Spin Observables by Density Matrix

Ravinder Rupchand Puri

A quantum system is described by a density matrix which determines the joint probabilities for simultaneous eigenstates of its observables. Since there do not exist any simultaneous eigenstates of non-commuting observables, the density matrix cannot provide any information about the joint probability of their eigenstates. The quasiprobability distributions (QPDs) constructed by using the density matrix provide a means of determining these joint probabilities. Here the QPDs for a system of N spin-1/2 are constructed and the joint probabilities for their components determined.

Alan McLachlan

Elliot Leader

Jun Sato, Masahiro Shiroishi

We have analytically obtained all the density matrix elements up to six lattice sites for the spin-1/2 Heisenberg XXZ chain at Δ = 1/2. We use the multiple integral formula of the correlation function for the massless XXZ chain derived by Jimbo and Miwa. As for the spin–spin correlation functions, we have newly obtained the fourth- and fifth-neighbour transverse correlation functions. We have calculated all the eigenvalues of the density matrix and analyse the eigenvalue distribution. Using these results the exact values of the entanglement entropy for the reduced density matrix up to six lattice sites have been obtained. We observe that our exact results agree quite well with the asymptotic formula predicted by the conformal field theory.

A. K. Opper

Paweł Caban, Jakub Rembieliński

We show that it is possible to define a Lorentz-covariant reduced spin density matrix for massive particles. Such a matrix allows one to calculate the mean values of observables connected with spin measurements (average polarizations). Moreover, it contains not only information about polarization of the particle but also information about its average kinematical state. We also use our formalism to calculate the correlation function in the Einstein-Podolsky-Rosen--Bohm type experiment with massive relativistic particles.