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Register a new userAn Inverse Mass Expansion for the Mutual Information in Free Scalar QFT at Finite Temperature
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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 (Phys. Rev. Lett. 71, 666 (1993)) 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 an $1/mu$ expansion, where $mu$ is the mass of the scalar field. Finally, we study the high and low temperature behaviour of the area law term.
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Entanglement entropy in free scalar field theory at its ground state is dominated by an area law term. However, when mixed states are considered this property ceases to exist. We show that in such cases the mutual information obeys an area law. The proportionality constant connecting the area to the mutual information has an interesting dependence on the temperature. At infinite temperature it tends to a finite value which coincides with the classical calculation.
We study the finite-temperature behavior of the Lipkin-Meshkov-Glick model, with a focus on correlation properties as measured by the mutual information. The latter, which quantifies the amount of both classical and quantum correlations, is computed exactly in the two limiting cases of vanishing magnetic field and vanishing temperature. For all other situations, numerical results provide evidence of a finite mutual information at all temperatures except at criticality. There, it diverges as the logarithm of the system size, with a prefactor that can take only two values, depending on whether the critical temperature vanishes or not. Our work provides a simple example in which the mutual information appears as a powerful tool to detect finite-temperature phase transitions, contrary to entanglement measures such as the concurrence.
In local scalar quantum field theories (QFTs) at finite temperature correlation functions are known to satisfy certain non-perturbative constraints, which for two-point functions in particular implies the existence of a generalisation of the standard K{a}ll{e}n-Lehmann representation. In this work, we use these constraints in order to derive a spectral representation for the shear viscosity arising from the thermal asymptotic states, $eta_{0}$. As an example, we calculate $eta_{0}$ in $phi^{4}$ theory, establishing its leading behaviour in the small and large coupling regimes.
In this paper, we investigate operator product expansion for thermal correlation function of the two scalar currents. Due to breakdown of Lorentz invariance at finite temperature, more operators of the same dimension appear in the operator product expansion than at zero temperature. We calculated Wilson coefficients in the short distance expansion and obtain operator product expansion for thermal correlation function in terms of quark condensate, gluon condensate, quark energy density and gluon energy density.
I discuss and extend the recent proposal of Leclair and Mussardo for finite temperature correlation functions in integrable QFTs. I give further justification for its validity in the case of one point functions of conserved quantities. I also argue that the proposal is not correct for two (and higher) point functions, and give some counterexamples to justify that claim.
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