arXiv subjects
Publications and source records attributed to J. P. Rodriguez.
The effect of anisotropy in the nearest-neighbor spin interactions that couple $N\geq 2$ consecutive spin-1/2 antiferromagnetic chains is studied theoretically by considering the limit where the coupling is purely of the Ising type. An analysis based on the equivalent Luttinger model reveals that the groundstate is an Ising antiferromagnet in general.
The classical ferromagnet is analyzed in two dimensions via a mean-field treatment of the CP$^1$ model valid in the limit of low temperature and of weak magnetic field. At high skyrmion densities, we find that the magnetization begins to decrease linearly with temperature, but it then crosses over to a Curie-law at higher temperature. The comparison of these results with recent Knight-shift experiments on the quantum Hall state is fair.
The issue of the decoupling of extreme type-II superconducting thin films ($λ_L\rightarrow\infty$) with weakly Josephson-coupled layers in magnetic field parallel to the layers is considered via the corresponding frustrated $XY$ model used to describe the mixed phase in the critical regime. For the general case of arbitrary field orientations such that the perpendicular magnetic field component is larger than the decoupling cross-over scale characteristic of layered superconductors, we obtain independent parallel and perpendicular vortex lattices. Specializing to the double-layer case, we compute the parallel lower-critical field with entropic effects included, and find that it vanishes exponentially as temperature approaches the layer decoupling transition in zero-field. The parallel reversible magnetization is also calculated in this case, where we find that it shows a cross-over phenomenon as a function of parallel field in the intermediate regime of the mixed phase in lieu of a true layer-decoupling transition. It is argued that such is the case for any finite number of layers, since the isolated double layer represents the weakest link.
The equivalence between the Lawrence-Doniach model for films of extreme type-II layered superconductors and a generalization of the back-scattering model for spin-1/2 electrons in one dimension is demonstrated. This fermion analogy is then exploited to obtain an anomalous $H_{\parallel}^{-1}$ tail for the parallel equilibrium magnetization of the minimal double layer case in the limit of high parallel magnetic fields $H_{\parallel}$ for temperatures in the critical regime.
The entropic corrections to the flux-line energy of extreme type-II superconductors are computed using a schematic dual Villain model description of the flux quanta. We find that the temperature profile of the lower-critical field vanishes polynomially at the transition with an exponent $ν\cong 2/3$ in the isotropic case, while it exhibits an inflection point for the case of weakly coupled layers in parallel magnetic field. It is argued that vestiges of these effects have already been observed in high-temperature superconductors.
By exploiting the internal gauge-invariance intrinsic to a spin-charge separated electron, we show that such degrees of freedom must be confined in two-dimensional superconductors experiencing strong inter-electron repulsion. We also demonstrate that incipient confinement in the normal state can prevent chiral spin-fluctuations from destroying the cross-over between strange and psuedo-gap regimes in under-doped high-temperature superconductors. Last, we suggest that the negative Hall anomaly observed in these materials is connected with this confinement effect.
The thermally driven confinement-deconfinement transition exhibited by lattice quantum electrodynamics in two space dimensions is re-examined in the context of the statistical gauge-fields common to anyon superconductors and to spin-liquids. Particle-hole excitations in both systems are bound by a confining string at temperatures below the transition temperature $T_c$. We argue that $T_c$ coincides with the actual critical temperature for anyon superconductivity. The corresponding specific-heat contribution, however, shows a {\it smooth} peak just below $T_c$ characteristic of certain high-temperature superconductors.
The partition function of the double-layer $XY$ model in the (dual) Villain form is computed exactly in the limit of weak coupling between layers. Both layers are found to be locked together through the Berezinskii-Kosterlitz-Thouless transition, while they become decoupled well inside the normal phase. These results are recovered in the general case of a finite number of such layers. When re-interpreted in terms of the dual problems of lattice anyon superconductivity and of spin-liquids, they also indicate that the essential nature of the transition into the normal state found in two dimensions persists in the case of a finite number of weakly coupled layers.
The square lattice spin-1/2 antiferromagnet containing a dilute concentration, $δ$, of randomly placed ferromagnetic nearest-neighbor bonds is studied at low-temperature via non-linear $σ$-model techniques and by exact diagonalization. We generally find that long-range N\' eel order is destroyed above a critical strength in the defective ferromagnetic exchange coupling-constant given by $|K_c|/J\sim δ^{-1/2}$. We also observe large statistical fluctuations both in the spin-stiffness and in the antiferromagnetic structure-factor near this critical point, suggesting the onset of a spin-glass phase.
The slow zero-sound mode expected near the Mott transition in strongly interacting two-dimensional Fermi systems that are neutral is shown to persist as the physical sound mode in the case that the fermion carries electronic charge and is embedded in a positive ionic background. The latter sound velocity softens completely precisely at the Mott transition, indicating that a zone-center structural transition will occur in the system. We suggest that this phonon-softening mechanism is related to the structural transitions commonly observed in the oxide superconductors.
The spin-stiffness of frustrated spin-1/2 Heisenberg models in one and two dimensions is computed for the first time by exact diagonalizations on small clusters that implement spin-dependent twisted boundary conditions. Finite-size extrapolation to the thermodynamic limit yields a value of $0.14\pm 0.01$ for the spin-stiffness of the unfrustrated planar antiferromagnet. We also present a general discussion of the linear-response theory for spin-twists, which ultimately leads to the moment sum-rule.
A model for spin-charge separated superconductivity in two dimensions is introduced where the phases of the spinon and holon order parameters couple gauge-invariantly to a statistical gauge-field representing chiral spin-fluctuations. The model is analyzed in the continuum limit and in the low-temperature limit. In both cases we find that physical electronic phase correlations show a superconducting-normal phase transition of the Berezinskii-Kosterlitz-Thouless type, while statistical gauge-field excitations are found to be strictly gapless. The normal-to-superconductor phase boundary for this model is also obtained as a function of carrier density, where we find that its shape compares favorably with that of the experimentally observed phase diagram for the oxide superconductors.