Bond asymmetry and high-Tc superconductivity

Journal ArticleWe propose a simple mechanism, anchored in weak-coupling BCS theory, which ties together the following facts: high Tc; quasi two dimensionality; orthorhombic distortion and/or disordered lines of oxygen; proximity to a metal-insulator transition; and anomalously small isotope effects

Summing the Instanton Series in N=2 Superconformal Large-N QCD

We consider the multi-instanton collective coordinate integration measure in N=2 supersymmetric SU(N) gauge theory with N_F fundamental hypermultiplets. In the large-N limit, at the superconformal point where N_F=2N and all VEVs are turned off, the k-instanton moduli space collapses to a single copy of AdS_5*S^1. The resulting k-instanton effective measure is proportional to N^{1/2} g^4 Z_k^(6), where Z_k^(6) is the partition function of N=(1,0) SYM theory in six dimensions reduced to zero dimensions. The multi-instanton can in fact be summed in closed form. As a hint of an AdS/CFT duality, with the usual relation between the gauge theory and string theory parameters, this precisely matches the normalization of the charge-k D-instanton measure in type IIB string theory compactified to six dimensions on K3 with a vanishing two-cycle.Comment: 12 pages, amslate

Simulations of Information Transport in Spin Chains

Transport of quantum information in linear spin chains has been the subject of much theoretical work. Experimental studies by nuclear spin systems in solid-state by NMR (a natural implementation of such models) is complicated since the dipolar Hamiltonian is not solely comprised of nearest-neighbor XY-Heisenberg couplings. We present here a similarity transformation between the XY-Heisenberg Hamiltonian and the grade raising Hamiltonian, an interaction which is achievable with the collective control provided by radio-frequency pulses in NMR. Not only does this second Hamiltonian allows us to simulate the information transport in a spin chain, but it also provides a means to observe its signature experimentally

Inhomogeneous Nuclear Spin Flips

We discuss a feedback mechanism between electronic states in a double quantum dot and the underlying nuclear spin bath. We analyze two pumping cycles for which this feedback provides a force for the Overhauser fields of the two dots to either equilibrate or diverge. Which of these effects is favored depends on the g-factor and Overhauser coupling constant A of the material. The strength of the effect increases with A/V_x, where V_x is the exchange matrix element, and also increases as the external magnetic field B_{ext} decreases.Comment: 5 pages, 4 figures (jpg

Canonical representation for electrons and its application to the Hubbard model

A new representation for electrons is introduced, in which the electron operators are written in terms of a spinless fermion and the Pauli operators. This representation is canonical, invertible and constraint-free. Importantly, it simplifies the Hubbard interaction. On a bipartite lattice, the Hubbard model is reduced to a form in which the exchange interaction emerges simply by decoupling the Pauli subsystem from the spinless fermion bath. This exchange correctly reproduces the large $U$ superexchange. Also derived, for $U=\pm\infty$, is the Hamiltonian to study Nagaoka ferromagnetism. In this representation, the infinite-$U$ Hubbard problem becomes elegant and easier to handle. Interestingly, the ferromagnetism in Hubbard model is found to be related to the gauge invariance of the spinless fermions. Generalization of this representation for the multicomponent fermions, a new representation for bosons, the notion of a `soft-core' fermion, and some interesting unitary transformations are introduced and discussed in the appendices.Comment: 10+ pages, 3 Figure

Anomalous dynamics in two- and three- dimensional Heisenberg-Mattis spin glasses

We investigate the spectral and localization properties of unmagnetized Heisenberg-Mattis spin glasses, in space dimensionalities $d=2$ and 3, at T=0. We use numerical transfer-matrix methods combined with finite-size scaling to calculate Lyapunov exponents, and eigenvalue-counting theorems, coupled with Gaussian elimination algorithms, to evaluate densities of states. In $d=2$ we find that all states are localized, with the localization length diverging as $\omega^{-1}$, as energy $\omega \to 0$. Logarithmic corrections to density of states behave in accordance with theoretical predictions. In $d=3$ the density-of-states dependence on energy is the same as for spin waves in pure antiferromagnets, again in agreement with theoretical predictions, though the corresponding amplitudes differ.Comment: RevTeX4, 9 pages, 9 .eps figure

Baryons with Many Colors and Flavors

Using recently-developed diagrammatic techniques, I derive some general results concerning baryons in the $1/N$ expansion, where $N$ is the number of QCD colors. I show that the spin-flavor relations which hold for baryons in the large-$N$ limit, as well as the form of the corrections to these relations at higher orders in $1/N$, hold even if $N_F / N \sim 1$, where $N_F$ is the number of light quark flavors. I also show that the amplitude for a baryon to emit $n$ mesons is $O(1 / N^{n / 2 - 1})$, and that meson loops attached to baryon lines are unsupressed in the large-$N$ limit, independent of $N_F$. For $N_F > 2$, there are ambiguities in the extrapolation away from $N = 3$ because the baryon flavor multiplets for a given spin grow with $N$. I argue that the $1/N$ expansion is valid for baryons with spin $O(1)$ and {\it arbitrary} flavor quantum numbers, including e.g. baryons with isospin and/or strangeness $O(N)$. This allows the formulation of a large-$N$ expansion in which it is not necessary to identify the physical baryons with particular large-$N$ states. $SU(N_F)$ symmetry can be made manifest to all orders in $1/N$, yet group theory factors must be evaluated explicitly only for $N_F = N = 3$. To illustrate this expansion, I consider the non-singlet axial currents, baryon mass splittings, and matrix elements of \mybar ss and \mybar s \gam_\mu \gam_5 s in the nucleon.Comment: 19 pages, plain TeX, 4 uuencoded postscrip figures, LBL-35539, NSF-ITP-94-4

Valley Bifurcation in an O(3)O(3) σ\sigma Model: Implications for High-Energy Baryon Number Violation

The valley method for computing the total high-energy anomalous cross section $S_{anom}$ is the extension of the optical theorem to the case of instanton-antiinstanton backgrounds. As a toy model for baryon number violation in Electroweak theory, we consider a version of the $O(3)$ $\sigma$ model in which the conformal invariance is broken perturbatively. We show that at a critical energy the saddle-point values of the instanton size and instanton-antiinstanton separation bifurcate into complex conjugate pairs. This nonanalytic behavior signals the breakdown of the valley method at an energy where $S_{anom}$ is still exponentially suppressed. (Figures replaced 5/3/93).Comment: (14 pages, Los Alamos Preprint LA-UR-93-811). 3 uuencoded figures include

Soluble extension of the Ising model

Journal ArticleIn this note we wish to relate a somewhat trivial, but surprising, soluble extension of the multidimensional Ising model. Our extension was motivated by recent experiments on a real material, dysprosium aluminum garnet (DyAlG), which closely resembles an ideal three-dimensional Ising model,1 except for what appeared to be one unfortunate detail: The electronic (Ising) spins are connected not just to their electronic neighbors, but also to their own dysprosium nuclei by a fairly large hyperfine interaction