Starting with the known exact solution of the one-dimensional supersymmetric t-J model, the authors investigate ground-state properties of the system in the presence of an external magnetic field. By analytical calculations they find a representation of the magnetization curves and the susceptibility using the dressed charge matrix and the charge and spin densities: the dressed properties are given by a set of coupled integral equations which are derived from the Bethe ansatz equations in the thermodynamic limit. Some special results are found analytically, namely the magnetic field at which saturation occurs and the corresponding susceptibility. Furthermore they show the vanishing of the lower critical field. The dependence of magnetization and susceptibility on the magnetic field is calculated numerically for various particle densities.
We study the integrable SU( M ) and SU q ( M ) quantum spin chains in the high-magnetic-field region at zero temperature. For M =4 we found second-order phase transitions at two different fields, H 1 and H 2 . At both transition points, the magnetization curve versus magnetic field has cusps with discontinuities in the magnetic susceptibility. We clarify the mechanism of the phase transitions, from which we conclude that the SU( M ) and S U q ( M ) quantum spin chains undergo ( M -2) times field-induced phase transitions at zero temperature.
The density matrix renormalization group and quantum Monte Carlo methods are used to describe coupled trimer chains in a magnetic field
h. The Hamiltonian contains exchange terms involving the intratrimer coupling
J1 (taken as the unit of energy) and the intertrimer coupling
J2, plus the Zeeman interaction for a magnetic field
h along the
z direction. Results for the magnetization per trimer
m are calculated in regimes of positive and negative values of the ratio
J=J2/J1, from which the rich field-induced ground state phase diagram
h versus
J is derived, with the presence of a Luttinger liquid, the 1/3 plateau (
m=1/2), and the one of fully polarized magnetization (
m=3/2). Also, zero-field Lanczos calculation of the spin-wave dispersion from the 1/3 plateau for
Sz=1 is shown at the previous regimes of
J values. In addition, we also report on the decay of correlation functions of trimers along open chains, as well as the average two-magnon distribution. The ground state is ferrimagnetic for $0<J\ensuremath{\le}1$, and is a singlet for $\ensuremath{-}1\ensuremath{\le}J<0$. In the singlet phase, the spin correlation functions along the legs present an antiferromagnetic power-law decay, similar to the spin-1/2 linear chain, thus suggesting that the ground state is made of three coupled antiferromagnetically oriented chains. In the singlet phase, the dimensionless thermal magnetic susceptibility per site normalized by
1/∣J∣ gets closer to $1/{\ensuremath{\pi}}^{2}$ as the temperature $T\ensuremath{\rightarrow}0$. For the ferrimagnetic phase, we fit the susceptibility to the experimental data for the compound
Pb3Cu3(PO4)4 and estimate the model exchange couplings:
J1=74.8K and
J=0.4. These values imply a range of energies for the magnon excitations that are in accord with the data from neutron scattering experiments on
Pb3Cu3(PO4)4 for two excitation modes. The 1/3 plateau closes only at
1/∣J∣=0 with
J<0.
The exact phase diagrams of the one-dimensional Hubbard model, both attractive and repulsive, in the presence of an arbitrary magnetic field h for various electron concentrations n and on-site interaction strengths U <0 or U >0 are calculated and investigated. The exact ground-state properties, namely, the ground-state energy, the average spin (magnetization), the concentration of the doubly occupied sites, the kinetic energy, the chemical potential, the spin (magnetic) susceptibility and the charge compressibility, are calculated and examined over a wide range of interaction strengths U for various h and n . It is found that the spin susceptibility at half-filling is non-analytic and changes discontinuously as U →0. The exact theory shows the absence of a charge energy gap in the U ⩽0 region for all n and provides, for the chemical potential, the rigorous upper and lower bounds for half-filled and empty bands respectively. The analytical results derived for the weak-coupling limit and asymptotic expansions for strong coupling are in full agreement with the numerical calculations.
It has been shown that there exists an additional magnetic phase transition of the magnetization curve for the S=1 SU(3) antiferromagnetic spin chain at zero temperature. As a the magnetic field decreases from the saturation field, there is a phase change at a critical field h c , where the magnetization curve versus the magnetic field has a cusp. The critical field is a boundary between two states, one of which contains the particles with the spin +1 and 0 and the other with the spin +1, 0 and -1. In this paper we estimate the critical field h c of the phase transition by examining the stability of these states.
The exact phase diagram and the ground-state properties of the one-dimensional Hubbard model with arbitrary on-site interaction of electrons are calculated over a wide range of magnetic field and electron concentrations by means of the Bethe-ansatz formalism. The ground-state properties, including the total energy, the average spin (magnetization) and spin (magnetic) susceptibility are investigated for both signs of the interaction strength U/t. The critical behavior near the onset of magnetization and magnetic saturation are also analyzed. At the onset of magnetization and near the magnetic saturation the spin susceptibility χ diverges at all U/t for half-filling case n=1, whereas for n≠1 it is always finite. The reverse susceptibility χ-1(U) exhibits anomalous hump, which increases with h or n, and shows discontinuity as U/t→±0 at infinitesimal h→0. The analytical results for the ground-state properties in strong and weak interaction limits are in full agreement with our numerical calculations.