A Critique of Two Metals

I argue that the conflict between the fermi-liquid and non-fermi-liquid metallic states viewed by Anderson as the central intellectual issue of cuprate superconductivity, and which motivates the recent criticism by Baskaran and Anderson [cond-mat/9706076] of the work of Zhang [cond-mat/9610140], is a fundamentally wrong concept. All experimental evidence points to adiabatic continuability of the strange metal into a conventional one, and thus to one metallic phase rather than two, and all attempts to account theoretically for the existence of a luttinger-liquid at zero temperature in spatial dimension greater than 1 have failed. I discuss the underlying reasons for this failure and then argue that the true higher-dimensional generalization of the luttinger-liquid behavior is a propensity of the system to order. I speculate about how the conflict between antiferromagnetism and superconductivity, the two principal kinds of order in this problem, might result in both the observed zero-temperature phase diagram of the cuprates and the luttinger-liquid phenomenology, i.e. the breakup of the electron into spinons and holons in certain regimes of doping and energy. The key idea is a quantum critical point regulating a first-order transition between these phases and toward which one is first attracted under renormalization before bifurcating between the two phases.Comment: 9 pages of RevTeX, 4 eps figure

Tunneling Gap as Evidence for Time-Reversal Symmetry Breaking at Surfaces of High-Temperature Superconductors

It is argued that recent Josephson junction and point-contact tunneling experiments, interpreted as intended by their authors, indicate that time-reversal symmetry breaking occurs at surfaces of cuprate superconductors. The variation among experiments and the failure of previous searches to find $T$-violation are ascribed to disorder and effects of 3-dimensionality. The ``anyon" approach to the $t$-$J$ model is shown to predict a conventional BCS order parameter of $d_{x^2-y^2} + i \epsilon \ d_{xy}$ symmetry, with $\epsilon$ roughly 3 times the doping fraction $\delta$, which is consistent with these experiments but not demonstrated by them.Comment: REVTex 3.0, 11 pages, no figure

Hiawatha's Valence Bonding

There is increasing circumstantial evidence that the cuprate superconductors, and correlated-electron materials generally, defy simple materials categorization because of their proximity to one or more continuous zero-temperature phase transitions. This implies that the fifteen-year confusion about the cuprates is not fundamental at all but simply overinterpreted quantum criticality--an effect that seems mysterious by virtue of its hypersensitivity to perturbations, i.e. to sample imperfections in experiment and small modifications of approximation schemes in theoretical modeling, but is really just an unremarkable phase transition of some kind masquerading as something important, a sheep in wolf's clothing. This conclusion is extremely difficult for most physicists even to think about because it requires admitting that an identifiable physical phenomenon might cause the scientific method to fail in some cases. For this reason I have decided to explain the problem in a way that is nonthreatening, easy to read, and fun--as a satire modeled after a similar piece of Lewis Carroll's I once read. My story is humorous fiction. Any similarity of the characters to living persons is accidental. My apologies to Henry W. Longfellow.Comment: 15 pages of RevTeX, 14 eps figure

Critical Waves and the Length Problem of Biology

It is pointed out that the mystery of how biological systems measure their lengths vanishes away if one premises that they have discovered a way to generate linear waves analogous to compressional sound. These can be used to detect length at either large or small scales using echo timing and fringe counting. It is shown that suitable linear chemical potential waves can, in fact, be manufactured by tuning to criticality conventional reaction-diffusion with a small number substances. Min oscillations in E. coli are cited as precedent resonant length measurement using chemical potential waves analogous to laser detection. Mitotic structures in eucaryotes are identified as candidates for such an effect at higher frequency. The engineering principle is shown to be very general and functionally the same as that used by hearing organs. PNAS Significance Statement: This paper invokes physical principles to address the question of how living things might use reaction-diffusion to measure out and regulate the many thousands of lengths required to make their body parts and internal organs. It argues that two ideas have been missing. One is that oscillation is necessary to achieve the necessary design stability and plasticity. The other is that the system must be tuned to criticality to stabilize the propagation velocity, thus enabling clocks to function as meter sticks. The broader significance is twofold: First, a fundamental piece of the machinery of life is probably invisible to present-day biochemical methods because they are too slow. Second, the simplicity of growth and form identified a century ago by D'Arcy Thompson is probably a symptom of biological engineering strategies, not primitive law.Comment: 8 pages, 5 figures, submitted to PNA

Parallels Between Quantum Antiferromagnetism and the Strong Interactions

I argue that there is a connection between quantum antiferromagnetism and the strong interactions. The underlying idea is that the t-J Hamiltonian and other models commonly studied in the context of cuprate superconductivity are near a quantum critical point at which quark-like objects and gauge fields with which they interact become the true elementary excitations at low energy scales. Away from the critical point these bind at low energy into familiar collective modes of various ordered states. As evidence I cite the ``semiconducting'' behavior of the f-sum rule at low doping, large-scale structure in the electron propagator, disappearance of the quasiparticle pole at small values of J/t, string resonances above the quasiparticle pole, and the physical similarity of the alleged quark-like objects to the spinon and holon excitations of 1-dimensional spin-1/2 antiferromagnets.Comment: 10 pages of LaTeX, 6 eps figure

Reply to the comment to Phy. Rev. Lett. 86, 3392 (2001) (cond-mat/0511607)

We provide our reply to the comment by Greiter and Schuricht (cond-mat/0511607).Comment: 1 pag

Spectroscopy of Matter Near Criticality

We propose that the finite-frequency susceptibility of matter near a class of zero-temperature phase transition exhibits distinctive excitonic structure similar to meson resonances. The specific case of a Landau level undergoing a transition to antiferromagnetism is considered as a prototype. A physical analogy is drawn between the behavior calculated for such systems by epsilon-expansion techniques and the behavior of 1-dimensional spin chains calculated by exact diagonalization. It is proposed that the correct low-energy description of such critical points is a relativistic gauge theory in spin-fractionalized coordinates, and conversely that the application of gauge theories to solids amounts to perturbation theory about critical points.Comment: 4 pages of RevTeX, 4 eps figure

Differential light scattering: probing the sonoluminescence collapse

We have developed a light scattering technique based on differential measurement and polarization (differential light scattering, DLS) capable in principle of retrieving timing information with picosecond resolution without the need for fast electronics. DLS was applied to sonoluminescence, duplicating known results (sharp turnaround, self-similar collapse); the resolution was limited by intensity noise to about 0.5 ns. Preliminary evidence indicates a smooth turnaround on a time scale of a few hundred picoseconds, and suggests the existence of subnanosecond features within a few nanoseconds of the turnaround.Comment: 5 pages, 4 EPS figures (LaTeX 2.09, RevTeX 3.1

The magnetic susceptibility of the t-J model at low hole doping

We compute the dynamical magnetic susceptibility of the t-J model in its commensurate flux phase at low hole doping. We compare the calculations with experiments and exact diagonalization studies.Comment: 4 pages REVTeX, 4 encapsulated postscript figures (included

Quantum Number Fractionalization in Antiferromagnets

This is a pedagogical introduction to the mathematics of 1-dimensional spin-1/2 antiferromagnets. Topics covered include the Haldane-Shastry Hamiltonian, vector ``supercharges'', conserved spin currents, spinons, the supersymmetric Kuramoto-Yokoyama Hamiltonian, and holons.Comment: 40 pages of LaTeX, 8 eps figure