Variational reduced density matrix method in the doubly-occupied configuration interaction space using four-particle N-representability conditions: Application to the XXZ model of quantum magnetism.

This work deals with the variational determination of the two-particle reduced density matrix (2-RDM) and the energy corresponding to the ground state of N-particle systems within the doubly occupied configuration interaction (DOCI) space. Here, we impose for the first time up to four-particle N-representability constraint conditions in the variational determination of the 2-RDM matrix elements using the standard semidefinite programming algorithms. The energies and 2-RDMs obtained from this treatment and the corresponding computational costs are compared with those arisen from previously reported less restrictive variational methods [D. R. Alcoba et al., J. Chem. Phys. 149, 194105 (2018)] as well as with the exact DOCI values. We apply the different approximations to the one-dimensional XXZ model of quantum magnetism, which has a rich phase diagram with one critical phase and constitutes a stringent test for the method. The numerical results show the usefulness of our treatment to achieve a high degree of accuracy.

Benchmarking the Variational Reduced Density Matrix Theory in the Doubly Occupied Configuration Interaction Space with Integrable Pairing Models.

The variational reduced density matrix theory has been recently applied with great success to models within the truncated doubly occupied configuration interaction space, which corresponds to the seniority zero subspace. Conservation of the seniority quantum number restricts the Hamiltonians to be based on the SU(2) algebra. Among them there is a whole family of exactly solvable Richardson-Gaudin pairing Hamiltonians. We benchmark the variational theory against two different exactly solvable models, the Richardson-Gaudin-Kitaev and the reduced BCS Hamiltonians. We obtain exact numerical results for the so-called [Formula: see text] N-representability conditions in both cases for systems that go from 10 to 100 particles. However, when random single-particle energies as appropriate for small superconducting grains are considered, the exactness is lost but still a high accuracy is obtained.

[Using Karnofsky's scale to measure the quality of life]. / Indice de Karnofsky para medir la calidad de vida.

Karnofsky's scale is one of the indexes most frequently used to measure cancer patients' quality of life. The main problem encountered when trying to verify it is the degree of subjectivity inherent in it. Due to this, an attempt was made to create a more objective measuring instrument based on Karnofsky's scale. To this end, a retrospective study involving 300 outpatients was carried out. For these patients, their Karnofsky index was determined by two independent agents: the patient's oncologist and the nursing team which complied its measure based on a survey answered by the patient himself/herself. The differences between these two methods proved to be statistically insignificant.