arXiv subjects
Publications and source records attributed to Ulrich Bilstein.
We calculate the magnetization profiles of the $σ_j^x$ and $σ_j^z$ operators for the XX-model with hermitian boundary terms. We study the profiles on the finite chain and in the continuum limit. The results are discussed in the context of conformal invariance. We also discuss boundary excitations and their effect on the magnetization profiles.
It is shown that an operator (in general non-local) commutes with the Hamiltonian describing the finite XX quantum chain with certain non-diagonal boundary terms. In the infinite volume limit this operator gives the "topological" charge.
We compute the continuum limit of the spectra for the XX-model with arbitrary complex boundary fields. In the case of hermitian boundary terms one obtains the partition functions of the free compactified boson field on a cylinder with Neumann-Neumann, Dirichlet-Neumann or Dirichlet-Dirichlet boundary conditions. This applies also for certain non-hermitian boundaries. For special cases we also compute the free surface energy. For certain non-hermitian boundary terms the results are more complex.Here one obtains logarithmic corrections to the free surface energy. The asymmetric version of the XX-model with boundaries (this includes the Dzyaloshinsky-Moriya interaction)is also discussed.
This is the first of three papers dealing with the XX finite quantum chain with arbitrary, not necessarily hermitian, boundary terms. This extends previous work where the periodic or diagonal boundary terms were considered. In order to find the spectrum and wave-functions an auxiliary quantum chain is examined which is quadratic in fermionic creation and annihilation operators and hence diagonalizable. The secular equation is in general complicated but several cases were found when it can be solved analytically. For these cases the ground-state energies are given. The appearance of boundary states is also discussed and in view to the applications considered in the next papers, the one and two-point functions are expressed in terms of Pfaffians.
The spectrum of the non-hermitian asymmetric XXZ-chain with additional non-diagonal boundary terms is studied. The lowest lying eigenvalues are determined numerically. For the ferromagnetic and completely asymmetric chain that corresponds to a reaction-diffusion model with input and outflow of particles the smallest energy gap which corresponds directly to the inverse of the temporal correlation length shows the same properties as the spatial correlation length of the stationary state. For the antiferromagnetic chain with both boundary terms, we find a conformal invariant spectrum where the partition function corresponds to the one of a Coulomb gas with only magnetic charges shifted by a purely imaginary and a lattice-length dependent constant. Similar results are obtained by studying a toy model that can be diagonalized analytically in terms of free fermions.