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Understanding the structure of quantum correlations in a many-body system is key to its computational treatment. For fermionic systems, correlations can be defined as deviations from Slater determinant states. The link between fermionic correlations and efficient computational physics methods is actively studied but remains ambiguous. We make progress in establishing this connection mathematically. In particular, we find a rigorous classification of states relative to $k$-fermion correlations, which admits a computational physics interpretation. Correlations are captured by a measure $\omega_k$, a function of $k$-fermion reduced density matrix that we call twisted purity. Vanishing of $\omega_k$ for a given $k$ puts the state in a class $G_k$ of correlated states. Sets $G_k$ are nested in $k$, Slater determinants correspond to $k = 1$. Various physically relevant states are in or close to $G_{k=O(1)}$, including truncated configuration-interaction states, perturbation series around Slater determinants, and some nonperturbative eigenstates of the 1D Hubbard model. For each $k = O(1)$, we give an explicit ansatz with a polynomial number of parameters that covers all states in $G_k$. Potential applications of this ansatz and its connections to the coupled-cluster wavefunction are discussed., Comment: 5+13 pages, 2 figures

Recent analysis of the viability of solid state-based relic neutrino detectors has revealed the fundamental necessity for the use of heavy, $A>100$, $\beta$-decayers as neutrino targets. Of all heavy isotopes, $^{171}$Tm and $^{151}$Sm stand out for their sufficiently low decay energies, reasonable half-life times and stable daughter nuclei. However, the crucial bit of information, that is the soft neutrino capture cross-section is missing for both isotopes. The main reason for that is a particular type of $\beta$-decay, which precludes a simple link between the isotope's half-life time and the neutrino capture rate. Here we propose an experimental method to bypass this difficulty and obtain the capture cross-section of a soft neutrino by a given isotope from the isotope's $\beta$-spectrum., Comment: 11 pages

Beta-spectrum of radioactive atoms was long ago predicted to bear an imprint of the Cosmic Neutrino Background (C$\nu$B). Over the years, it has been recognised that the best chance of achieving the signal-to-noise ratio required for the observation of this effect lies with solid-state designs. Here we bring to the fore a fundamental quantum limitation on the type of beta-decayer that can be used in such a design. We derive a simple usability criterion and show that $^3\rm H$, which is the most popular choice, fails to meet it. We provide a list of potentially suitable isotopes and discuss why their use in C$\nu$B detection requires further research.

The correction to the area law for the bipartite min-entanglement entropy of weakly and locally interacting fermions is calculated based on a perturbative extension of the flow equation holography method. Explicit calculations for the one- and two-dimensional case (and similarly for higher dimensions) show that the leading correction to the entanglement entropy of non-interacting fermions up to $U^2$ in the interaction strength does not change the scaling, but only affects the pre-factor of the leading logarithmic term multiplying it by the quasiparticle residue. A term sub-leading to the area law is also present. It is proportional to $U^2$ in the interaction strength and scales linearly with the system size.

In this work we consider the Kitaev Toric Code with specific open boundary conditions. Such a physical system has a highly degenerate ground state determined by the degrees of freedom localised at the boundaries. We can write down an explicit expression for the ground state of this model. Based on this, the entanglement properties of the model are studied for two types of bipartition: one, where the subsystem A is completely contained in B; and the second, where the boundary of the system is shared between A and B. In the former configuration, the entanglement entropy is the same as for the periodic boundary condition case, which means that the bulk is completely decoupled from the boundary on distances larger than the correlation length. In the latter, deviations from the torus configuration appear due to the edge states and lead to an increase of the entropy. We then determine an effective theory for the boundary of the system. In the case where we apply a small magnetic field as a perturbation the degrees of freedom on the boundary acquire a dispersion relation. The system can there be described by a Hamiltonian of the Ising type with a generic spin-exchange term.