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 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.
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.
Understanding the behaviour of topologically ordered lattice systems at finite temperature is a way of assessing their potential as fault-tolerant quantum memories. We compute the natural extension of the topological entanglement entropy for T > 0, namely the subleading correction $I_{textrm{topo}}$ to the area law for mutual information. Its dependence on T can be written, for Abelian Kitaev models, in terms of information-theoretic functions and readily identifiable scaling behaviour, from which the interplay between volume, temperature, and topological order, can be read. These arguments are extended to non-Abelian quantum double models, and numerical results are given for the $D(S_3)$ model, showing qualitative agreement with the Abelian case.
In this work we study Podolsky electromagnetism in thermodynamic equilibrium. We show that a Podolsky mass-dependent modification to the Stefan-Boltzmann law is induced and we use experimental data to limit the possible values for this free parameter.
We consider weakly-coupled QFT in AdS at finite temperature. We compute the holographic thermal two-point function of scalar operators in the boundary theory. We present analytic expressions for leading corrections due to local quartic interactions in the bulk, with an arbitrary number of derivatives and for any number of spacetime dimensions. The solutions are fixed by judiciously picking an ansatz and imposing consistency conditions. The conditions include analyticity properties, consistency with the operator product expansion, and the Kubo-Martin-Schwinger condition. For the case without any derivatives we show agreement with an explicit diagrammatic computation. The structure of the answer is suggestive of a thermal Mellin amplitude. Additionally, we derive a simple dispersion relation for thermal two-point functions which reconstructs the function from its discontinuity.