Entanglement entropy of fermions in any dimension and the Widom conjecture

We consider the target space entanglement in quantum mechanics of non-interacting fermions at finite temperature. Unlike pure states investigated in arXiv:2105.13726, the (R\'enyi) entanglement entropy for thermal states does not follow a simple bound because all states in the infinite-dimensional Hilbert space are involved. We investigate a general formula of the target space R\'enyi entropy for $N$ fermions at finite temperature, and present numerical results of the entropy...

We investigate the behavior of entanglement-entropy on a broad scale, that is, a large class of systems, Hamiltonians and states describing the interaction of many degrees of freedom. It is one of our aims to show which general characteristics are responsible for the different types of quantitative behavior of entantglement-entropy. Our main lesson is that what really matters is the degree of degeneracy of the spectrum of certain nearby reference Hamiltonians. For calculation...

I compute the leading contribution to the ground state Renyi entropy $S_{\alpha}$ for a region of linear size $L$ in a Fermi liquid. The result contains a universal boundary law violating term simply related the more familiar entanglement entropy. I also obtain a universal crossover function that smoothly interpolates between the zero temperature result and the ordinary thermal Renyi entropy of a Fermi liquid. Formulas for the entanglement entropy of more complicated regions,...

It is often observed in the ground state of spatially-extended quantum systems with local interactions that the entropy of a large region is proportional to its surface area. In some cases, this area law is corrected with a logarithmic factor. This contrasts with the fact that in almost all states of the Hilbert space, the entropy of a region is proportional to its volume. This paper shows that low-energy states have (at most) an area law with the logarithmic correction, prov...

We study the entanglement entropy of random partitions in one- and two-dimensional critical fermionic systems. In an infinite system we consider a finite, connected (hypercubic) domain of linear extent $L$, the points of which with probability $p$ belong to the subsystem. The leading contribution to the average entanglement entropy is found to scale with the volume as $a(p) L^D$, where $a(p)$ is a non-universal function, to which there is a logarithmic correction term, $b(p)L...

We report on the calculation of the symmetry resolved entanglement entropies in two-dimensional many-body systems of free bosons and fermions by \emph{dimensional reduction}. When the subsystem is translational invariant in a transverse direction, this strategy allows us to reduce the initial two-dimensional problem into decoupled one-dimensional ones in a mixed space-momentum representation. While the idea straightforwardly applies to any dimension $d$, here we focus on the ...

We develop a first-principle approach to compute the counting statistics in the ground-state of $N$ noninteracting spinless fermions in a general potential in arbitrary dimensions $d$ (central for $d>1$). In a confining potential, the Fermi gas is supported over a bounded domain. In $d=1$, for specific potentials, this system is related to standard random matrix ensembles. We study the quantum fluctuations of the number of fermions ${\cal N}_{\cal D}$ in a domain $\cal{D}$ of...

We study the entanglement entropy and particle number cumulants for a system of disordered noninteracting fermions in $d$ dimensions. We show, both analytically and numerically, that for a weak disorder the entanglement entropy and the second cumulant (particle number variance) are proportional to each other with a universal coefficient. The corresponding expressions are analogous to those in the clean case but with a logarithmic factor regularized by the mean free path rathe...

We study the entanglement properties of non-Hermitian free fermionic models with translation symmetry using the correlation matrix technique. Our results show that the entanglement entropy has a logarithmic correction to the area law in both one-dimensional and two-dimensional systems. For any one-dimensional one-band system, we prove that each Fermi point of the system contributes exactly 1/2 to the coefficient c of the logarithmic correction. Moreover, this relation between...

We study the scaling of entanglement in low-energy states of quantum many-body models on lattices of arbitrary dimensions. We allow for unbounded Hamiltonians such that systems with bosonic degrees of freedom are included. We show that if at low enough temperatures the specific heat capacity of the model decays exponentially with inverse temperature, the entanglement in every low-energy state satisfies an area law (with a logarithmic correction). This behaviour of the heat ca...