We compute the entropy of entanglement in the ground states of a general class of quantum spin-chain Hamiltonians — those that are related to quadratic forms of Fermi operators — between the first N spins and the rest of the system in the limit of infinite total chain length. We show that the entropy can be expressed in terms of averages over the classical compact groups and establish an explic...

let $n,t_1,...,t_k$ be distinct positive integers. a toeplitz graph $g=(v, e)$ denoted by $t_n$ is a graph, where $v ={1,...,n}$ and $e= {(i,j) : |i-j| in {t_1,...,t_k}}$.in this paper, we present some results on decomposition of toeplitz graphs.

By using asymptotics of Toeplitz+Hankel determinants, we establish formulae for the moments characteristic polynomials random orthogonal and symplectic matrices, as matrix size tends to infinity. Our results are analogous those that Fahs obtained unitary matrices in (Fahs B. 2021 Communications Mathematical Physics 383 , 685–730. (doi: 10.1007/s00220-021-03943-0 )). A key feature derive is phas...

In this paper we show a new inequality that generalizes to the unit sphere Lebedev-Milin of exponentiation functions on circle. It may also be regarded as counterpart second in Szegö limit theorem Toeplitz determinants On other hand, is variant several classical inequalities Moser-Trudinger type sphere. The incorporates deviation center mass from origin into optimal Aubin for with centered at o...