Scaling Regimes, Crossovers, and Lattice Corrections in 2D Heisenberg Antiferromagnets

We study scaling behavior in 2D, S=1/2 and S=1 Heisenberg antiferromagnets using the data on full q-dependences of the equal time structure factor and the static susceptibility, calculated through high temperature expansions. We also carry out comparisons with a model of two coupled S=1/2 planes with the interlayer coupling tuned to the T=0 critical point. We separately determine the spin-wave velocity c and mass $m=c/\xi$, in addition to the correlation length, $\xi$, and find that c is temperature dependent; only for T\alt JS, it approaches its known T=0 value $c_0$. Despite this temperature dependent spin-wave velocity, full q- and $\omega$-dependences of the dynamical susceptibility $\chi(\bf q,\omega)$ agree with the universal scaling functions computable for the $\sigma$-model, for temperatures upto $T_0 \sim 0.6c_0/a$. Detailed comparisons show that below $T_0$ the S=1 model is in the renormalized classical (RC) regime, the two plane model is in the quantum critical (QC) regime, and the S=1/2 model exhibits a RC-QC crossover, centered at T=0.55J. In particular, for the S=1/2 model above this crossover and for the two-plane model at all T, the spin-wave mass is in excellent agreement with the universal QC prediction, $m\simeq 1.04\,T$. In contrast, for the S=1/2 model below the RC-QC crossover, and for the S=1 model at all T, the behavior agrees with the known RC expression. For all models nonuniversal behavior occurs above $T\sim 0.6c_0/a$. Our results strongly support the conjecture of Chubukov and Sachdev that the S=1/2 model is close to the T=0 critical point to exhibit QC behavior.Comment: 13 pages, REVTeX with attached PostScript (see file for addl info

Order-Disorder Transition in a Two-Layer Quantum Antiferromagnet

We have studied the antiferromagnetic order -- disorder transition occurring at $T=0$ in a 2-layer quantum Heisenberg antiferromagnet as the inter-plane coupling is increased. Quantum Monte Carlo results for the staggered structure factor in combination with finite-size scaling theory give the critical ratio $J_c = 2.51 \pm 0.02$ between the inter-plane and in-plane coupling constants. The critical behavior is consistent with the 3D classical Heisenberg universality class. Results for the uniform magnetic susceptibility and the correlation length at finite temperature are compared with recent predictions for the 2+1-dimensional nonlinear $\sigma$-model. The susceptibility is found to exhibit quantum critical behavior at temperatures significantly higher than the correlation length.Comment: 11 pages (5 postscript figures available upon request), Revtex 3.

Violation of the Wiedemann-Franz Law in a Large-N Solution of the t-J Model

We show that the Wiedemann-Franz law, which holds for Landau Fermi liquids, breaks down in a large-n treatment of the t-J model. The calculated ratio of the in-plane thermal and electrical conductivities agrees quantitatively with experiments on the normal state of the electron-doped Pr_{2-x}Ce_xCuO_4 (x = 0.15) cuprate superconductor. The violation of the Wiedemann-Franz law in the uniform phase contrasts with other properties of the phase that are Fermi liquid like.Comment: 4 pages, 2 figures. Typos corrected, one added reference, revised discussion of experiment on 214 cuprate material (x = 0.06

Disorder Induced Phase Transition in a Random Quantum Antiferromagnet

A two-dimensional Heisenberg model with random antiferromagnetic nearest-neighbor exchange is studied using quantum Monte Carlo techniques. As the strength of the randomness is increased, the system undergoes a transition from an antiferromagnetically ordered ground state to a gapless disordered state. The finite-size scaling of the staggered structure factor and susceptibility is consistent with a dynamic exponent $z = 2$.Comment: Revtex 3.0, 10 pages + 5 postscript figures available upon request, UCSBTH-94-1

The phase diagram of quantum systems: Heisenberg antiferromagnets

A novel approach for studying phase transitions in systems with quantum degrees of freedom is discussed. Starting from the microscopic hamiltonian of a quantum model, we first derive a set of exact differential equations for the free energy and the correlation functions describing the effects of fluctuations on the thermodynamics of the system. These equations reproduce the full renormalization group structure in the neighborhood of a critical point keeping, at the same time, full information on the non universal properties of the model. As a concrete application we investigate the phase diagram of a Heisenberg antiferromagnet in a staggered external magnetic field. At long wavelengths the known relationship to the Quantum Non Linear Sigma Model naturally emerges from our approach. By representing the two point function in an approximate analytical form, we obtain a closed partial differential equation which is then solved numerically. The results in three dimensions are in good agreement with available Quantum Monte Carlo simulations and series expansions. More refined approximations to the general framework presented here and few applications to other models are briefly discussed.Comment: 17 pages, 7 figure

