相关论文: A Special Case Of A Conjecture By Widom With Impli…
We show that the entanglement entropy associated to a region grows faster than the area of its boundary surface. This is done by proving a special case of a conjecture due to Widom that yields a surprisingly simple expression for the…
We show that entanglement entropy of free fermions scales faster then area law, as opposed to the scaling $L^{d-1}$ for the harmonic lattice, for example. We also suggest and provide evidence in support of an explicit formula for the…
We study the asymptotic growth of the entanglement entropy of ground states of non-interacting (spinless) fermions in $\mathbb R^3$ subject to a non-zero, constant magnetic field perpendicular to a plane. As for the case with no magnetic…
We prove a logarithmically enhanced area law for all R\'enyi entanglement entropies of the ground state of a free gas of relativistic Dirac fermions. Such asymptotics occur in any dimension if the modulus of the Fermi energy is larger than…
We study the entanglement entropy of connected bipartitions in free fermion gases of N particles in arbitrary dimension d. We show that the von Neumann and Renyi entanglement entropies grow asymptotically as N^(1-1/d) ln N, with a prefactor…
A system of fermions forming a Fermi surface exhibits a large degree of quantum entanglement, even in the absence of interactions. In particular, the usual case of a codimension one Fermi surface leads to a logarithmic violation of the area…
In a remarkable paper [Phys. Rev. Lett. 96, 100503 (2006)], Dimitri Gioev and Israel Klich conjectured an explicit formula for the leading asymptotic growth of the spatially bi-partite von-Neumann entanglement entropy of non-interacting…
We consider the fermionic entanglement entropy for the free Dirac field in a bounded spatial region of Minkowski spacetime. In order to make the system ultraviolet finite, a regularization is introduced. An area law is proven in the…
We study bipartite entanglement entropies in the ground and excited states of model fermion systems, where a staggered potential, $\mu_s$, induces a gap in the spectrum. Ground state entanglement entropies satisfy the `area law', and the…
We obtain a central limit theorem for bulk counting statistics of free fermions in smooth domains of $\mathbb{R}^n$ with an explicit description of the covariance structure. This amounts to a study of the asymptotics of norms of commutators…
We prove a two-term quasi-classical trace asymptotic formula for the functions of multi-dimensional Wiener-Hopf operators with discontinuous symbols. The discontinuities occur on the surfaces which are assumed to be piece-wise smooth. Such…
We consider a multi-dimensional continuum Schr\"odinger operator which is given by a perturbation of the negative Laplacian by a compactly supported potential. We establish both an upper and a lower bound on the bipartite entanglement…
We study the entanglement entropies of an interval on the infinite line in the free fermionic spinless Schr\"odinger field theory at finite density and zero temperature, which is a non-relativistic model with Lifshitz exponent $z=2$. We…
The entanglement entropy in a quantum field theory between two regions of space has been shown in simple cases to be proportional to the volume of the hypersurface separating the regions. We prove that this is true for a free scalar field…
We consider the symmetry resolved R\'enyi entropies in the one dimensional tight binding model, equivalent to the spin-1/2 XX chain in a magnetic field. We exploit the generalised Fisher-Hartwig conjecture to obtain the asymptotic behaviour…
We consider the entanglement entropy for a free $U(1)$ theory in $3 + 1$ dimensions in the extended Hilbert space definition. By taking the continuum limit carefully we obtain a replica trick path integral which calculates this entanglement…
We introduce a systematic framework to calculate the bipartite entanglement entropy of a compact spatial subsystem in a one-dimensional quantum gas which can be mapped into a noninteracting fermion system. We show that when working with a…
We consider fermionic ground states of the Landau Hamiltonian, $H_B$, in a constant magnetic field of strength $B>0$ in $\mathbb R^2$ at some fixed Fermi energy $\mu>0$, described by the Fermi projection $P_B:= 1(H_B\le \mu)$. For some…
We consider the ideal Fermi gas of indistinguishable particles without spin but with electric charge, confined to a Euclidean plane $\mathbb R^2$ perpendicular to an external constant magnetic field of strength $B>0$. We assume this…
This study investigates the scaling behavior of the ground-state entanglement entropy in a model of free fermions on folded cubes. An analytical expression is derived in the large-diameter limit, revealing a strict adherence to the area…