We investigate the entanglement entropy of a class of $N$ -particle excited state of fermions confined in a two-dimensional harmonic trap rotating at an angular frequency $Ω$ . The excited state is constructed by filling a particular set of $N$ single-particle energy levels. We analytically compute the Rényi entropies of order $q$ in a disc of radius $r$ around the centre of the trap, and the cumulants corresponding to number fluctuations of fermions within the disc. We found that the area law scaling of entanglement entropy holds even for a class of excited states. We also verified the well-known series expansion of entanglement entropy in terms of the particle number cumulants for non-interacting fermions. We further derive the centered cumulant generating function, demonstrating that the associated probability distribution function in the disc has identical scaling properties, up to a variable shift, to the known ground-state result. Finally, we extend our result to an annular region, showing that both the Rényi entropy and particle number cumulants of the annulus decompose into sums of the corresponding quantities of the two bounding discs. These additive relations hold as long as the width of the annulus is sufficiently large.We investigate the entanglement entropy of a class of $N$-particle excited state of fermions confined in a two-dimensional harmonic trap rotating at an angular frequency $Ω$. The excited state is constructed by filling a particular set of $N$ single-particle energy levels. We analytically compute the Rényi entropies of order $q$ in a disc of radius $r$ around the centre of the trap, and the cumulants corresponding to number fluctuations of fermions within the disc. We found that the area law scaling of entanglement entropy holds even for a class of excited states. We also verified the well-known series expansion of entanglement entropy in terms of the particle number cumulants for non-interacting fermions. We further derive the centered cumulant generating function, demonstrating that the associated probability distribution function in the disc has identical scaling properties, up to a variable shift, to the known ground-state result. Finally, we extend our result to an annular region, showing that both the Rényi entropy and particle number cumulants of the annulus decompose into sums of the corresponding quantities of the two bounding discs. These additive relations hold as long as the width of the annulus is sufficiently large.

cond-mat.stat-mechCross-listedarXiv:2608.05722Aug 7, 20260 citations

Exact relations between particle fluctuations and entanglement in Fermi gases

Pasquale Calabrese, Mihail Mintchev, Ettore Vicari

We derive exact relations between the Rényi entanglement entropies and the particle-number fluctuations of (connected and disjoint) spatial regions in systems of N non-interacting fermions in arbitrary dimension. We prove that the asymptotic large- N behavior of the entanglement entropies is proportional to the variance of the particle number. We also consider 1D Fermi gases with a localized impurity, where all particle cumulants contribute to the asymptotic large- N behavior of the entanglement entropies. The particle cumulant expansion turns out to be convergent for all integer-order Rényi entropies (except for the von Neumann entropy) and the first few cumulants provide already a good approximation. Since the particle cumulants are accessible to experiments, these relations may provide a measure of entanglement in these systems.We derive exact relations between the Rényi entanglement entropies and the particle-number fluctuations of (connected and disjoint) spatial regions in systems of N non-interacting fermions in arbitrary dimension. We prove that the asymptotic large- N behavior of the entanglement entropies is proportional to the variance of the particle number. We also consider 1D Fermi gases with a localized impurity, where all particle cumulants contribute to the asymptotic large- N behavior of the entanglement entropies. The particle cumulant expansion turns out to be convergent for all integer-order Rényi entropies (except for the von Neumann entropy) and the first few cumulants provide already a good approximation. Since the particle cumulants are accessible to experiments, these relations may provide a measure of entanglement in these systems.

arXiv:1111.4836Europhysics Letters (EPL)Apr 1, 2012135 citations

Calculation of Entanglement Entropy in Fermion Lattices

Michelle Storms, Rajiv R. P. Singh

Bulletin of the American Physical SocietyOct 4, 20130 citations

Full counting statistics and entanglement in a disordered free fermion system

Michael Bantegui, Joseph A. Burg, Gregory Levine

Bulletin of the American Physical SocietyFeb 28, 20120 citations

We investigate the entanglement entropy of a class of

N

-particle excited state of fermions confined in a two-dimensional harmonic trap rotating at an angular frequency

Ω

. The excited state is constructed by filling a particular set of

N

single-particle energy levels. We analytically compute the Rényi entropies of order

q

in a disc of radius

r

around the centre of the trap, and the cumulants corresponding to number fluctuations of fermions within the disc. We found that the area law scaling of entanglement entropy holds even for a class of excited states. We also verified the well-known series expansion of entanglement entropy in terms of the particle number cumulants for non-interacting fermions. We further derive the centered cumulant generating function, demonstrating that the associated probability distribution function in the disc has identical scaling properties, up to a variable shift, to the known ground-state result. Finally, we extend our result to an annular region, showing that both the Rényi entropy and particle number cumulants of the annulus decompose into sums of the corresponding quantities of the two bounding discs. These additive relations hold as long as the width of the annulus is sufficiently large.