Hasuk Francis Song

The scaling of entanglement entropy and, more recently, the full entanglement spectrum have become useful tools for characterizing certain universal features of quantum many-body systems. We motivate the importance of entanglement in the study of many-body systems by considering the “gratuitously big” size of Hilbert space and the need for generic ansatzes that efficiently represent useful wave functions. In addition, we study the scaling of the entanglement entropy in the two-dimensional spin-1/2 Heisenberg antiferromagnet, where our work and other recent work indicate that a subleading logarithmic term contains universal information about the number of Goldstone modes in the symmetry-broken phase. Although entanglement entropy is difficult to measure experimentally, we show that for systems that can be mapped to non-interacting fermions both the von Neumann entanglement entropy and generalized R’{e}nyi entropies can be related exactly to the cumulants of number fluctuations, which are accessible experimentally. In principle, this also extends to the full entanglement spectrum. Such systems include free fermions in all dimensions, the integer quantum Hall states and topological insulators in two dimensions, strongly repulsive bosons in one-dimensional optical lattices, and the spin-1/2 XX chain, both pure and strongly disordered. The same formalism can be used for analyzing entanglement entropy generation in quantum point contacts with non-interacting electron reservoirs. Beyond the non-interacting case, we show that in analogy to the full counting statistics used in mesoscopic transport, fluctuations give important information about many-body systems including the location of quantum critical points.