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.
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.
We investigate the Hubbard Hamiltonian on ladders where the number of sites per rung alternates between two and three. These geometries are bipartite with nonequal 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 groundstate 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.
The effect of antiferromagnetic interchain coupling in alternating spin-(1,1/2) chains is studied by means of spin-wave theory and density-matrix renormalization group (DMRG). In particular, two limiting cases are investigated, the two-leg ladder and its two-dimensional (2D) generalization. Results of the ground-state properties like energy, spin gap, magnetizations, and correlation functions are reported for the whole range of the interchain coupling ${J}_{\ensuremath{\perp}}.$ For the 2D case the spin-wave results predict a smooth dimensional crossover from 1D to 2D keeping the ground state always ordered. For the ladder system, the DMRG results show that any ${J}_{\ensuremath{\perp}}>0$ drives the system to a gapped ground state. Furthermore the behavior of the correlation functions closely resemble the uniform spin-1/2 ladder. For ${J}_{\ensuremath{\perp}}$ lower than 0.3, however, the gap behaves quadratically as $\ensuremath{\Delta}\ensuremath{\sim}{0.6J}_{\ensuremath{\perp}}^{2}.$ Finally, it is argued that the behavior of the spin gap for an arbitrary number of mixed coupled spin chains is analogous to that of the uniform spin-1/2 chains.
Motivated by recent experiments on ultracold fermionic spin-1/2 6Li atoms in a Lieb lattice at various Hubbard repulsion U and filling fractions n (Lebrat et al., arXiv:2404.17555), we conduct a density matrix renormalization group (DMRG) analysis of the Hubbard model on a two-leg Lieb ladder. At half-filling, we find a ferrimagnetic Mott insulating ground state, consistent with Lieb's theorem. Away from half-filling, a state with finite total spin S2=0 and vanishing charge gap persists down to filling nc≈2/3. For lower, incommensurate fillings, the system is described by a Luttinger liquid with one charge and one spin mode. Intriguingly, in a narrow window near nc=2/3, close to the onset of ferromagnetic order, we identify a superconducting Luther-Emery phase with dominant sxy-wave pairing.
We investigate a ladder system with two inequivalent legs, namely, a Hubbard chain and a one-dimensional electron gas. Analytical approximations, the density-matrix renormalization group method, and continuous-time quantum Monte Carlo simulations are used to determine ground-state properties, gaps, and spectral functions of this system at half-filling. Evidence for the existence of four different phases as a function of the Hubbard interaction and the rung hopping is presented. First, a Luttinger liquid exists at very weak interchain hopping. Second, a Kondo-Mott insulator with spin and charge gaps induced by an effective rung exchange coupling is found at moderate interchain hopping or strong Hubbard interaction. Third, a spin-gapped paramagnetic Mott insulator with incommensurate excitations and pairing of doped charges is observed at intermediate values of the rung hopping and the interaction. Fourth, the usual correlated band insulator is recovered for large rung hopping. We show that the wave numbers of the lowest single-particle excitations are different in each insulating phase. In particular, the three gapped phases exhibit markedly different spectral functions. We discuss the relevance of asymmetric two-leg ladder systems as models for atomic wires deposited on a substrate.
The origin of metallic ferromagnetism is a long-standing problem in condensed matter physics, because it is a strong coupling phenomenon essentially. It was also known that one dimensional systems have a lesser chance of showing ferromagnetism in the ground states. In fact, for a class of one-dimensional correlated electron systems including the simple Hubbard chain, the ground state was proved to be nonmagnetic. Several authors have been studied whether ferromagnetism is stabilized or not by taking neglected terms in the simple Hubbard chain into account. It was shown that a positive next-nearest neighbor hopping leads to ferromagnetism for less-than-half filled systems in strong correlation regime on the basis of DMRG calculations. We call this model the railroad–trestle-lattice Hubbard model below. The railroad–trestle lattice is graphically shown in Fig. 1. In this article, we treat the problem of ferromagnetism of the nearly half-filled extended Hubbard ladder with an additional intersite repulsion V . The Hamiltonian is H 1⁄4 t P hi; ji; ðc y i cj þ c y j ci Þ þU P i nini# þV P hi; ji ninj, where ci represent electron creation operators, ni 1⁄4 P c y i ci , and hi; ji denotes nearest-neighbor pairs of the sites on the two-leg ladder. Vojta et al. made a DMRG study of this model in strong coupling region. Tsuchiizu and Suzumura recently studied this model by using the weakcoupling bosonization method, motivated by the experimental observation of a charge-density-wave in the selfdoped ladder compound Sr14 xCaxCu24O41. 7,8) We first mention the half-filled case, i.e., electron density n 1⁄4 1. When U < 3V , the ground state has the checkerboard-type charge-ordering shown in Fig. 2 due to the intersite repulsion. (The sublattice consisting of doubly occupied sites is defined as A-sublattice.) Our main concern is what happens when holes are doped into this chargeordered insulating state. By using the DMRG method, Vojta et al. calculated the checkerboard-type charge-ordering correlation function from quarter-filling to half-filling, 1=2 n 1, where U 1⁄4 8t was chosen. They confirmed that the long-range charge-order correlation is obtained for V VcðnÞ ’ U=3. They also found that the total spin of the doped charge-ordering state is not zero, i.e., the charge ordering coexists with ferromagnetism. However, the origin of this ferromagnetism was not clarified. The main purpose of this paper is to get intuitive understanding of the ferromagnetism in the doped charge-ordered state. In order to attack this issue, we assume t U, V and use strong coupling expansion. Then, we calculate the effective Hamiltonian for holes doped into the charge-ordered state at half-filling. When holes are introduced, they enter the A-sublattice sites [see Fig. 3(a)]. If we totally neglect the bare hopping term in H, then we have the ground state degeneracy concerned with the way of arrangement of doped holes. The introduction of the bare hopping term resolves this degeneracy and is expected to induce an ordering of the doped holes. In order to write down the second-order effective Hamiltonian with respect to t, it is convenient to carry out the particle–hole transformation for the A-sublattice according to c‘ 1⁄4 a‘ , where a y ‘ are the creation operators of the A-sublattice holes. Within the two-hole approximation, we obtain the following effective Hamiltonian:
In the present work the numerical density matrix renormalization group (DMRG) algorithm is used to analyze the ground state properties of the Hubbard model with transverse spin-exchange. The DMRG algorithm, which was developed by White in 1992, is based on the following simple but effective concept: the ground-state wavefunction as well as the low energy excitations of a large interacting chain are obtained by increasing the lattice size iteratively, starting with a small one that can be diagonalized exactly. The exponentially growing Hilbert space is controlled by a renormalization procedure in which 'less important' degrees of freedom are integrated out. Motivated by recent experimental findings showing evidence for the competition or even coexistence of triplet superconductivity and ferromagnetism we focused our investigations on a rather simple extension of the Hubbard model including transverse spin exchange between electrons on nearest-neighbour sites. In the half-filled case, we showed that the phase diagram obtained in the weak-coupling limit has to be modified. A new phase, described by spin and charge excitation gap, shows long-range order in the longitudinal spin correlation, whereas superconducting correlations are surpressed and decay exponentially as expected for the case of a finite charge gap. In general, the presence of a repulsive on-site Coulomb interaction U leads to an enlargement of the sectors with nonvanishing charge gap at the expense of the sectors with spin gap. We extend our analysis to the case of a quarter-filled band. Depending on the value J/t the model belongs either to a gapless excitation phase or to a spin gapped phase with gapless charge degrees of freedom.