Coherent State Wavefunction for Spin-Dependent Correlations

Stefano Fantoni, John W. Lawson, S. A. Vitiello +1 more

Mohammad Ali Vesaghi, Mohsen Babamoradi, Mehdi Heidari Saani

Many electron calculations on a simplest realistic two electron system i.e. H2molecule was applied and as the consequence correlation effects was reflected accurately in the wavefunctions of H2. Zanardi’s entanglement measurement, demonstrated that the maximum of entanglement for the ground state happens when U =J and this resolved the controversial conclusion of U = 0 for maximum entanglement. It was shown that the ground and third excited states are maximally entangled. These maximally entangled states and also the minimally entangled states are correlated to their spin’s property. The wavefunctions of the not magnetic (S = 0) ground and excited states explicitly depend on correlation parameters whereas the first excited states which is magnetic (S2 = 2 and Sz≠0) is not entangled. The second excited state is not magnetic but its wavefunction does not depend on correlation parameters therefore it is a moderately entangled state. In any case, by switching on a magnetic field an entangled state with Sz = 0 can be extracted from a not entangled degenerate magnetic state. We suggest that in a realistic molecular scale system, there is two criteria for finding maximally entangled electronic states, first the system should be in moderately correlated regime and second the system should have a non-magnetic (Sz = 0) electronic state.

Mostafa Mansour, Zakaria Dahbi, M. Essakhi +1 more

John W. Lawson, S. A. Vitiello, Kevin E. Schmidt +1 more

We propose a variational wave function which uses coherent states to represent the spin state of particles, and describes systems with spin-dependent correlations. Spin states are parametrized by a continuous variable that looks like a classical spin vector. Correlation operators are represented as simple integrals, without commutator terms, which can be evaluated using standard or Monte Carlo techniques. Explicit calculations on liquid ${}^{3}$He using our wave function give good agreement with standard methods. Applications to systems in condensed matter and nuclear physics are discussed.

Diego Barberena, Nigel Cooper

The localization transition of the sub-Ohmic spin-boson model generates boson bath correlations that are, at low frequencies, analytically inaccessible to standard coherent-state-polaron variational ansatzes. In this paper, we introduce a ``squeezed polaron'' wavefunction incorporating generic Gaussian boson-boson correlations induced by the spin impurity. This gives the correct critical power-law scaling of bath observables near the localization transition together with a systematically improved ground state energy and a more accurate determination of the critical coupling. Our wavefunction captures the correct mean-field nature of the transition in the deep sub-Ohmic region. It also displays non-mean-field critical exponents in the shallow sub-Ohmic regime. Using the squeezed polaron as a starting point, we derive scattering phase shifts for bosons, and show how they encode the emergent energy scale that vanishes at the localization transition.

Frank W. Bobrowicz