We investigate the low-lying excitation of the antiferromagnetic zigzag spin ladder with M\"obius boundary condition. Using the Lanczos and Householder diagonalization methods, we calculate the excitation spectrum of the zigzag ladder in the momentum space. We then show that the topological defect generated by the M\"obius boundary provides the clear evidence of the single-spinon excitation. On the basis of the obtained single-spinon dispersion curve, we analyze the two-spinon scattering states under the usual periodic boundary condition. We further discuss the interaction effect between the spinons, and the connection to the cusp singularity in the magnetization process.
Abstract Non-compact Conformal Field Theories (CFTs) are central to several aspects of string theory and condensed matter physics. They are characterised, in particular, by the appearance of a continuum of conformal dimensions. Surprisingly, such CFTs have been identified as the continuum limits of lattice models with a finite number of degrees of freedom per site. However, results have so far been restricted to the case of periodic boundary conditions, precluding the exploration via lattice models of aspects of non-compact boundary CFTs and the corresponding D-brane constructions. The present paper follows a series of previous works on a ℤ2-staggered XXZ spin chain, whose continuum limit is known to be a non-compact CFT related with the Euclidian black hole sigma model. By using the relationship of this spin chain with an integrable
D22 D 2 2 vertex model, we here identify integrable boundary conditions that lead to a continuous spectrum of boundary exponents, and thus correspond to non-compact branes. In the context of the Potts model on a square lattice, they correspond to wired boundary conditions at the physical antiferromagnetic critical point. The relations with the boundary parafermion theories are discussed as well. We are also able to identify a boundary renormalisation group flow from the non-compact boundary conditions to the previously studied compact ones.
We study the long wavelength limit of a spin-
21 Heisenberg antiferromagnetic two-leg ladder, treating the interchain coupling in a nonperturbative way. We perform a mean field analysis and then include the fluctuations in an exact way. This allows for a discussion of the phase diagram of the system and provides an effective-field theory for the low-energy excitations. The coset fermionic Lagrangian obtained corresponds to a perturbed
SU(4)1/U(1) conformal field theory (CFT). This effective theory is naturally embedded in a ${\mathrm{SU}(2)}_{2}\ifmmode\times\else\texttimes\fi{}{Z}_{2}$ CFT, where perturbations are easily identified in terms of conformal operators in the two sectors. Crossed and zigzag ladders are also discussed using the same approach.
Low dimensional magnetic models.-We continued our study of the physical properties of the so-called magnetic ladder systems.We have considered anisotropic two-leg ladder models with S=1/2 and S=1 spins on the rungs, using the density matrix renormalization group (DMRG) method.We have generalized the numerical procedure to allow to take into account the symmetries of the models in order to reduce the dimension of the matrix to be diagonalized or to achieve better accuracy.We have determined the boundaries of the extended region in the parameter space, where the gapped Haldane phase exists.In our study of the scaling limit of the one dimensional XXZ Heisenberg chain we have found, that the limiting model possesses spin 1/2 massive particles, and possibly can be identified with the Sine-Gordon chain.One-dimensional fermionic models.-We continued the study of the models defined through the relativistic limit of the Hubbard chain by investigating the scaling limit of the one dimensional attractive Hubbard model at less than half filling.Like in the half filled band case, also this model possesses both massive and massless dressed particles.Now, unlike the half filled case, only the massive particles are described by Bethe Ansatz type equations, nevertheless the massless excitations still fit into the framework of a conform field theory.Theory of dissipative motion of heavy particles.-We studied the low temperature behaviour of two level systems (TLS) interacting with the conduction electrons in various models and approximations.We continued the study of the region below the Kondo temperature by the use of the model with electron spin degeneracy N f > 2. The only stable fixed point and the exponents of the leading irrelevant operators are equivalent to those of the spin 1/2 Kondo model, but there are essentially more irrelevant operators in our case.We studied the role of the electron-hole symmetry in the low temperature behaviour of TLS, moreover the differences between the scaling methods starting from path integrals and Matsubara technique.We showed that the breaking of the electron-hole symmetry results in electron assisted tunneling, but the contribution cannot bring the system to the two-channel Kondo fixed point.
This study addresses low-energy properties of two-leg spin-1 ladders with antiferromagnetic (AF) intrachain coupling under a uniform or staggered external field
H, and a few of their modifications. The generalization to spin-
S ladders is also discussed. In the strong AF rung(interchain)-coupling ${J}_{\ensuremath{\perp}}$ region, degenerate perturbation theory applied to spin-
S ladders predicts
2S critical curves in the parameter space $({J}_{\ensuremath{\perp}},H)$ for the staggered-field case, in contrast to
2S finite critical regions for the uniform-field case. All critical areas belong to a universality with central charge
c=1. On the other hand, we employ Abelian and non-Abelian bosonization techniques in the weak rung-coupling region. They show that in the spin-1 ladder, a sufficiently strong uniform field engenders a
c=1 critical state regardless of the sign of ${J}_{\ensuremath{\perp}}$, whereas the staggered field is expected not to yield any singular phenomena. From the bosonization techniques, new field-theoretical expressions of string order parameters in the spin-1 systems are also proposed.
The boundary critical behavior of the two-dimensional (2D) quantum antiferromagnetic (AF) XXZ model coupled with either a dangling $\mathrm{spin}\text{\ensuremath{-}}1/2$ XXZ chain or a dangling two-leg ladder on the boundary is studied with the bosonization and renormalization group analysis. A rich boundary phase diagram is obtained in each case. In the dangling chain case, the boundary either develops a long-range AF order in the easy-plane or the easy-axis direction with extraordinary critical behavior or has a valence bond solid order with ordinary boundary critical behavior. In the case of a dangling two-leg ladder, besides the possible easy-plane or easy-axis AF-ordered phases on the boundary with extraordinary critical behavior, the boundary can form a singlet phase with ordinary critical behavior without breaking any symmetry. These results are consistent with recent numerical simulations on the boundary critical behavior of 2D quantum spin models.