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Acta Physica Polonica A

Ground-State Spin of Hubbard Ladder Model with Infinite Electron Repulsion

Vladyslav O. Cheranovskii, E. V. Ezerskaya, Douglas J. Klein, V. V. Tokarev

Published Apr 1, 2017• 0 citations
Publisher

Abstract

We apply perturbation theory and cyclic spin permutation formalism to study the lowest energy states of the infinite-repulsion Hubbard model on n-leg ladders with alternating values of one-site energies αi for neighboring rungs.We establish the "ferromagnetic" character of ladder ground-state at electron densities in the interval 1 -(2n) -1 ≤ ρ ≤ 1 and sufficiently large alternation of one-site energies of neighbor rungs of the ladder.We also show the stability of this state against the small deviations of the values of αi in contrast to the case of two-leg ladder formed by weakly interacting neighbor rungs with equal one-site energies.

DOI
10.12693/aphyspola.131.916

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We apply perturbation theory and cyclic spin permutation formalism to study the lowest energy states of the infinite-repulsion Hubbard model on n-leg ladders with alternating values of one-site energies αi for neighboring rungs.We establish the "ferromagnetic" character of ladder ground-state at electron densities in the interval 1 -(2n) -1 ≤ ρ ≤ 1 and sufficiently large alternation of one-site energies of neighbor rungs of the ladder.We also show the stability of this state against the small deviations of the values of αi in contrast to the case of two-leg ladder formed by weakly interacting neighbor rungs with equal one-site energies.
We investigate the ground-state magnetic properties of the Hubbard model on a two-leg ladder with interchain Coulomb repulsion. When both the on-site and the interchain Coulomb repulsions are infinitely large, we show exactly that the model exhibits saturated ferromagnetism in the ground states for the electron filling factor 1/4<n<1/2.1/4<n<1/2.1/4<n<1/2. The explicit expression of the saturated ferromagnetic ground state is also obtained. By using numerical calculations, we find that ferromagnetism remains stable for sufficiently large values of these interactions, and that the interchain Coulomb repulsion induces tendencies to ferromagnetism, especially on the 1/4-filling side for small values of the interchain hopping parameter.
Low-energy states of the Hubbard model with infinite electron repulsion on an anisotropic triangular strip-type lattice formed by weakly interacting linear segments are studied. The estimates of the stability region boundaries for the ferromagnetic ground state of the lattice are obtained in first order perturbation theory in the interaction between the segments. It is shown that a magnetic transition accompanied by a jumpwise variation of the total spin of the ground state from the minimum to the maximum value is possible for lattices with cyclic boundary conditions and the number of electrons greater than the number of segments by unity.
The ground-state phase diagram of a Heisenberg $\text{spin}\ensuremath{-}\frac{1}{2}$ system on a two-leg ladder with rung alternation is studied by combining analytical approaches with numerical simulations. For the case of ferromagnetic leg exchanges a unique ferrimagnetic ground state emerges, whereas for the case of antiferromagnetic leg exchanges several different ground states are stabilized depending on the ratio between exchanges along legs and rungs. For the more general case of a honeycomb-ladder model for the case of ferromagnetic leg exchanges besides the usual rung-singlet and saturated ferromagnetic states we obtain a ferrimagnetic Luttinger liquid phase with both linear and quadratic low-energy dispersions and ground-state magnetization continuously changing with system parameters. For the case of antiferromagnetic exchanges along legs, different dimerized states including states with additional topological order are suggested to be realized.
We study the infinite-UUU Hubbard model on ladders of two, four, and six legs with nearest- (t)(t)(t) and next-nearest- $({t}^{\ensuremath{'}})$ neighbor hoppings by means of the density-matrix renormalization group algorithm. In particular, we analyze the stability of the Nagaoka state for several values of ${t}^{\ensuremath{'}}$ when we vary the electron density $\ensuremath{\rho}$ from half filling to the low-density limit. We build the two-dimensional phase diagram, where the fully spin polarized and paramagnetic states prevail. We find that the inclusion of a nonfrustrating next-nearest-neighbor hopping stabilizes the fully spin polarized phase up until $|{t}^{\ensuremath{'}}/t|=0.5$. Surprisingly, for this value of ${t}^{\ensuremath{'}}$, the ground state is fully spin polarized for almost any electron density $1\ensuremath{\gtrsim}\ensuremath{\rho}\ensuremath{\gtrsim}0$, connecting the Nagaoka state to itinerant ferromagnetism at low density. Also, we find that the previously found checkerboard insulator phase at ${t}^{\ensuremath{'}}=0$ and $\ensuremath{\rho}=0.75$ is unstable against ${t}^{\ensuremath{'}}$.
The estimations of the stability region of the lattice ferromagnetic ground state in the space of model parameters are found. For the triangular lattice strip formed by L segments with the total number of electrons N=L+1 we derived the effective Hamiltonians describing the low-energy states of the strips and obtained the analytical estimations for above stability region. The possibility of the magnetic transition with the jump of the ground-state spin between minimal and maximal values has also been shown. For the strip with N=L and an alternating value of the one-site potential energy, we have obtained the exact relation between electron parameters, which provides the ferromagnetic character of the lattice ground state. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 253–259, 2001
We investigate the Hubbard Hamiltonian on ladders where the number of sites per rung alternates between two and three. These geometries are bipartite with non-equal or equal number of sites on the two sublattices. Thus they share a key feature of the Hubbard model in a class of lattices which Lieb has shown analytically to exhibit long-range ferrimagnetic order, while being amenable to powerful numeric approaches developed for quasi-one-dimensional geometries. The Density Matrix Renormalization Group (DMRG) method is used to obtain the ground state properties, e.g. excitation gaps, charge and spin densities as well as their correlation functions at half-filling. We show the existence of long-range ferrimagnetic order in the one-dimensional ladder geometries. Our work provides detailed quantitative results which complement the general theorem of Lieb for generalized bipartite lattices. It also addresses the issue of how the alternation between quasi-long range order and spin liquid behavior for uniform ladders with odd and even numbers of legs might be affected by a regular alternation pattern.