Pressure, compressibility, and contact of the two-dimensional attractive Fermi gas

Using ab initio lattice methods, we calculate the finite temperature thermodynamics of homogeneous two-dimensional spin-1/2 fermions with attractive short-range interactions. We present results for the density, pressure, compressibility, and quantum anomaly (i.e. Tan's contact) for a wide range of temperatures and coupling strengths, focusing on the unpolarized case. Within our statistical and systematic uncertainties, our prediction for the density equation of state differs quantitatively from the prediction by Luttinger-Ward theory in the strongly coupled region of parameter space, but otherwise agrees well with it. We also compare our calculations with the second- and third-order virial expansion, with which they are in excellent agreement in the low-fugacity regime.Comment: 7 pages, 8 figures, including supplemental material

Entanglement, noise, and the cumulant expansion

We put forward a simpler and improved variation of a recently proposed method to overcome the signal-to-noise problem found in Monte Carlo calculations of the entanglement entropy of interacting fermions. The present method takes advantage of the approximate lognormal distributions that characterize the signal-to-noise properties of other approaches. In addition, we show that a simple rewriting of the formalism allows circumvention of the inversion of the restricted one-body density matrix in the calculation of the $n$-th R\'enyi entanglement entropy for $n>2$. We test our technique by implementing it in combination with the hybrid Monte Carlo algorithm and calculating the $n=2,3,4, \dots, 10$ R\'enyi entropies of the 1D attractive Hubbard model. We use that data to extrapolate to the von Neumann ($n=1$) and $n\to\infty$ cases.Comment: Significantly expanded manuscript; improved presentation, new data and figures, new approach to the calculation of $n>2$ R\'enyi entropies. 8 pages, 8 figure