual information in coupled harmonic systems at finite temperature. Interestingly, we find that the mutual information does not vanish at infinite temperature, but it rather reaches a specific finite value, which can be attributed to classical correlations solely. We further obtain high and low temperature expansions for both quantities. Then, we extend the analysis performed in the seminal paper by Srednicki [1] for free real scalar field theories in Minkowski space-time in 3 + 1 dimensions at a thermal state. We find that the mutual information obeys an area law, similar to that obeyed by the entanglement entropy at vanishing temperature. The coefficient of this area law does not vanish at infinite temperature. Then, we calculate this coefficient perturbatively in a 1/μ expansion, where μ is the mass of the scalar field. Finally, we study the high and low temperature behaviour of the area law term.

DOI: 10.1007/jhep02(2020)091

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arXiv:1907.08508 · Journal of High Energy Physics

An inverse mass expansion for the mutual information in free scalar QFT at finite temperature

Dimitrios Katsinis, Georgios Pastras

Published Feb 1, 2020• 6 citations

arXiv HTML PDF

Abstract

DOI: 10.1007/jhep02(2020)091

Related papers

An inverse mass expansion for entanglement entropy in free massive scalar field theory

Dimitrios Katsinis, Georgios Pastras

We extend the entanglement entropy calculation performed in the seminal paper by Srednicki (Phys Rev Lett 71:666, 1993) for free real massive scalar field theories in $1+1$ 1 + 1 , $2+1$ 2 + 1 and $3+1$ 3 + 1 dimensions. We show that the inverse of the scalar field mass can be used as an expansion parameter for a perturbative calculation of the entanglement entropy. We perform the calculation for the ground state of the system and for a spherical entangling surface at third order in the inverse mass expansion. The calculated entanglement entropy contains a leading area law term, as well as subleading terms that depend on the regularization scheme, as expected. Universal terms are non-perturbative effects in this approach. Interestingly, this perturbative expansion can be used to approximate the coefficient of the area law term, even in the case of a massless scalar field in $2+1$ 2 + 1 and $3+1$ 3 + 1 dimensions. The presented method provides the spectrum of the reduced density matrix as an intermediate result, which is an important advantage in comparison to the replica trick approach. Our perturbative expansion underlines the relation between the area law and the locality of the underlying field theory.We extend the entanglement entropy calculation performed in the seminal paper by Srednicki (Phys Rev Lett 71:666, 1993) for free real massive scalar field theories in $$1+1$$ 1 + 1 , $$2+1$$ 2 + 1 and $$3+1$$ 3 + 1 dimensions. We show that the inverse of the scalar field mass can be used as an expansion parameter for a perturbative calculation of the entanglement entropy. We perform the calculation for the ground state of the system and for a spherical entangling surface at third order in the inverse mass expansion. The calculated entanglement entropy contains a leading area law term, as well as subleading terms that depend on the regularization scheme, as expected. Universal terms are non-perturbative effects in this approach. Interestingly, this perturbative expansion can be used to approximate the coefficient of the area law term, even in the case of a massless scalar field in $$2+1$$ 2 + 1 and $$3+1$$ 3 + 1 dimensions. The presented method provides the spectrum of the reduced density matrix as an intermediate result, which is an important advantage in comparison to the replica trick approach. Our perturbative expansion underlines the relation between the area law and the locality of the underlying field theory.

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Abstract Relative entropy is a powerful measure of the dissimilarity between two statistical field theories in the continuum. In this work, we study the relative entropy between Gaussian scalar field theories in a finite volume with different masses and boundary conditions. We show that the relative entropy depends crucially on d , the dimension of Euclidean space. Furthermore, we demonstrate that the mutual information between two disjoint regions in $\mathbb {R}^d$ R d is finite if the two regions are separated by a finite distance and satisfies an area law. We then construct an example of “touching” regions between which the mutual information is infinite. We argue that the properties of mutual information in scalar field theories can be explained by the Markov property of these theories.Abstract Relative entropy is a powerful measure of the dissimilarity between two statistical field theories in the continuum. In this work, we study the relative entropy between Gaussian scalar field theories in a finite volume with different masses and boundary conditions. We show that the relative entropy depends crucially on d , the dimension of Euclidean space. Furthermore, we demonstrate that the mutual information between two disjoint regions in $$\mathbb {R}^d$$ R d is finite if the two regions are separated by a finite distance and satisfies an area law. We then construct an example of “touching” regions between which the mutual information is infinite. We argue that the properties of mutual information in scalar field theories can be explained by the Markov property of these theories.

arXiv:2307.15548Annales Henri PoincaréDec 17, 20242 citations

We extend the entanglement entropy calculation performed in the seminal paper by Srednicki (Phys Rev Lett 71:666, 1993) for free real massive scalar field theories in

1+1

1 + 1 ,

2+1

2 + 1 and

3+1

3 + 1 dimensions. We show that the inverse of the scalar field mass can be used as an expansion parameter for a perturbative calculation of the entanglement entropy. We perform the calculation for the ground state of the system and for a spherical entangling surface at third order in the inverse mass expansion. The calculated entanglement entropy contains a leading area law term, as well as subleading terms that depend on the regularization scheme, as expected. Universal terms are non-perturbative effects in this approach. Interestingly, this perturbative expansion can be used to approximate the coefficient of the area law term, even in the case of a massless scalar field in

2+1

2 + 1 and

3+1

3 + 1 dimensions. The presented method provides the spectrum of the reduced density matrix as an intermediate result, which is an important advantage in comparison to the replica trick approach. Our perturbative expansion underlines the relation between the area law and the locality of the underlying field theory.

We prove a

β^{2}

area law for the quantum mutual information of thermal states of local lattice Hamiltonians: for any bipartitioning

A|B

and all inverse temperatures

β

below a critical value

β^{*}

, we show

\mathcal{I}_β(A,B) \leqslant \tilde{f}(β)\, β^{2}\,|\partial_{AB}|

, where

|\partial_{AB}|

denotes the size of the boundary region and

\tilde{f}(β)

remains finite as

β\to 0

. This quadratic scaling improves the relationship between high-temperature correlations and macroscopic thermodynamics. While a linear area law implicitly permits a loose, temperature-independent upper bound on extractable work and binding energy, the quadratic scaling ensures that the nonequilibrium free energy available after decoupling regions and the total energy of the interface both are proportional to the area of the interface of

A|B

and vanish as

β

at high temperatures. These results show that the high-temperature mutual information and correlation are suppressed, respectively, quadratically and linearly in inverse temperature, which are consistent with the expected thermal decoupling in macroscopic thermodynamic quantities.

\mathbb {R}^d

R d is finite if the two regions are separated by a finite distance and satisfies an area law. We then construct an example of “touching” regions between which the mutual information is infinite. We argue that the properties of mutual information in scalar field theories can be explained by the Markov property of these theories.