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arXiv:1905.05838 · Physical review. B./Physical review. B

Magnetic phase diagram of the infinite- U Hubbard model with nearest- and next-nearest-neighbor hoppings

G. G. Blesio, M. G. Gonzalez, Franco T. Lisandrini

Published May 14, 2019• 7 citations
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Abstract

We study the infinite-$U$ Hubbard model on ladders of two, four, and six legs with nearest- $(t)$ 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 ${t}^{\ensuremath{'}}$.

DOI
10.1103/physrevb.99.174411

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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′)({t}^{\ensuremath{'}})(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′{t}^{\ensuremath{'}}t\ensuremath′ when we vary the electron density \ensuremathρ\ensuremath{\rho}\ensuremathρ 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|{t}^{\ensuremath{'}}/t|=0.5∣t\ensuremath′/t∣=0.5. Surprisingly, for this value of t\ensuremath′{t}^{\ensuremath{'}}t\ensuremath′, the ground state is fully spin polarized for almost any electron density 1\ensuremath≳\ensuremathρ\ensuremath≳01\ensuremath{\gtrsim}\ensuremath{\rho}\ensuremath{\gtrsim}01\ensuremath≳\ensuremathρ\ensuremath≳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{t}^{\ensuremath{'}}=0t\ensuremath′=0 and \ensuremathρ=0.75\ensuremath{\rho}=0.75\ensuremathρ=0.75 is unstable against t\ensuremath′{t}^{\ensuremath{'}}t\ensuremath′.
We apply the density matrix renormalization group to study the phase diagram of the infinite U Hubbard model on 2- to 6-leg ladders. Where the results are largely insensitive to the ladder width, we consider the results representative of the 2D square lattice. We find a fully polarized ferromagnetic Fermi liquid phase when n, the density of electrons per site, is in the range 1>n≳0.800. For n=3/4 we find an unexpected insulating checkerboard phase with coexisting bond-density order with 4 sites per unit cell and block-spin antiferromagnetic order with 8 sites per unit cell. For 3/4>n, all ladders with width >2 have unpolarized ground states.
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.
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 magnetic properties of the two-dimensional Hubbard model with nearest-neighbor (t) and next-nearest-neighbor (t2{t}_{2}t2​) hopping and on-site repulsion U. We first calculate the mean-field phase diagram as a function of band filling and U. Because of the Van Hove singularity in the density of states, we find a ferromagnetic phase extending to zero U for certain band filling. For the half-filled band case, antiferromagnetism sets in at a finite value of U if t2{t}_{2}t2​\ensuremath{\ne}0. We study the behavior of spin-spin correlation functions for small lattices of up to N=64 atoms using Monte Carlo simulations, as well as exact diagonalization for N=4. Our results show enhanced ferromagnetic correlations in some regions, but apparently no ferromagnetic long-range order. In the half-filled case, our numerical results are consistent with a nonzero critical U. For a non-half-filled band our results suggest that there is no long-range order.
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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.