Schwinger Bosons Approaches to Quantum Antiferromagnetism (original) (raw)
Quantum antiferromagnet at finite temperature: A gauge-field approach
Physical review. B, Condensed matter, 1994
Starting from the CP N−1 model description of the thermally disordered phase of the D = 2 quantum antiferromagnet, we examine the interaction of the Schwinger-boson spin-1/2 mean-field excitations with the generated gauge (chirality) fluctuations in the framework of the 1/N expansion. This interaction dramatically supresses the one-particle motion, but enhances the staggered static susceptibility. This means that actual excitations in the system are represented by the collective spin-1 excitations , whereas one-particle excitations disappear from the problem. We also show that massive fluctuations of the constraint field are significant for the susceptibility calculations. A connection with the problem of a particle in random magnetic field is discussed.
Schwinger-boson mean-field theory of the Heisenberg ferrimagnetic spin chain
Physical Review B, 1999
The Schwinger boson mean field theory is applied to the quantum ferrimagnetic Heisenberg chain. There is a ferrimagnetic long range order in the ground state. We observe two branches of the low lying excitation and calculate the spin reduction, the gap of the antiferromagnetic branch, and the spin fluctuation at T = 0K. These results agree with the established numerical results quite well. At finite temperatures, the long range order is destroyed because of the disappearance of the Bose condensation. The thermodynamic observables, such as the free energy, magnetic susceptibility, specific heat, and the spin correlation at T > 0K, are calculated. The T χ uni has a minimum at intermediate temperatures and the spin correlation length behaves as T -1 at low temperatures. These qualitatively agree with the numerical results and the difference is small at low temperatures.
Quantum Spin-1/2 Antiferromagnetic Chains and Strongly Coupled Multiflavor Schwinger Models
We review the correspondence between strongly coupled lattice multiflavor Schwinger models and SU (N ) antiferromagnetic chains. We show that finding the low lying states of the gauge models is equivalent to solving an SU (N ) Heisenberg antiferromagnetic chain. For the two-flavor lattice Schwinger model the massless excitations correspond to gapless states of the Heisenberg chain, while the massive states are created by fermion transport in the ground state of the spin chain. Our analysis shows explicitly how spinons may arise in lattice gauge theories. In this section the Bethe ansatz solution of the antiferromagnetic Heisenberg chain [18] is discussed in detail. Moreover we shall compare the exact solution given by L.D. Faddeev and L.A. Takhtadzhyan in with a study of finite size chains of 4, 6 and 8 sites. We show that already these very small finite systems exhibit spectra that match very well with the thermodynamic limit solution. We suggest to the reader interested in the subject the references .
Physical Review B, 2004
The nearest-neighbor quantum-antiferromagnetic (AF) Heisenberg model for spin 1/2 on a twodimensional square lattice is studied in the auxiliary-fermion representation. Expressing spin operators by canonical fermionic particles requires a constraint on the fermion charge Qi = 1 on each lattice site i , which is imposed approximately through the thermal average. The resulting interacting fermion system is first treated in mean-field theory (MFT), which yields an AF ordered ground state and spin waves in quantitative agreement with conventional spin-wave theory. At finite temperature a self-consistent approximation beyond mean field is required in order to fulfill the Mermin-Wagner theorem. We first discuss a fully self-consistent approximation, where fermions are renormalized due to fluctuations of their spin density, in close analogy to FLEX. While static properties like the correlation length, ξ(T ) ∝ exp(a J/T ) , come out correctly, the dynamical response lacks the magnon-like peaks which would reflect the appearance of short-range order at low T . This drawback, which is caused by overdamping, is overcome in a 'minimal self-consistent approximation' (MSCA), which we derive from the equations of motion. The MSCA features dynamical scaling at small energy and temperature and is qualitatively correct both in the regime of order-parameter relaxation at long wavelengths λ > ξ and in the short-range-order regime at λ < ξ . We also discuss the impact of vertex corrections and the problem of pseudo-gap formation in the single-particle density of states due to long-range fluctuations. Finally we show that the (short-range) magnetic order in MFT and MSCA helps to fulfill the constraint on the local fermion occupancy.
Strong-coupling expansion for the Hubbard model in arbitrary dimension using slave bosons
Physical Review B, 1996
A strong-coupling expansion for the antiferromagnetic phase of the Hubbard model is derived in the framework of the slave-boson mean-field approximation. The expansion can be obtained in terms of moments of the density of states of freely hopping electrons on a lattice, which in turn are obtained for hypercubic lattices in arbitrary dimension. The expansion is given for the case of half-filling and for the energy up to fifth order in the ratio of hopping integral t over on-site interaction U , but can straightforwardly be generalized to the non-half-filled case and be extended to higher orders in t/U. For the energy the expansion is found to have an accuracy of better than 1% for U/t ≥ 8. A comparison is given with an earlier perturbation expansion based on the Linear Spin Wave approximation and with a similar expansion based on the Hartree-Fock approximation. The case of an infinite number of spatial dimensions is discussed.
