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DMRG study of ferromagnetism in a one-dimensional Hubbard model

S. Daul, R. M. Noack

Published Jan 1, 2008• 17 citations
OpenAlex

Abstract

The one dimensional Hubbard model with nearest and (negative) next-nearest neighbour hopping has been studied with the densitymatrix renormalization group (DMRG) method. A large region of ferromagnetism has been found for finite density and finite on-site interaction. PACS: 74.25.Ha, 75.10.Lp 1

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We examined a one-dimensional Hubbard model with nearest- and next-nearest-neighbor hopping with up to 32 sites by means of the density-matrix renormalization-group method. The model has two energy bands and includes the flat-band model studied by Tasaki as a special case. The model with finite band dispersion is found to show metallic (saturated) ferromagnetism for a sufficiently strong interaction. No partially polarized ground state is found. The interaction necessary to realize a ferromagnetic ground state becomes weak when the electron density is decreased from the quarter-filling.
Ferromagnetism in the one-dimensional Hubbard model with the next-nearest-neighbor hopping is explored by using the exact-diagonalization method in a small cluster and the equation-of-motion method in the thermodynamic limit with electron density n = 3/2. With these two complementary methods, it is found that an intermediate value of the next-nearest-neighbor hopping amplitude t1 tends to stabilize the fully polarized ferromagnetic state under the condition that the on-site coulomb interaction U is sufficiently large in our model. The ground-state phase diagram of the model is presented in the t1—U plane.
We study the phase diagram of the one-dimensional Hubbard model with next-nearest-neighbor hopping using exact diagonalization, the density-matrix renormalization group, the Edwards variational ansatz, and an adaptation of weak-coupling calculations on the two-chain Hubbard model. We find that a substantial region of the strong-coupling phase diagram is ferromagnetic, and that three physically different limiting cases are connected in one ferromagnetic phase. At a point in the phase diagram at which there are two Fermi points at weak coupling, we study carefully the phase transition from the paramagnetic state to the fully polarized one as a function of the on-site Coulomb repulsion. We present evidence that the transition is second order and determine the critical exponents numerically. In this parameter regime, the system can be described as a Luttinger liquid at weak coupling. We extract the Luttinger-liquid parameters and show how their behavior differs from that of the nearest-neighbor Hubbard model. The general weak-coupling phase diagram can be mapped onto that of the two-chain Hubbard model. We exhibit explicitly the adapted phase diagram and determine its validity by numerically calculating spin and charge gaps using the density-matrix renormalization group.
The spin gap of a one-dimensional repulsive Hubbard model is numerically calculated with the density-matrix renormalization group, with a special emphasis on the effect of a next-nearest-neighbor hopping ${(t}^{\ensuremath{'}})$ and the nearest-neighbor ferromagnetic exchange (J)(J)(J) interaction. At half filling, a significant spin gap opens if $|{t}^{\ensuremath{'}}|\ensuremath{\simeq}|t|$ and J=0J=0J=0, in agreement with the weak-coupling theory, while the gap is strongly suppressed by the introduction of JJJ. On the other hand, the quarter-filled system has very small spin gaps regardless of the values of ${t}^{\ensuremath{'}}$ and JJJ. Implications for the CuO2{\mathrm{CuO}}_{2}CuO2​ chain in Sr14Cu24O41{\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}Sr14​Cu24​O41​ and related materials are discussed.
We study the one-dimensional Hubbard model with nearest-neighbor and next-nearest-neighbor hopping integrals by using the density-matrix renormalization group method and Hartree-Fock approximation. Based on the calculated results for the spin gap, total-spin quantum number, and Tomonaga-Luttinger-liquid parameter, we determine the ground-state phase diagram of the model in the entire filling and wide parameter region. We show that, in contrast to the weak-coupling regime where a spin-gapped liquid phase is predicted in the region with four Fermi points, the spin gap vanishes in a substantial region in the strong-coupling regime. It is remarkable that a large variety of phases, such as the paramagnetic metallic phase, spin-gapped liquid phase, singlet and triplet superconducting phases, and fully polarized ferromagnetic phase, appear in such a simple model in the strong-coupling regime.
We study the existence of ferromagnetism in one dimensional Hubbard Model with on site interaction and nearest and next nearest neighbor hopping. Using the Hubbard I approximation, a self consistent equation for $$, the particle density with spin $σ$ is obtained. We find that ferromagnetism exists over a wide range of values of the next nearest neighbor hopping element t' when on-site interaction U is large. The phase diagram as a function of t'/t and the electron density $$ has been obtained by numerically solving the self consistent equation. It is found that the maximum density at which ferromagnetism can occur, peaks around t′/t≈−0.53t'/t \approx -0.53t′/t≈−0.53. We show that this phenomenon is a result of the peculiar way in which the t' term modifies the density of states.