Critical behaviour of a spin-tube model in a magnetic field

We show that the low-energy physics of the spin-tube model in presence of a critical magnetic field can be described by a broken SU(3) spin chain. Using the Lieb-Schultz-Mattis Theorem we characterize the possible magnetization plateaus and study the critical behavior in the region of transition between the plateaus m=1/2 and m=3/2 by means of renormalization group calculations performed on the bosonized effective continuum field theory. We show that in certain regions of the parameter space of the effective theory the system remains gapless, and we compute the spin-spin correlation functions in these regions. We also discuss the possibility of a plateau at m=1, and show that although there exists in the continuum theory a term that might cause the appearance of a plateau there, such term is unlikely to be relevant. This conjecture is proved by DMRG techniques. The modifications of the three-leg ladder Hamiltonian that might show plateaus at m =1,5/6,7/6 are discussed, and we give the expected form of correlation functions on the m=1 plateau.Comment: RevTeX, 43 pages, 5 EPS figure

Replica Method for Wide Correlators in Gaussian Orthogonal, Unitary And Symplectic Random Matrix Ensembles

We calculate connected correlators in Gaussian orthogonal, unitary and symplectic random matrix ensembles by the replica method in the 1/N-expansion. We obtain averaged one-point Green's functions up to the next-to-leading order O(1/N) and wide two-level correlators up to the first nontrivial order O(1/N^2) and wide three-level correlators up to the first nontrivial order $O(1/N^4)$ by carefully treating fluctuations in saddle-point evaluation.Comment: LaTeX 21 pages, a new result on wide three-level correlators adde

Phase diagram of a 1 dimensional spin-orbital model

We study a 1 dimensional spin-orbital model using both analytical and numerical methods. Renormalization group calculations are performed in the vicinity of a special integrable point in the phase diagram with SU(4) symmetry. These indicate the existence of a gapless phase in an extended region of the phase diagram, missed in previous studies. This phase is SU(4) invariant at low energies apart from the presence of different velocities for spin and orbital degrees of freedom. The phase transition into a gapped dimerized phase is in a generalized Kosterlitz-Thouless universality class. The phase diagram of this model is sketched using the density matrix renormalization group technique.Comment: 11 pages, 5 figures, new references adde

Equivalence of Several Chern-Simons Matter Models

Not only does Chern-Simons (CS) coupling characterize statistics, but also spin and scaling dimension of matter fields. We demonstrate spin transmutation in relativistic CS matter theory, and moreover show equivalence of several models. We study CS vector model in some details, which provide consistent check to the assertion of the equivalence.Comment: latex, 7page, IFT-478-UNC/NUP-A-93-15 A version within the length limit for Phys. Rev. Letts (in press

On gonihedric loops and quantum gravity

We present an analysis of the gonihedric loop model, a reformulation of the two dimensional gonihedric spin model, using two different techniques. First, the usual regular lattice statistical physics problem is mapped onto a height model and studied analytically. Second, the gravitational version of this loop model is studied via matrix models techniques. Both methods lead to the conclusion that the model has $c_{matter}=0$ for all values of the parameters of the model. In this way it is possible to understand the absence of a continuous transition

Quantum-fluctuation-induced collisions and subsequent excitation gap of an elastic string between walls

An elastic string embedded between rigid walls is simulated by means of the density-matrix renormalization group. The string collides against the walls owing to the quantum-mechanical zero-point fluctuations. Such ``quantum entropic'' interaction has come under thorough theoretical investigation in the context of the stripe phase observed experimentally in doped cuprates. We found that the excitation gap opens in the form of exponential singularity DeltaE ~ exp(-Ad^sigma) (d: wall spacing) with the exponent sigma =0.6(3), which is substantially smaller than the meanfield value sigma=2. That is, the excitation gap is much larger than that anticipated from meanfield, suggesting that the string is subjected to robust pinning potential due to the quantum collisions. This feature supports Zaanen's ``order out of disorder'' mechanism which would be responsible to the stabilization of the stripe phase

Gapless Excitation above a Domain Wall Ground State in a Flat Band Hubbard Model

We construct a set of exact ground states with a localized ferromagnetic domain wall and with an extended spiral structure in a deformed flat-band Hubbard model in arbitrary dimensions. We show the uniqueness of the ground state for the half-filled lowest band in a fixed magnetization subspace. The ground states with these structures are degenerate with all-spin-up or all-spin-down states under the open boundary condition. We represent a spin one-point function in terms of local electron number density, and find the domain wall structure in our model. We show the existence of gapless excitations above a domain wall ground state in dimensions higher than one. On the other hand, under the periodic boundary condition, the ground state is the all-spin-up or all-spin-down state. We show that the spin-wave excitation above the all-spin-up or -down state has an energy gap because of the anisotropy.Comment: 26 pages, 1 figure. Typos are fixe