Zero-variance principle for Monte Carlo algorithms

We present a general approach to greatly increase at little cost the efficiency of Monte Carlo algorithms. To each observable to be computed we associate a renormalized observable (improved estimator) having the same average but a different variance. By writing down the zero-variance condition a fundamental equation determining the optimal choice for the renormalized observable is derived (zero-variance principle for each observable separately). We show, with several examples including classical and quantum Monte Carlo calculations, that the method can be very powerful.Comment: 9 pages, Latex, to appear in Phys. Rev. Let

Application of the density matrix renormalization group method to finite temperatures and two-dimensional systems

The density matrix renormalization group (DMRG) method and its applications to finite temperatures and two-dimensional systems are reviewed. The basic idea of the original DMRG method, which allows precise study of the ground state properties and low-energy excitations, is presented for models which include long-range interactions. The DMRG scheme is then applied to the diagonalization of the quantum transfer matrix for one-dimensional systems, and a reliable algorithm at finite temperatures is formulated. Dynamic correlation functions at finite temperatures are calculated from the eigenvectors of the quantum transfer matrix with analytical continuation to the real frequency axis. An application of the DMRG method to two-dimensional quantum systems in a magnetic field is demonstrated and reliable results for quantum Hall systems are presented.Comment: 33 pages, 18 figures; corrected Eq.(117

Enhancement of Pairing Correlation and Spin Gap through Suppression of Single-Particle Dispersion in One-Dimensional Models

We investigate the effects of suppression of single-particle dispersion near the Fermi level on the spin gap and the singlet-pairing correlation by using the exact diagonalization method for finite-size systems. We consider strongly correlated one-dimensional models, which have flat band dispersions near wave number k=\pi/2, if the interactions are switched off. Our results for strongly correlated models show that the spin gap region expands as the single-particle dispersion becomes flatter. The region where the singlet-pairing correlation is the most dominant also expands in models with flatter band dispersions. Based on our numerical results, we propose a pairing mechanism induced by the flat-band dispersion.Comment: 5 pages, including 5 eps figures, to appear in J.Phys.Soc.Jpn Vol.69 No.

Moduli Spaces of Cold Holographic Matter

We use holography to study (3+1)-dimensional N=4 supersymmetric Yang-Mills theory with gauge group SU(Nc), in the large-Nc and large-coupling limits, coupled to a single massless (n+1)-dimensional hypermultiplet in the fundamental representation of SU(Nc), with n=3,2,1. In particular, we study zero-temperature states with a nonzero baryon number charge density, which we call holographic matter. We demonstrate that a moduli space of such states exists in these theories, specifically a Higgs branch parameterized by the expectation values of scalar operators bilinear in the hypermultiplet scalars. At a generic point on the Higgs branch, the R-symmetry and gauge group are spontaneously broken to subgroups. Our holographic calculation consists of introducing a single probe Dp-brane into AdS5 times S^5, with p=2n+1=7,5,3, introducing an electric flux of the Dp-brane worldvolume U(1) gauge field, and then obtaining explicit solutions for the worldvolume fields dual to the scalar operators that parameterize the Higgs branch. In all three cases, we can express these solutions as non-singular self-dual U(1) instantons in a four-dimensional space with a metric determined by the electric flux. We speculate on the possibility that the existence of Higgs branches may point the way to a counting of the microstates producing a nonzero entropy in holographic matter. Additionally, we speculate on the possible classification of zero-temperature, nonzero-density states described holographically by probe D-branes with worldvolume electric flux.Comment: 56 pages, 8 PDF images, 4 figure

Quantification of volumetric morphometry and optical property in the cortex of human cerebellum at micrometer resolution

