We study the phase diagram of one-dimensional quantum ferrimagnets by using a numerical exact diagonalization of a finite size system along with a field-theoretical nonlinear $\ensuremath{\sigma}$ model of the quantum ferrimagnets at zero temperature and its effective description in the presence of the external magnetic field in terms of the quantum $\mathrm{XY}$ model. The low- and high-field phases correspond, respectively, to the classical N\'eel and the fully polarized ferromagnetic states where in the intermediate magnetic field ${(h}_{c1}<h<{h}_{c2}),$ it is an $XXZ+h$ model with easy plane anisotropy, which possess the spiral (superfluid) states that carry the dissipationless spin supercurrent. We derive the critical exponents, and then will study the stability of the $\mathrm{XY}$ spiral state against these spin-supercurrents and the hard axis fluctuations. We will show a first order phase transition from the easy plane spiral state to a saturated ferromagnetic state occurs at ${h=h}_{c2}$ if the spin supercurrent reaches its critical value.We study the phase diagram of one-dimensional quantum ferrimagnets by using a numerical exact diagonalization of a finite size system along with a field-theoretical nonlinear $\ensuremath{\sigma}$ model of the quantum ferrimagnets at zero temperature and its effective description in the presence of the external magnetic field in terms of the quantum $\mathrm{XY}$ model. The low- and high-field phases correspond, respectively, to the classical N\'eel and the fully polarized ferromagnetic states where in the intermediate magnetic field ${(h}_{c1}<h<{h}_{c2}),$ it is an $XXZ+h$ model with easy plane anisotropy, which possess the spiral (superfluid) states that carry the dissipationless spin supercurrent. We derive the critical exponents, and then will study the stability of the $\mathrm{XY}$ spiral state against these spin-supercurrents and the hard axis fluctuations. We will show a first order phase transition from the easy plane spiral state to a saturated ferromagnetic state occurs at ${h=h}_{c2}$ if the spin supercurrent reaches its critical value.

arXiv:cond-mat/0101194Physical review. B, Condensed matterMar 19, 20017 citations

Ferromagnetism in the Hubbard model

Andreas Mielke, Hal Tasaki

Communications in Mathematical PhysicsNov 1, 1993369 citations

Lieb and hole-doped ferrimagnetism, spiral, resonating valence-bond states, and phase separation in large-U $AB_{2}$ Hubbard chainsLieb and hole-doped ferrimagnetism, spiral, resonating valence-bond states, and phase separation in large-U $AB_{2}$ Hubbard chains

V. M. Martinez Alvarez, Mauricio D. Coutinho-Filho

The ground state (GS) properties of the quasi-one-dimensional $AB_2$ Hubbard model are investigated taking the effects of charge and spin quantum fluctuations on equal footing. In the strong-coupling regime, we derive a low-energy Lagrangian suitable to describe the ferrimagnetic phase at half filling and the phases in the hole-doped regime. At half filling, a perturbative spin-wave analysis allows us to find the GS energy, sublattice magnetizations, and Lieb total spin per unit cell of the effective quantum Heisenberg model, in very good agreement with previous results. In the challenging hole doping regime away from half filling, we derive the corresponding $t\textrm{-}J$ Hamiltonian. Under the assumption that charge and spin quantum correlations are decoupled, the evolution of the second-order spin-wave modes in the doped regime unveils the occurrence of spatially modulated spin structures and the emergence of phase separation in the presence of resonating-valence-bond states. We also calculate the doping-dependent GS energy and total spin per unit cell, in which case it is shown that the spiral ferrimagnetic order collapses at a critical hole concentration. Notably, our analytical results in the doped regime are in very good agreement with density matrix renormalization group studies, where our assumption of spin-charge decoupling is numerically supported by the formation of charge-density waves in anti-phase with the modulation of the magnetic structure.The ground state (GS) properties of the quasi-one-dimensional $AB_2$ Hubbard model are investigated taking the effects of charge and spin quantum fluctuations on equal footing. In the strong-coupling regime, we derive a low-energy Lagrangian suitable to describe the ferrimagnetic phase at half filling and the phases in the hole-doped regime. At half filling, a perturbative spin-wave analysis allows us to find the GS energy, sublattice magnetizations, and Lieb total spin per unit cell of the effective quantum Heisenberg model, in very good agreement with previous results. In the challenging hole doping regime away from half filling, we derive the corresponding $t\textrm{-}J$ Hamiltonian. Under the assumption that charge and spin quantum correlations are decoupled, the evolution of the second-order spin-wave modes in the doped regime unveils the occurrence of spatially modulated spin structures and the emergence of phase separation in the presence of resonating-valence-bond states. We also calculate the doping-dependent GS energy and total spin per unit cell, in which case it is shown that the spiral ferrimagnetic order collapses at a critical hole concentration. Notably, our analytical results in the doped regime are in very good agreement with density matrix renormalization group studies, where our assumption of spin-charge decoupling is numerically supported by the formation of charge-density waves in anti-phase with the modulation of the magnetic structure.

arXiv:1702.03609Feb 13, 20170 citations

\mathrm{XY}

model. The low- and high-field phases correspond, respectively, to the classical N\'eel and the fully polarized ferromagnetic states where in the intermediate magnetic field

{(h}_{c1}<h<{h}_{c2}),

it is an

XXZ+h

model with easy plane anisotropy, which possess the spiral (superfluid) states that carry the dissipationless spin supercurrent. We derive the critical exponents, and then will study the stability of the

\mathrm{XY}

spiral state against these spin-supercurrents and the hard axis fluctuations. We will show a first order phase transition from the easy plane spiral state to a saturated ferromagnetic state occurs at

{h=h}_{c2}

if the spin supercurrent reaches its critical value.

Lieb and hole-doped ferrimagnetism, spiral, resonating valence-bond states, and phase separation in large-U

AB_{2}

Hubbard chains

The ground state (GS) properties of the quasi-one-dimensional

AB_2

Hubbard model are investigated taking the effects of charge and spin quantum fluctuations on equal footing. In the strong-coupling regime, we derive a low-energy Lagrangian suitable to describe the ferrimagnetic phase at half filling and the phases in the hole-doped regime. At half filling, a perturbative spin-wave analysis allows us to find the GS energy, sublattice magnetizations, and Lieb total spin per unit cell of the effective quantum Heisenberg model, in very good agreement with previous results. In the challenging hole doping regime away from half filling, we derive the corresponding

t\textrm{-}J

Hamiltonian. Under the assumption that charge and spin quantum correlations are decoupled, the evolution of the second-order spin-wave modes in the doped regime unveils the occurrence of spatially modulated spin structures and the emergence of phase separation in the presence of resonating-valence-bond states. We also calculate the doping-dependent GS energy and total spin per unit cell, in which case it is shown that the spiral ferrimagnetic order collapses at a critical hole concentration. Notably, our analytical results in the doped regime are in very good agreement with density matrix renormalization group studies, where our assumption of spin-charge decoupling is numerically supported by the formation of charge-density waves in anti-phase with the modulation of the magnetic structure.