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Register a new userFinite-temperature mutual information in a simple phase transition
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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.
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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.
Atomic many-body phase transitions and quantum criticality have recently attracted much attention in non-standard optical lattices. Here we perform an experimental study of finite-temperature superfluid transition of bosonic atoms confined in a three dimensional triangular lattice, whose structure can be continuously deformed to dimensional crossover regions including quasi-one and two dimensions. This non-standard lattice system provides a versatile platform to investigate many-body correlated phases. For the three dimensional case, we find that the finite temperature superfluid transition agrees quantitatively with the Gutzwiller mean field theory prediction, whereas tuning towards reduced dimensional cases, both quantum and thermal fluctuation effects are more dramatic, and the experimental measurement for the critical point becomes strongly deviated from the mean field theory. We characterize the fluctuation effects in the whole dimension crossover process. Our experimental results imply strong many-body correlations in the system beyond mean field description, paving a way to study quantum criticality near Mott-superfluid transition in finite temperature dimension-crossover lattices.
We study the temporal evolution of the mutual information (MI) in a one-dimensional Kitaev chain, coupled to a fermionic Markovian bath, subsequent to a global quench of the chemical potential. In the unitary case, the MI (or equivalently the bipartite entanglement entropy) saturates to a steady-state value (obeying a volume law) following a ballistic growth. On the contrary, we establish that in the dissipative case the MI is exponentially damped both during the initial ballistic growth as well as in the approach to the steady state. We observe that even in a dissipative system, postquench information propagates solely through entangled pairs of quasiparticles having a finite lifetime; this quasiparticle picture is further corroborated by the out-of-equilibrium analysis of two-point fermionic correlations. Remarkably, in spite of the finite lifetime of the quasiparticles, a finite steady-state value of the MI survives in asymptotic times which is an artifact of nonvanishing two-point correlations. Further, the finite lifetime of quasiparticles renders to a finite length scale in these steady-state correlations.
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 quantify the emergent complexity of quantum states near quantum critical points on regular 1D lattices, via complex network measures based on quantum mutual information as the adjacency matrix, in direct analogy to quantifying the complexity of EEG/fMRI measurements of the brain. Using matrix product state methods, we show that network density, clustering, disparity, and Pearsons correlation obtain the critical point for both quantum Ising and Bose-Hubbard models to a high degree of accuracy in finite-size scaling for three classes of quantum phase transitions, $Z_2$, mean field superfluid/Mott insulator, and a BKT crossover.
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