The surface of the human cerebellar cortex is much more tightly folded than the cerebral cortex. Volumetric analysis of cerebellar morphometry in magnetic resonance imaging studies suffers from insufficient resolution, and therefore has had limited impact on disease assessment. Automatic serial polarization-sensitive optical coherence tomography (as-PSOCT) is an emerging technique that offers the advantages of microscopic resolution and volumetric reconstruction of large-scale samples. In this study, we reconstructed multiple cubic centimeters of ex vivo human cerebellum tissue using as-PSOCT. The morphometric and optical properties of the cerebellar cortex across five subjects were quantified. While the molecular and granular layers exhibited similar mean thickness in the five subjects, the thickness varied greatly in the granular layer within subjects. Layer-specific optical property remained homogenous within individual subjects but showed higher cross-subject variability than layer thickness. High-resolution volumetric morphometry and optical property maps of human cerebellar cortex revealed by as-PSOCT have great potential to advance our understanding of cerebellar function and diseases

Control of Superconducting Correlations in High-Tc Cuprates

A strategy to enhance d-wave superconducting correlations is proposed based on our numerical study for correlated electron models for high-Tc cuprates. We observe that the pairing is enhanced when the single-electron level around (pi,0) is close to the Fermi level E_F, while the d-wave pairing interaction itself contains elements to disfavor the pairing due to shift of the (pi,0)-level. Angle-resolved photoemission results in the cuprates are consistently explained in the presence of the d-wave pairing interaction. Our proposal is the tuning of the (pi,0)-level under the many-body effects to E_F by optimal design of band structure.Comment: 4 pages, 6 eps figure

Superconductivity from correlated hopping

We consider a chain described by a next-nearest-neighbor hopping combined with a nearest-neighbor spin flip. In two dimensions this three-body term arises from a mapping of the three-band Hubbard model for CuO$_2$ planes to a generalized $t-J$ model and for large O-O hopping favors resonance-valence-bond superconductivity of predominantly $d$-wave symmetry. Solving the ground state and low-energy excitations by analytical and numerical methods we find that the chain is a Luther-Emery liquid with correlation exponent $K_{\rho} = (2-n)^2/2$, where $n$ is the particle density.Comment: 10 pages, RevTeX 3.0 + 2 PostScript figs. Accepted for publication in Phys.Rev.

Thermodynamic and diamagnetic properties of weakly doped antiferromagnets

Finite-temperature properties of weakly doped antiferromagnets as modeled by the two-dimensional t-J model and relevant to underdoped cuprates are investigated by numerical studies of small model systems at low doping. Two numerical methods are used: the worldline quantum Monte Carlo method with a loop cluster algorithm and the finite-temperature Lanczos method, yielding consistent results. Thermodynamic quantities: specific heat, entropy and spin susceptibility reveal a sizeable perturbation induced by holes introduced into a magnetic insulator, as well as a pronounced temperature dependence. The diamagnetic susceptibility introduced by coupling of the magnetic field to the orbital current reveals an anomalous temperature dependence, changing character from diamagnetic to paramagnetic at intermediate temperatures.Comment: LaTeX, 10 pages, 10 figures, submitted to Phys. Rev.

The Operator Product Expansion of the Lowest Higher Spin Current at Finite N

For the N=2 Kazama-Suzuki(KS) model on CP^3, the lowest higher spin current with spins (2, 5/2, 5/2,3) is obtained from the generalized GKO coset construction. By computing the operator product expansion of this current and itself, the next higher spin current with spins (3, 7/2, 7/2, 4) is also derived. This is a realization of the N=2 W_{N+1} algebra with N=3 in the supersymmetric WZW model. By incorporating the self-coupling constant of lowest higher spin current which is known for the general (N,k), we present the complete nonlinear operator product expansion of the lowest higher spin current with spins (2, 5/2, 5/2, 3) in the N=2 KS model on CP^N space. This should coincide with the asymptotic symmetry of the higher spin AdS_3 supergravity at the quantum level. The large (N,k) 't Hooft limit and the corresponding classical nonlinear algebra are also discussed.Comment: 62 pages; the footnotes added, some redundant appendices removed, the presentations in the whole paper improved and to appear in JHE

Anomalous Zero Sound

We show that the anomalous term in the current, recently suggested by Son and Yamamoto, modifies the structure of the zero sound mode in the Fermi liquid in a magnetic field.Comment: 14 pages, 2 figure