We present a self-contained theory for the exact calculation of particle number counting statistics of non-interacting indistinguishable particles in the canonical ensemble. This general framework introduces the concept of auxiliary partition functio
ns, and represents a unification of previous distinct approaches with many known results appearing as direct consequences of the developed mathematical structure. In addition, we introduce a general decomposition of the correlations between occupation numbers in terms of the occupation numbers of individual energy levels, that is valid for both non-degenerate and degenerate spectra. To demonstrate the applicability of the theory in the presence of degeneracy, we compute energy level correlations up to fourth order in a bosonic ring in the presence of a magnetic field.
We analyze fermions after an interaction quantum quench in one spatial dimension and study the growth of the steady state entanglement entropy density under either a spatial mode or particle bipartition. For integrable lattice models, we find excelle
nt agreement between the increase of spatial and particle entanglement entropy, and for chaotic models, an examination of two further neighbor interaction strengths suggests similar correspondence. This result highlights the generality of the dynamical conversion of entanglement to thermodynamic entropy under time evolution that underlies our current framework of quantum statistical mechanics.
Operationally accessible entanglement in bipartite systems of indistinguishable particles could be reduced due to restrictions on the allowed local operations as a result of particle number conservation. In order to quantify this effect, Wiseman and
Vaccaro [Phys. Rev. Lett. 91, 097902 (2003)] introduced an operational measure of the von Neumann entanglement entropy. Motivated by advances in measuring Renyi entropies in quantum many-body systems subject to conservation laws, we derive a generalization of the operational entanglement that is both computationally and experimentally accessible. Using the Widom theorem, we investigate its scaling with the size of a spatial subregion for free fermions and find a logarithmically violated area law scaling, similar to the spatial entanglement entropy, with at most, a double-log leading-order correction. A modification of the correlation matrix method confirms our findings in systems of up to $10^5$ particles.
We investigate wetting phenomena near graphene within the Dzyaloshinskii-Lifshitz-Pitaevskii theory for light gases composed of hydrogen, helium and nitrogen in three different geometries where graphene is either affixed to an insulating substrate, s
ubmerged or suspended. We find that the presence of graphene has a significant effect in all configurations. In a suspended geometry where graphene is able to wet on only one side, liquid film growth becomes arrested at a critical thickness which may trigger surface instabilities and pattern formation analogous to spinodal dewetting. These phenomena are also universally present in other two-dimensional materials.
We investigate the scaling of the R{e}nyi entanglement entropies for a particle bipartition of interacting spinless fermions in one spatial dimension. In the Tomonaga-Luttinger liquid regime, we calculate the second R{e}nyi entanglement entropy and s
how that the leading order finite-size scaling is equal to a universal logarithm of the system size plus a non-universal constant. Higher-order corrections decay as power-laws in the system size with exponents that depend only on the Luttinger parameter. We confirm the universality of our results by investigating the one dimensional $t-V$ model of interacting spinless fermions via exact-diagonalization techniques. The resulting sensitivity of the particle partition entanglement to boundary conditions and statistics supports its utility as a probe of quantum liquids.
We aim to understand how the van der Waals force between neutral adatoms and a graphene layer is modified by uniaxial strain and electron correlation effects. A detailed analysis is presented for three atoms (He, H, and Na) and graphene strain rangin
g from weak to moderately strong. We show that the van der Waals potential can be significantly enhanced by strain, and present applications of our results to the problem of elastic scattering of atoms from graphene. In particular we find that quantum reflection can be significantly suppressed by strain, meaning that dissipative inelastic effects near the surface become of increased importance. Furthermore we introduce a method to independently estimate the Lennard-Jones parameters used in an effective model of He interacting with graphene, and determine how they depend on strain. At short distances, we find that strain tends to reduce the interaction strength by pushing the location of the adsorption potential minima to higher distances above the deformed graphene sheet. This opens up the exciting possibility of mechanically engineering an adsorption potential, with implications for the formation and observation of anisotropic low dimensional superfluid phases.