Heisenberg model with Dzyaloshinskii-Moriya interaction: A mean-field Schwinger-boson study
Physical Review B, 1996
We present a Schwinger-boson approach to the Heisenberg model with Dzyaloshinskii-Moriya interaction. We write the anisotropic interactions in terms of Schwinger bosons keeping the correct symmetries present in the spin representation, which allows us to perform a conserving mean-field approximation. Unlike previous studies of this model by linear spin-wave theory, our approach takes into account magnon-magnon interactions and includes the effects of three-boson terms characteristic of noncollinear phases. The results reproduce the linear spin-wave predictions in the semiclassical large-S limit, and show a small renormalization in the strong quantum limit S = 1/2.
MAGNETIC COUPLINGS IN THE HUBBARD MODEL
The half-filled Hubbard model can be analyzed in terms of quasi-electron and spin wave excitations; the latter are described by í µí°» í µí°» = − 1 2 ∑ í µí°½ í µí±í µí± í µí°» í µí½ í µí² í µí½ í µí² í µí±í µí± The quantities J mn were calculated and the resulting thermodynamic quantities in the one-dimensional (1D) case are in very good agreement with exact results. We outline here our approximate treatment of the Hubbard [1] hamiltonian, í µí°» ̂ = ∑ ∈ 0 í µí± ̂ í µí±í µí¼ í µí±í µí¼ + ∑ í µí± í µí±í µí±í µí¼ í µí±í µí±í µí¼ í µí»¼ í µí±í µí¼ + í µí± í µí±í µí¼ + í µí± ∑ í µí± ̂ í µí±↑ í µí± ̂ í µí°½↓ í µí± and we summarize our results. For simplicity we take V jjΣ equal to a constant V when the lattice sites i,j are nearest neighbors and zero otherwise. The unperturbed (U= 0) half bandwidth B is proportional to V; e.g. when the site {i} forms a simple cubic lattice B = 6V. In the binary, self-consistent, static approximation (see, e.g., Cyrot's [2] work) one replaces the term í µí±í µí± ̂ í µí±↑ í µí± ̂ í µí± ↓ by í µí± í µí±í µí¼ í µí± ̂ í µí±í µí¼ ; e iς is a random variable which takes the values U(n-μ)/2 and U(n + μ)/2 each with probability 1 2 ;n is the average number of electrons per site and μ is a quantity to be determined self-consistently by the condition í µí¼ = 〈í µí± ̅ í µí±↑ 〉 í µí±= í µí±¢ − 〈 í µí± ̅ í µí± ↓ 〉 í µí± =í µí±¢ where the bar indicates quantum mechanical average and 〈 〉 í µí±= í µí±¢ denotes configurational average under the condition thatí µí± í µí±↑ = U(n — μ)/2 and í µí± í µí±↓ = U(n + μ)/2.. The quantity μ can be interpreted as the magnitude of a local moment, which can take two values ±μ. We call ρ(E) the average density of states corresponding to the effective hamiltonian resulting from the substitution of í µí±í µí± ̂ í µí±↑ í µí± ̂ í µí±↓ by í µí± í µí±í µí¼ í µí± ̂ í µí± í µí¼ .
Journal of Physics: Condensed Matter, 2009
We study a triangular frustrated antiferromagnetic Heisenberg model with nearest-neighbor interaction J 1 and third-nearest-neighbor interactions J 3 by means of Schwinger-boson mean-field theory. It is shown that an incommensurate phase exists in a finite region in the parameter space for an antiferromagnetic J 3 while J 1 can be either positive or negtaive. A detailed solution is presented to disclose the main features of this incommensurate phase. A gapless dispersion of quasiparticles leads to the intrinsic T 2 -law of specific heat. The local magnetization is significantly reduced by quantum fluctuations (for S = 1 case, a local magnetization is estimated as m = S i ≈ 0.6223). The magnetic susceptibility is linear in temperature at low temperatures. We address possible relevance of these results to the low-temperature properties of NiGa 2 S 4 . From a careful analysis of the incommensurate spin wave vector, the interaction parameters for NiGa 2 S 4 are estimated as, J 1 ≈ −3.8755K and J 3 ≈ 14.0628K, in order to account for the experimental data.
Journal of the Physical Society of Japan, 1998
The low temperature magnetization process of the ferromagnetic-antiferromagnetic Heisenberg chain is studied using the interacting boson approximation. In the low field regime and near the saturation field, the spin wave excitations are approximated by the δ function boson gas for which the Bethe ansatz solution is available. The finite temperature properties are calculated by solving the integral equation numerically. The comparison is made with Monte Carlo calculation and the limit of the applicability of the present approximation is discussed.