Narrow Results

Four point correlation functions for many electrons at finite temperature in periodic lattice of dimension d (≥1) are analyzed by the perturbation theory with respect to the coupling constant. The correlation functions are characterized as a limit of finite dimensional Grassmann integrals. A lower bound on the radius of convergence and an upper bound on the perturbation series are obtained by evaluating the Taylor expansion of logarithm of the finite dimensional Grassmann Gaussian integrals. The perturbation series up to second-order is numerically implemented along with the volume-independent upper bounds on the sum of the higher order terms in the 2-dimensional case.

Using Hodge diagram combinatorial data, we study qubit and fermionic Fock spaces from the point of view of type II superstring black holes based on complex compactifications. Concretely, we establish a one-to-one correspondence between qubits, fermionic spaces and extremal black holes in maximally supersymmetric supergravity obtained from type II superstring on complex toroidal and Calabi–Yau compactifications. We interpret the differential forms of the $n$-dimensional complex toroidal compactification as states of $n$-qubits encoding information on extremal black hole charges. We show that there are $2^n$ copies of $n$ qubit systems which can be split as $2^n=2^{n-1}+2^{n-1}$. More precisely, $2^{n-1}$ copies are associated with even $D$-brane charges in type IIA superstring and the other $2^{n-1}$ ones correspond to odd $D$-brane charges in IIB superstring. This correspondence is generalized to a class of Calabi–Yau manifolds. In connection with black hole charges in type IIA superstring, an $n$-qubit system has been obtained from a canonical line bundle of $n$ factors of one-dimensional projective space ${ℂ\mathbb{P}}^1.$