4. The Ground States of One and Two Dimensional Quantum Spin Systems with Spin Polarons

邦夫 石田

M W Long, R. Fehrenbacher

For a quasi-one dimensional sawtooth topology the authors show that the quantum mechanical ground state of the Heisenberg Hamiltonian has only nearest neighbour singlet correlations. The ground state is multiply degenerate with precisely as many ground states as atoms in the system. In fact they can associate each ground state with a special site that has a fixed spin. Allowing this special site to become a hole, in a frustrated t-J description, allows them to deduce the ground state for the motion of one hole in the presence of the Heisenberg interactions. When the hopping is unfrustrated they look at the competition between t and J and find a reasonable description for a 'polaron'. The polaron maintains low spin.

А. А. Овчинников, V. Ya. Krivnov, Д. В. Дмитриев

Yue-Ran Shi, Ruijin Liu, Wei Zhang

We investigate the Fermi-polaron system with one mobile impurity immersed atop a two-component interacting fermion bath in one- and two-dimensional square lattices, where the impurity atom interacts with only one species (the spin-up component) of the background. The ground state with a given total momentum can be approximated by an extended Gaussian state, which is constructed from the combination of Gaussian states and a non-Gaussian polaronic transformation (Lee-Low-Pines transformation). In the few-body limit, the variational energies of two- and three-body systems show good agreement with exact results, which indicates the validity of the non-Gaussian variational method. We then move on to the many-body limit, i.e., the polaron problem with an interacting background. We choose two representative fillings of the background fermions, $\ensuremath{\rho}=1/4,1/2$, and obtain the corresponding ground states. Our results show that the system will undergo a smooth crossover from a Fermi-polaron to a Bose-polaron system as the interaction between background fermions increases. We further analyze the double occupancy and momentum distribution of the background fermions and find that the impurity will not significantly affect the background pairing.

Ola Bratteli, Akitaka Kishimoto, Derek W. Robinson

Pang Xiao‐feng

The influences of the squeezing–antisqueezing effect arising from variations of the electron density and motion of polarons and nonadiabatic phonon fluctuations on the properties of the ground state and the binding energy of the polaron in the Holstein model of coupled one-dimensional electron–phonon systems with spin 1/2 in the cases of high and low electron densities have been studied by using the Bogolyubov transformation and a new ansatz for states that includes correlation effects among the one-phonon coherent and two-phonon squeezed and polaronic states. The results obtained show that the squeezing–antisqueezing (correlation) effect results in that the ground state energy of the systems is significantly lowered, and the binding energy of the polaron is considerably increased. Thus, the stability of the systems and of the polaron are obviously enhanced in such a case when compared with the uncorrelated case. This shows that the ground state determined by the new state ansatz is most stable, and the new ansatz introduced here is very relevant for the coupled electron–phonon systems, especially in strongly coupled and largely squeezed cases.