Bulletin of the American Physical Society
2007 APS March Meeting
Volume 52, Number 1
Monday–Friday, March 5–9, 2007; Denver, Colorado
Session H22: GSNP Student Award Session and Exactly Solvable Models |
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Sponsoring Units: GSNP Chair: Sidney Redner, Boston University Room: Colorado Convention Center 108 |
Tuesday, March 6, 2007 8:00AM - 8:12AM |
H22.00001: Probing large length scale behavior of spin glasses with patchwork dynamics Creighton Thomas See MAR07-2006-004072 in Session X29. [Preview Abstract] |
Tuesday, March 6, 2007 8:12AM - 8:24AM |
H22.00002: The Product Space and its Consequences for Economic Growth Cesar Hidalgo See MAR07-2006-000468 in Session A22. [Preview Abstract] |
Tuesday, March 6, 2007 8:24AM - 8:36AM |
H22.00003: Strain Hardening and Plastic Deformation in Polymer Glasses Robert S. Hoy See MAR07-2006-005404 in Session X25. [Preview Abstract] |
Tuesday, March 6, 2007 8:36AM - 8:48AM |
H22.00004: A Statistical Ensemble for Soft Granular Matter Silke Henkes See MAR07-2006-002889 in Session J22. [Preview Abstract] |
Tuesday, March 6, 2007 8:48AM - 9:00AM |
H22.00005: Liquid metal flow in a spherical shell: recent results Santiago Andres Triana See MAR07-2006-005434 in Session K1. [Preview Abstract] |
Tuesday, March 6, 2007 9:00AM - 9:12AM |
H22.00006: Universality of Synchrony Kevin Wood See MAR07-2006-006788 in Session S22. [Preview Abstract] |
Tuesday, March 6, 2007 9:12AM - 9:24AM |
H22.00007: Diameter of Random Clusters in Potts Models D. W. Blair, Jon Machta We report measurements of cluster diameter -- the maximum over all pairs of connected vertices of the minimum path length between the vertices -- in numerical simulations of random clusters in q-state Potts models in two and three dimensions. Although the diameter is not a thermodynamic quantity, it is expected to display critical behavior for Potts models models as the size of the largest cluster diverges at the critical point. We have developed an efficient algorithm for measuring the diameter, and have obtained results using the Swendsen-Wang algorithm both for equilibrating the model and for identifying clusters. [Preview Abstract] |
Tuesday, March 6, 2007 9:24AM - 9:36AM |
H22.00008: DNA unzipping and the unbinding of directed polymers in a random media Yariv Kafri, Anatoli Polkovnikov We consider the unbinding of a directed polymer in a random media from a wall in $d=1+1$ dimensions and a simple one-dimensional model for DNA unzipping. Using the replica trick we show that the restricted partition functions of these problems are {\em identical} up to an overall normalization factor. Our finding gives an example of a generalization of the stochastic matrix form decomposition to disordered systems; a method which effectively allows to reduce the dimensionality of the problem. The equivalence between the two problems, for example, allows us to derive the probability distribution for finding the directed polymer a distance $z$ from the wall. We discuss implications of these results for the related Kardar-Parisi-Zhang equation and the asymmetric exclusion process. [Preview Abstract] |
Tuesday, March 6, 2007 9:36AM - 9:48AM |
H22.00009: Molecular-field theory method for evaluating critical points of Ising model Kirill K. Zhuravlev The molecular-field theory is one of the most common approximations used to calculate properties of materials with Ising model. A generalization, improving the previous results of molecular-field theory, is proposed. This method distinguishes between two lattices with different geometries but equal number of nearest neighbors, such as square and diamond, and triangular and simple cubic lattices, a result, which is missing from most other mean-field approaches. Spontaneous magnetization as a function of temperature shows remarkable deviations from mean-field type of behavior and is in good agreement with exact results. [Preview Abstract] |
Tuesday, March 6, 2007 9:48AM - 10:00AM |
H22.00010: Extended universality and information theory Cintia Lapilli, Peter Pfeifer, Carlos Wexler Recently, we have discovered the {\em extended universality}, where entire families of systems behave identically both near and away from a critical point [1] if the temperature and a parameter describing the interaction between neighboring units of the system exceed a certain value. In the regime where the extended universality is present $T > T_{\rm eu}$, the thermodynamics of the system is {\em degenerate} in the sense that all thermodynamic observables of each system are independent of the interaction parameter, and a system with discrete degrees of freedom (i.e. the $p$-state clock model) behaves (from the point of view of all thermodynamic observables) exactly as if these degrees of freedom were continuous (i.e. the planar rotor or XY model). To the best of our knowledge there is only one comparable case where a similar sharp switchover between a discrete and a continuum description of a system is observed: this is in the areas of telecommunications, digital signal processing, and information theory: the Nyquist-Shannon sampling theorem [2]. In this talk we will give an interpretation of the extended universality in terms of the Nyquistâ€“Shannon sampling theorem. \noindent [1] Universality away from critical points in two-dimensional phase transitions, C.M. Lapilli, P. Pfeifer, and C. Wexler, Phys. Rev. Lett. {\bf 96}, 140603 (2006). \noindent [2] H. Nyquist, Trans. AIEE {\bf 47}, 617 (1928); [3] C.E. Shannon, Proc. Institute of Radio Engineers {\bf 37}, 10 (1949). [Preview Abstract] |
