The z-component dynamical spin correlation function S zz (q,w) of the s= 1 / 2 anisotropic XY chain is calculated exactly in the fermion representation. S zz consists of two parts: one (S m ) represents two fermion excitations and the other (S s ) describes scattering from thermally excited fermions. In the continuum limit, S s has the structure of the solitonic part of a classical sine-Gordon correlation function, but the soliton form factor is modified by quantum effects. S m has similarities with the spin-wave continuum form of S zz an isotropic spin chains. The continuum results are compared with those for a discrete chain.
The z-component dynamical spin correlation function S zz (q,w) of the s= 1 / 2 anisotropic XY chain is calculated exactly in the fermion representation. S zz consists of two parts: one (S m ) represents two fermion excitations and the other (S s ) describes scattering from thermally excited fermions. In the continuum limit, S s has the structure of the solitonic part of a classical sine-Gordon correlation function, but the soliton form factor is modified by quantum effects. S m has similarities with the spin-wave continuum form of S zz an isotropic spin chains. The continuum results are compared with those for a discrete chain.
We have studied two models for anisotropic quantum spin chains. (i) XY-chain with a field in the plane: The magnetization of the ferromagnet behaves as h1/3 for small fields, in agreement with scaling laws. The antiferromagnet shows a critical field at which the ground state is a simple Néel state and which separates power law from exponential decay of spatial correlations. (ii) Anisotropic XY-chain: The dynamic z-component spin correlation function can be decomposed into a spin wave and a soliton contribution. The nature of quantum soliton excitations is studied and their form compared to soliton solutions of classical equations of motion.
One-dimensional quantum spin-1/2 XY models admit the rigorous analysis not only of their static properties (i.e. the thermodynamic quantities and the equal-time spin correlation functions) but also of their dynamic properties (i.e. the different-time spin correlation functions, the dynamic susceptibilities, the dynamic structure factors).This becomes possible after exploiting the Jordan-Wigner transformation which reduces the spin model to a model of spinless noninteracting fermions.A number of dynamic quantities (e.g.related to transverse spin operator or dimer operator fluctuations) are entirely determined by two-fermion excitations and can be examined in much detail.We consider the spin-1/2 XY chain in a transverse ( z) magnetic field with the Hamiltonianand calculate the dynamic structure factorsis the dimer operator.The results for the dynamic transverse structure factor S zz (κ, ω) and for the dynamic dimer structure factor S DD (κ, ω) are known, whereas the analysis of the dynamic structure factor S zD (κ, ω) = (S Dz (κ, ω)) has not been reported so far.We compare different two-fermion dynamic quantities contrasting their generic and specific features.
The authors derive a continuum representation of the spin-one operators which provides the mapping of the spin-one anisotropic Heisenberg chain onto the Luttinger model. They show a schematic phase diagram of the Hamiltonian, and calculate a general two-spin dynamic correlation function at finite temperatures, valid in the massless domain of the Hamiltonian. This can be applied to obtain the transverse dynamic form factor, and results are compared with neutron scattering data on CsNiF3. The behaviour of the transverse correlation function is shown to be governed by a critical exponent eta u+or- which is a measured of quantum effects in the system, eta M+or- to 0 being the classical limit. Existing data on CsNiF3 are shown to be in the classical regime, and they make suggestions for further experiments to search for quantum fluctuations. They also indicate the limits of applicability of the quantum sine-Gordon theory to CsNIF3.
Dynamic xx and xy spin pair correlation functions for the isotropic spin-½ XY chain are calculated numerically for long open chains in the presence of a transverse ( z ) magnetic field at finite temperature. From these data the first numerical results for the dynamic structure factors S xx (κ,ω) and S xy (κ,ω) are obtained and compared with the known results for S zz (κ,ω). While S zz (κ,ω) is restricted to certain regions in the (κ,ω)-plane S xx (κ,ω) and S xy (κ,ω) are not. Nevertheless, the numerical results show that the latter structure factors are quite small outside the regions defined by S zz (κ,ω) and moreover, that they may in many circumstances, especially at low temperature, be approximately described by a small number of broadened excitation branches.
