Direct Observation of Field-Induced Incommensurate Fluctuations in a One-Dimensional S=1/2 Antiferromagnet

Neutron scattering from copper benzoate, Cu(C6D5COO)2 3D2O, provides the first direct experimental evidence for field-dependent incommensurate low energy modes in a one-dimensional spin S = 1/2 antiferromagnet. Soft modes occur for wavevectors q=\pi +- dq(H) where dq(H) ~ 2 \pi M(H)/g\mu_B as predicted by Bethe ansatz and spinon descriptions of the S = 1/2 chain. Unexpected was a field-induced energy gap $\Delta(H) \propto H^\alpha$, where $\alpha = 0.65(3)$ as determined from specific heat measurements. At H = 7 T (g\mu_B H/J = 0.52), the magnitude of the gap varies from 0.06 - 0.3 J depending on the orientation of the applied field.Comment: 11 pages, 5 postscript figures, LaTeX, Submitted to PRL 3/31/97, e-mail comments to [email protected]

Ordered phase and scaling in ZnZ_n models and the three-state antiferromagnetic Potts model in three dimensions

Based on a Renormalization-Group picture of $Z_n$ symmetric models in three dimensions, we derive a scaling law for the $Z_n$ order parameter in the ordered phase. An existing Monte Carlo calculation on the three-state antiferromagnetic Potts model, which has the effective $Z_6$ symmetry, is shown to be consistent with the proposed scaling law. It strongly supports the Renormalization-Group picture that there is a single massive ordered phase, although an apparently rotationally symmetric region in the intermediate temperature was observed numerically.Comment: 5 pages in REVTEX, 2 PostScript figure

Scattering Matrix and Excitation Spectrum of the Hubbard Model

We consider the one-dimensional Hubbard model at half filling. We show that both excitation spectrum and S-matrix are determined by the SO(4) symmetry of the model. The complete set of excitations is given by the scattering states four elementary excitations, which form the fundamental representation of SO(4). We evaluate the exact S-matrix, which satisfies the Yang-Baxter relation. The results for the repulsive and attractive Hubbard model are related by an interchange of spin and charge degrees of freedom.Comment: 8 pages, jyTeX (macro included - just TeX the file) ITP-SB-93-4

Algebraic Bethe ansatz approach for the one-dimensional Hubbard model

We formulate in terms of the quantum inverse scattering method the algebraic Bethe ansatz solution of the one-dimensional Hubbard model. The method developed is based on a new set of commutation relations which encodes a hidden symmetry of 6-vertex type.Comment: appendix additioned with Boltzmann weigths and R-matrix. Version to be published in J.Phys.A:math.Gen. (1997

The Origin of Degeneracies and Crossings in the 1d Hubbard Model

The paper is devoted to the connection between integrability of a finite quantum system and degeneracies of its energy levels. In particular, we analyze in detail the energy spectra of finite Hubbard chains. Heilmann and Lieb demonstrated that in these systems there are crossings of levels of the same parameter independent symmetry. We show that this apparent violation of the Wigner-von Neumann noncrossing rule follows directly from the existence of nontrivial conservation laws and is a characteristic signature of quantum integrability. The energy spectra of Hubbard chains display many instances of permanent (at all values of the coupling) twofold degeneracies that cannot be explained by parameter independent symmetries. We relate these degeneracies to the different transformation properties of the conserved currents under spatial reflections and the particle-hole transformation and estimate the fraction of doubly degenerate states. We also discuss multiply degenerate eigenstates of the Hubbard Hamiltonian. The wave functions of many of these states do not depend on the coupling, which suggests the existence of an additional parameter independent symmetry.Comment: 25 pages, 12 figure

Excitons in one-dimensional Mott insulators

We employ dynamical density-matrix renormalization group (DDMRG) and field-theory methods to determine the frequency-dependent optical conductivity in one-dimensional extended, half-filled Hubbard models. The field-theory approach is applicable to the regime of `small' Mott gaps which is the most difficult to access by DDMRG. For very large Mott gaps the DDMRG recovers analytical results obtained previously by means of strong-coupling techniques. We focus on exciton formation at energies below the onset of the absorption continuum. As a consequence of spin-charge separation, these Mott-Hubbard excitons are bound states of spinless, charged excitations (`holon-antiholon' pairs). We also determine exciton binding energies and sizes. In contrast to simple band insulators, we observe that excitons exist in the Mott-insulating phase only for a sufficiently strong intersite Coulomb repulsion. Furthermore, our results show that the exciton binding energy and size are not related in a simple way to the strength of the Coulomb interaction.Comment: 15 pages, 6 eps figures, corrected typos in labels of figures 4,5, and

Ground states of integrable quantum liquids

Based on a recently introduced operator algebra for the description of a class of integrable quantum liquids we define the ground states for all canonical ensembles of these systems. We consider the particular case of the Hubbard chain in a magnetic field and chemical potential. The ground states of all canonical ensembles of the model can be generated by acting onto the electron vacuum (densities $n1$), suitable pseudoparticle creation operators. We also evaluate the energy gaps of the non-lowest-weight states (non - LWS's) and non-highest-weight states (non - HWS's) of the eta-spin and spin algebras relative to the corresponding ground states. For all sectors of parameter space and symmetries the {\it exact ground state} of the many-electron problem is in the pseudoparticle basis the non-interacting pseudoparticle ground state. This plays a central role in the pseudoparticle perturbation theory.Comment: RevteX 3.0, 43 pages, preprint Univ.Evora, Portuga

Dynamical density correlation function of 1D Mott insulators in a magnetic field

We consider the one dimensional (1D) extended Hubbard model at half filling in the presence of a magnetic field. Using field theory techniques we calculate the dynamical density-density correlation function $\chi_{nn}(\omega,q)$ in the low-energy limit. When excitons are formed, a singularity appears in $\chi_{nn}(\omega,q)$ at a particular energy and momentum transfer.Comment: 7 pages, 4 figure

Dynamical Structure Factors of the S=1/2 Bond-Alternating Spin Chain with a Next-Nearest-Neighbor Interaction in Magnetic Fields

The dynamical structure factor of the S=1/2 bond-alternating spin chain with a next-nearest-neighbor interaction in magnetic field is investigated using the continued fraction method based on the Lanczos algorithm. When the plateau exists on the magnetization curve, the longitudinal dynamical structure factor shows a large intensity with a periodic dispersion relation, while the transverse one shows a large intensity with an almost dispersionless mode. The periodicity and the amplitude of the dispersion relation in the longitudinal dynamical structure factor are sensitive to the coupling constants. The dynamical structure factor of the S=1/2 two-leg ladder in magnetic field is also calculated in the strong interchain-coupling regime. The dynamical structure factor shows gapless or gapful behavior depending on the wave vector along the rung.Comment: 8 pages, 4 figures, to appear in Journal of the Physical Society of Japan, vol. 69, no. 10, (2000