Tuesday, March 6, 2007 10:00AM - 10:12AM |
H22.00011: Interacting anyons in one dimension: The Fibonacci chain Andreas Ludwig, Adrian Feiguin, Simon Trebst, Matthias Troyer, Alexei Kitaev, Zhenghan Wang, Michael Freedman We discuss generalizations of quantum spin chains using anyonic degrees of freedom. The simplest model for interacting anyons in one dimension is closely related to the Fibonacci topological quantum field theory. The Hamiltonian favors neighboring anyons to fuse into the trivial channel, similar to the quantum Heisenberg spin chain favoring neighboring spins to form spin singlets. Numerical simulations show that the model is critical with a dynamical critical exponent z=1. It is described by a conformal field theory with central charge c=7/10. An exact solution of this model is given by mapping to a Temperley-Lieb algebra. We discuss the excitation spectra for finite systems, and generalizations to dimerized chains and ladders. [Preview Abstract] |
Tuesday, March 6, 2007 10:12AM - 10:24AM |
H22.00012: Zeros of the dispersion relation of the elementary excitation and the correlation length of strongly correlated quantum systems Yuichi Nakamura We argue that the imaginary part of a zero of the dispersion relation of the elementary excitation of quantum systems is equal to the inverse correlation length. We confirm the relation for the Hubbard model[1] in the half-filled case; it has been confirmed only for the S=1/2 antiferromagnetic XXZ chain[2]. In order to search zeros of the dispersion relation in the complex momentum space efficiently, we introduce a non-Hermitian generalization of quantum systems by adding an imaginary vector potential ig to the momentum operator[3]. We also show for the half-filled Hubbard model the reason why the non-Hermitian critical point[4] is equal to the inverse correlation length[5] by noting the dispersion relation of the charge excitation. \newline [1] Y. Nakamura and N. Hatano, in preparation. \newline [2] K. Okunishi, Y. Akutsu, N. Akutsu and T. Yamamoto, Phys. Rev. B 64 (2001) 104432. \newline [3] Y. Nakamura and N. Hatano, Physica B 378-380 (2006) 292; J. Phys. Soc. Jpn. 75 (2006) 114001. \newline [4] T. Fukui and N. Kawakami, Phys. Rev. B 58 (1998) 16051. \newline [5] C. A. Stafford and A. J. Millis, Phys. Rev. B 48 (1993) 1409. [Preview Abstract] |
Tuesday, March 6, 2007 10:24AM - 10:36AM |
H22.00013: Gauge covariant Keldysh formulation of Wigner representation through deformational quantization Naoyuki Sugimoto, Shigeki Onoda, Naoto Nagaosa Non-linear responses such as nonlinear optical effects are of great current interests from the fundamental physics and application viewpoints. Therefore a microscopic quantum theory for these non-linear processes in non-equilibrium state is called for. The extension of the Kubo formula or the Keldysh formula to the nonlinear response preserving gauge-covariance is not straightforward. We developed a gauge-covariant Keldysh formulation with a general electromagnetic field[1]. Such a formulation is realized by replacing the Moyal product in the Wigner space by the star product which is given by deformational quantization. We derived the explicit form of this star product. Our formula has the following merits. (1) The star product facilitates an order-by-order calculation of an observable in terms of the electromagnetic field. (2) The gauge-invariance of the formula is clearly seen, and we do not have to worry about the Ward identity, because the formula is given by gauge-covariant Wigner space. We will mention about an application of this method to Zener tunneling problem in the presence of dissipation. [1] N. Sugimoto, S. Onoda and N. Nagaosa, cond-mat/0611142. [Preview Abstract] |
Tuesday, March 6, 2007 10:36AM - 10:48AM |
H22.00014: Combining the density matrix renormalization group and truncated spectrum approach for two-dimensional strongly correlated systems Yury Adamov, Robert Konik We propose a combined numerical and analytical approach to two dimensional strongly correlated systems which are representable as arrays of one-dimensional exactly solvable systems. In our approach the exact solution provides us a compact representation of one-dimensional subsystems that makes it numerically feasible to treat the interactions between subsystems using a DMRG algorithm. This compact representation comes about through a simple truncation of the spectrum. To illustrate our approach, we consider an array of interacting quantum Ising chains. The results are then compared with an analytical RPA treatment of the same system. [Preview Abstract] |
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