A variational estimate of the free energy of a quantum spin chain based on the stochastic behavior of the quantization axes is proposed. It allows a description of the nonlinear excitations and quantum spin waves within the same framework. For an easy-plane ferromagnet with an external field in the plane it reveals that the nonlinear excitations (solitons) are predominantly described by the classical degrees of freedom. Considerable effort has been devoted to the theoretical description1 and experimental verification of the existence of nonlinear excitations. In this field magnetic chain systems have played an important part.2 Chain systems with an easy-plane anisotropy, such as (C6 H11 NH3 )CuBr3 (CHAB) and CsNiF3 , which are subjected to a symmetry breaking field, were found to be soliton bearing.3 Theoretically the description of the nonlinear effect is based on the mapping of the spin dynamics on a sine-Gordon model. Further research4 indicated that the interpretation of the thermodynamical properties of real systems in terms of the sine-Gordon model required however quantum and anisotropy corrections. Since the dipolar interactions between the spins in the chain are considered to be negligible, the direction of the spin chain in configuration space with respect to any preferred direction in spin space does not enter explicitly in the Hamiltonian. This makes it interesting to define a site-dependent z direction in spin space which makes an angle (Θn ,φn ) with the z direction in configuration space. The model Hamiltonian can then be written in terms of the spin operators defined with respect to the site-dependent quantization axis. The representation with equal quantization axis for all the sites is related to the representation with different quantization axes at each site by a rotation in spin space. The unitary transformation that describes the rotation contains the angles (Θn ,φn ), which we have treated as random variables. Based on this observation we have proposed a new variational approach for the quantum spin chain. We will outline the main results here. A full account is published elsewhere.5 In our approach the free energy of the system can be separated in a quantum part and a classical part. The free energy F of the chain is then approximated by an upper bound F<Fcl +Fqm , where βFcl =−ln[E(exp−βVcl )] and βFqm =−ln Tr(exp−β〈Hqm 〉). The first part is a configurational classical free energy, depending on the choice of the probability distribution for the quantization axes via the expectation E. The second contribution is the free energy of a modified quantum chain, whose parameters are classical averages and can be obtained from the configurational classical free energy. For easy-plane ferromagnetic chains, the nonlinear excitations are comprised in the classical part, whereas the quantum part contains predominantly linear excitations. For those thermodynamical quantities that are insensitive to the contribution of the quantum excitations, the chain is thermodynamically equivalent with a classical sine-Gordon system. The out-of-plane corrections are incorporated in the quantum part of the free energy. This behavior is corroborated experimentally by measurements of the excess heat capacity of CHAB for different magnetic fields with the same in-plane component.6 The validity of our approach is, however, not restricted to easy-plane ferromagnetic chains. Also for more complex systems with, for example, an orthorhombic or helical symmetry, the introduction of stochastic quantization axes can shed new light on some of the thermodynamical properties of these quantum systems in terms of their classical equivalent.
We introduce a nonperturbative framework for quantizing chiral solitons in interacting quantum spin chains. This approach provides a direct lattice extension of the well-established S -duality between the sine-Gordon and Thirring models, thereby bridging the gap between continuum dualities and their lattice counterparts. By constructing the quantum chiral-soliton operators explicitly, we show how their unconventional dynamics appear in the excitation spectrum and correlation functions across the full Brillouin zone. A key result is that the dominant soliton tunneling amplitude alternates in sign, sgn ( t 1 + ) = ( − 1 ) 2 S + 1 , sharply distinguishing half-odd-integer from integer spin chains. We further identify characteristic signatures of these chiral excitations in the dynamical spin structure factor, demonstrating their visibility in inelastic neutron scattering. Our results open a route to experimentally probing nonperturbative features of dual quantum field theories in condensed-matter settings.