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一维自旋－1/2XY模型的磁场效应

周宗立, 黄凯, 娄平

Published Dec 25, 2008• 0 citations
OpenAlex

Abstract

By using Haldane's harmonic-fluid approach-bosonization, we study the spin-1/2XY model in external magnetic field. The bosonization procedure is changed in the presence of an external field. We study the model without external field firstly, and then the perturbation due to the external magnetic field is bosonized separately, We add the bosonized perturbation to the Hamiltonian of the one-dimensional spin-1/2 model, then we get the exactly bosonized model in external magnetic field. In terms of bosonized haimitonian, incommensurability problem can be solved by moving Fermi point. Therefore, we redefine the bononic field operator and get a new Hamiltonian, and the problem duo to perturbation is sovled, but the correlation functions are changed at the same time. Lastly the correlation functions are calculated newly. And we talk simply about the change of correlation function duo to shifting Fermi point, and virtues of bosonization compared with other techniques.

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By using Haldane's harmonic-fluid approach-bosonization, we study the spin-1/2XY model in external magnetic field. The bosonization procedure is changed in the presence of an external field. We study the model without external field firstly, and then the perturbation due to the external magnetic field is bosonized separately, We add the bosonized perturbation to the Hamiltonian of the one-dimensional spin-1/2 model, then we get the exactly bosonized model in external magnetic field. In terms of bosonized haimitonian, incommensurability problem can be solved by moving Fermi point. Therefore, we redefine the bononic field operator and get a new Hamiltonian, and the problem duo to perturbation is sovled, but the correlation functions are changed at the same time. Lastly the correlation functions are calculated newly. And we talk simply about the change of correlation function duo to shifting Fermi point, and virtues of bosonization compared with other techniques.
By using bosonization technique and Jordan-Wigner transformation,we study the spin(-1/2XY) model in external magnetic field.The bosonization procedure is changed in the presence of an external field.We study the model without external field firstly,and then the perturbation due to the external magnetic field is bosonized separately.We solve the incommensurability problem by redefining the bononic field operator,and correlation functions are calculated.Lastly,we talk simply about virtues of bosonization compared with other techniques.
The correlation functions of one-dimensional Hubbard model in the presence of external magnetic field was investigated through the conformal field technique. The long distance behaviour of the correlation functions and their critical exponents for the model in the presence of a magnetic field are established by solving the dressed charge matrix equations and setting the number of occupancies to one, as an alternative to the usual zero often used by authors in literatures. Our result shows the critical exponents of the correlation function grows monotonically with magnetic field and reduces to definite values at zero magnetic field around various Fermi points.
We exactly solve the ferromagnetic spin- 1/2 Ising model on the Bethe lattice in the presence of an external magnetic field by means of the equations of motion method within the Green's function formalism. In particular, such an approach is applied to an isomorphic model of localized Fermi particles interacting via an intersite Coulomb interaction. A complete set of eigenoperators is found together with the corresponding eigenvalues. The Green's functions and the correlation functions are written in terms of a finite set of parameters to be self-consistently determined. A procedure is developed that allows us to exactly fix the unknown parameters in the case of a Bethe lattice with any coordination number z. Nonlocal correlation functions up to four points are also provided together with a study of the relevant thermodynamic quantities.
The research presented here focuses on the theoretical investigation of spinons in quasi one-dimensional quantum spin chains from the perspective of neutron scattering, with emphasis placed on the calculation of dynamic spin structure factors for both unpolarised and polarised incident neutrons. Two anisotropic versions of the Heisenberg spin chain are considered for such an examination: the spin-1/21/21/2 antiferromagnetic XXZXXZXXZ model and the spin-1/21/21/2 ferromagnetic XYZXYZXYZ model.The XYZXYZXYZ model supports spinon scattering (modelled at finite temperature) and is related to the so-called Villain mode. The introduction of a perturbation in the form of an external transverse magnetic field or Dzyaloshinskii-Moriya interaction (DMI) leads to the emergence of incommensurability in the system; such a result is a signature of fractional excitations. The presence of these interactions also give rise to a chiral response associated with the spinons in the polarised term of the scattering cross section. The inelastic scattering cross section is computed for both unpolarised and polarised neutrons.In relation to the antiferromagnetic XXZXXZXXZ model, emphasis is on spinon pair creation (modelled at T=0rmKT = 0 {rm K}T=0rmK). Motivated by the presence of a chiral response in the case of the XYZXYZXYZ model mentioned above, a new technique is developed in order to incorporate DMI and the transverse magnetic field so that one can determine if there is a chiral property associated with the two-spinon system. This technique is numerical in nature and is based on Green function methods. Using the results produced by the Green function approach, the inelastic cross section in the presence of an external transverse magnetic field is computed for the first time. The result is compared with experimental neutron scattering data; good agreement is demonstrated between theory and experiments on rmCsCoBr3{rm CsCoBr}_3rmCsCoBr3​.Finally, the Green function approach is generalised to account for the interactions between spin chains in magnetic compounds described by a staggered field. Various dynamic structure factors are computed for this scenario with results compared to experiment; good agreement between the theory and experiments on rmRbCoCl3{rm RbCoCl}_3rmRbCoCl3​ is shown.
The exact solution of the two-dimensional (2D) Ising model at an external magnetic field is derived by a modified Clifford algebraic approach. At first, the transfer matrices are analyzed in three representations, i.e., Clifford algebraic representation, transfer tensor representation and schematic representation, to inspect nonlocal effects in this many-body interacting system. It is ensured that nontrivial topological structures exist in this system, which is analogous to (but different with) those in the three-dimensional (3D) Ising model at zero magnetic field. Therefore, the approaches developed for the 3D Ising models are modified to be appropriable for solving analytically the solution of the 2D Ising model at a magnetic field. An additional rotation, serving as a topological Lorentz transformation, is applied for dealing with the topological problems in the present system. The rotation angle for the transformation is determined by Yang-Baxter relations and a subsequent average of rotation angles treating the linear change of the topological actions. Application of a magnetic field increases the magnetization, shifting the critical point to higher temperatures. At the temperature above the critical point, the magnetization keeps zero until a critical field at which it jumps rapidly as a first-order magnetization process. The partition function and the magnetization obtained are helpful for understanding the physical properties, in particular, the magnetization processes of the 2D magnetic materials.