Fractional helicity, Lorentz symmetry breaking, compactification and anyons

We construct the covariant, spinor sets of relativistic wave equations for a massless field on the basis of the two copies of the R-deformed Heisenberg algebra. For the finite-dimensional representations of the algebra they give a universal description of the states with integer and half-integer helicity. The infinite-dimensional representations correspond formally to the massless states with fractional (real) helicity. The solutions of the latter type, however, break down the (3+1)$D$ Poincar\'e invariance to the (2+1)$D$ Poincar\'e invariance, and via a compactification on a circle a consistent theory for massive anyons in $D$=2+1 is produced. A general analysis of the ``helicity equation'' shows that the (3+1)$D$ Poincar\'e group has no massless irreducible representations with the trivial non-compact part of the little group constructed on the basis of the infinite-dimensional representations of sl(2,\CC). This result is in contrast with the massive case where integer and half-integer spin states can be described on the basis of such representations, and means, in particular, that the (3+1)$D$ Dirac positive energy covariant equations have no massless limit.Comment: 19 pages; minor changes, references added. To appear in Nucl. Phys.

Pairing symmetry of superconducting graphene

The possibility of intrinsic superconductivity in alkali-coated graphene monolayers has been recently suggested theoretically. Here, we derive the possible pairing symmetries of a carbon honeycomb lattice and discuss their phase diagram. We also evaluate the superconducting local density of states (LDOS) around an isolated impurity. This is directly related to scanning tunneling microscopy experiments, and may evidence the occurrence of unconventional superconductivity in graphene.Comment: Eur. Phys. J. B, to appea

Crossover and scaling in a nearly antiferromagnetic Fermi liquid in two dimensions

We consider two-dimensional Fermi liquids in the vicinity of a quantum transition to a phase with commensurate, antiferromagnetic long-range order. Depending upon the Fermi surface topology, mean-field spin-density-wave theory predicts two different types of such transitions, with mean-field dynamic critical exponents $z=1$ (when the Fermi surface does not cross the magnetic zone boundary, type $A$) and $z=2$ (when the Fermi surface crosses the magnetic zone boundary, type $B$). The type $A$ system only displays $z=1$ behavior at all energies and its scaling properties are similar (though not identical) to those of an insulating Heisenberg antiferromagnet. Under suitable conditions precisely stated in this paper, the type $B$ system displays a crossover from relaxational behavior at low energies to type $A$ behavior at high energies. A scaling hypothesis is proposed to describe this crossover: we postulate a universal scaling function which determines the entire, temperature-, wavevector-, and frequency-dependent, dynamic, staggered spin susceptibility in terms of 4 measurable, $T=0$, parameters (determining the distance, energy, and order parameter scales, plus one crossover parameter). The scaling function contains the full scaling behavior in all regimes for both type $A$ and $B$ systems. The crossover behavior of the uniform susceptibility and the specific heat is somewhat more complicated and is also discussed. Explicit computation of the crossover functions is carried out in a large $N$ expansion on a mean-field model. Some new results for the critical properties on the ordered side of the transition are also obtained in a spin-density wave formalism. The possible relevance of our results to the doped cuprate compounds is briefly discussed.Comment: 20 pages, REVTeX, 6 figures (uuencoded compressed PostScript file for figures is appended

Quantitative Treatment of Decoherence

We outline different approaches to define and quantify decoherence. We argue that a measure based on a properly defined norm of deviation of the density matrix is appropriate for quantifying decoherence in quantum registers. For a semiconductor double quantum dot qubit, evaluation of this measure is reviewed. For a general class of decoherence processes, including those occurring in semiconductor qubits, we argue that this measure is additive: It scales linearly with the number of qubits.Comment: Revised version, 26 pages, in LaTeX, 3 EPS figure

An Integrated TCGA Pan-Cancer Clinical Data Resource to Drive High-Quality Survival Outcome Analytics

For a decade, The Cancer Genome Atlas (TCGA) program collected clinicopathologic annotation data along with multi-platform molecular profiles of more than 11,000 human tumors across 33 different cancer types. TCGA clinical data contain key features representing the democratized nature of the data collection process. To ensure proper use of this large clinical dataset associated with genomic features, we developed a standardized dataset named the TCGA Pan-Cancer Clinical Data Resource (TCGA-CDR), which includes four major clinical outcome endpoints. In addition to detailing major challenges and statistical limitations encountered during the effort of integrating the acquired clinical data, we present a summary that includes endpoint usage recommendations for each cancer type. These TCGA-CDR findings appear to be consistent with cancer genomics studies independent of the TCGA effort and provide opportunities for investigating cancer biology using clinical correlates at an unprecedented scale. Analysis of clinicopathologic annotations for over 11,000 cancer patients in the TCGA program leads to the generation of TCGA Clinical Data Resource, which provides recommendations of clinical outcome endpoint usage for 33 cancer types