An alternative analytic treatment of the Gutzwiller ansatz

Jay D. Mancini, Vassilios Fessatidis, Ivana Djuric +1 more

Haiming Deng, Hui Dai, Jiahao Huang +5 more

We present a cluster Gutzwiller mean-field study for ground states and time-evolution dynamics in the Bose-Hubbard ladder (BHL), which can be realized by loading Bose atoms in double-well optical lattices. In our cluster mean-field approach, we treat each double-well unit of two lattice sites as a coherent whole for composing the cluster Gutzwiller ansatz, which may remain some residual correlations in each two-site unit. For an unbiased BHL, in addition to conventional superfluid phase and integer Mott insulator phases, we find that there are exotic fractional insulator phases if the interchain tunneling is much stronger than the intrachain one. The fractional insulator phases cannot be found by using a conventional mean-field treatment based upon the single-site Gutzwiller ansatz. For a biased BHL, we find there appear single-atom tunneling and interaction blockade if the system is dominated by the interplay between the on-site interaction and the interchain bias. In the many-body Landau-Zener process, in which the interchain bias is linearly swept from negative to positive or vice versa, our numerical results are qualitatively consistent with the experimental observation [Nat. Phys. 7, 61 (2011)]. Our cluster bosonic Gutzwiller treatment is of promising perspectives in exploring exotic quantum phases and time-evolution dynamics of bosonic particles in superlattices.

P. Fazekas

We study the ground state of a Hamiltonian introduced by Kolb and Penson for modelling situations in which small electron pairs are formed. The Hamiltonian consists of a tight binding band term, and a term describing the nearest neighbour hopping of electron pairs. We give a Gutzwiller-type variational treatment, first with a single-parameter Ansatz treated in the single site Gutzwiller approximation, and then with more complicated trial wave functions, and an improved Gutzwiller approximation. The calculation yields a transition from a partially paired normal state, in which the spin susceptibility has a diminished value, into a fully paired state.

K. Noatschk, C. Martens, G. Seibold

Mohammad Mahdi Valizadeh, Jamshid Moradi Kurdestany, S. Satpathy

W. Brenig, E. Müller‐Hartmann

Abstract We discuss a variational ground state wave function for the symmetric periodic Anderson model with commensurate spin density order. The energy of this ansatz is evaluated in closed form. Our approach generalizes a variational treatment proposed recently by Strack and Vollhardt and results in significantly lower energy. Contrary to the Gutzwiller ansatz the wave function recovers the Schrieffer‐Wolff limit for large Coulomb repulsion. We clarify the relation of our approach to unrestricted Hartree‐Fock and present a comparison with existing quantum Monte Carlo calculations for one dimension.