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Center for Nonlinear Studies |
The last few years have seen a surge in study of entanglement entropy in different fields of theoretical physics. In condensed matter, entanglement entropy, and various generalizations such as Renyi/Tsallis entropy, mutual information and entanglement spectrum, have been considered a useful tool for characterizing exotic quantum phases and quantum phase transitions that denies a description by a conventional symmetry breaking paradigm of Landau. Yet relatively little attention has been dedicated to that of the conventional long-range ordered phases or critical phases. In this talk, I will talk about a series of work that focuses on the entanglement entropy of such "well-understood" phases, and show that they have non-trivial entanglement properties due to either the long-range order, or the quantum criticality. In the first part, I will focus on entanglement entropy of long-range ordered systems[1]: a ferromagnetic model, an antiferromagnetic model, and a set of free boson models with long-range hopping, and show that in all these cases, the entanglement entropy (or the mutual information at finite temperatures) scales as ~ log L. For the second part, I shall discuss the entanglement entropy of Fermi liquids in two dimensions[2], which is one of the simplest and well-understood quantum critical phases. In the absence of interaction, the entanglement entropy of free fermions is solved by Gieov and Klich[3], using the Widom's conjecture, and scales as the area-law enhanced by a logarithmic factor, E ~ L^{d-1} log L. We re-derive this result via high dimensional bosonization, generalize the method to take into account the Fermi liquid interaction, and show that the entanglement entropy is not renormalized by the interactions.
Host: Nikolai Sinitsyn, T-4: PHYS OF CONDENSED MATTER, nsinitsyn@lanl.gov