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arXiv:cond-mat/0101194 · Physical review. B, Condensed matter

Superfluid spiral state of quantum ferrimagnets in a magnetic field

Ramin Abolfath, A. Langari

Published Mar 19, 2001• 7 citations
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Abstract

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.

DOI
10.1103/physrevb.63.144414

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We investigate the phase diagram of an anisotropic ferrimagnetic spin-(1/2, 1) in the presence of a non-commuting (transverse) magnetic field. We find a magnetization plateau for the isotropic case while there is no plateau for the anisotropic ferrimagnet. The magnetization plateau can appear only when the Hamiltonian has the U (1) symmetry in the presence of the magnetic field. The anisotropic model is driven by the magnetic field from the Néel phase for low fields to the spin-flop phase for intermediate fields and then to the paramagnetic phase for high fields. We find the quantum critical points and their dependence on the anisotropy of the aforementioned field-induced quantum phase transitions. The spin-flop phase corresponds to the spontaneous breaking of Z 2 symmetry. We use the numerical density matrix renormalization group and analytic spin wave theory to find the phase diagram of the model. The energy gap, sublattice magnetization and total magnetization parallel and perpendicular to the magnetic field are also calculated. The elementary excitation spectra are obtained via the spin wave theory in the three different regimes depending on the strength of the magnetic field.
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We explore how the spiral spin (SP) state, a spin singlet known to accompany fully polarized ferromagnetic (F) states in the Hubbard model, is related with the F state in the thermodynamic limit using the density-matrix renormalization group and exact diagonalization. We first obtain an indication that when the F state is the ground state the SP state is also eligible as the ground state in that limit. We then follow the general argument by Koma and Tasaki [J. Stat. Phys. 76, 745 (1994)] to find that (i) the SP state possesses a kind of order parameter, and (ii) although the SP state does not break the SU(2) symmetry in finite systems, it does so in the thermodynamic limit by making a linear combination with other states that are degenerate in that limit. We also calculate the one-particle spectral function and dynamical spin and charge susceptibilities for various one-dimensional finite-size lattices. We find that the excitation spectra of the SP state and the F state are almost identical. The present results suggest that the SP and the F states are equivalent in the thermodynamic limit. These properties may be exploited to determine the magnetic phase diagram from finite-size studies.