Search results for "Renormalization group"
showing 10 items of 206 documents
Rigidity of random networks of stiff fibers in the low-density limit.
2001
Rigidity percolation is analyzed in two-dimensional random networks of stiff fibers. As fibers are randomly added to the system there exists a density threshold ${q=q}_{\mathrm{min}}$ above which a rigid stress-bearing percolation cluster appears. This threshold is found to be above the connectivity percolation threshold ${q=q}_{c}$ such that ${q}_{\mathrm{min}}=(1.1698\ifmmode\pm\else\textpm\fi{}{0.0004)q}_{c}.$ The transition is found to be continuous, and in the universality class of the two-dimensional central-force rigidity percolation on lattices. At percolation threshold the rigid backbone of the percolating cluster was found to break into rigid clusters, whose number diverges in the…
Parallelization strategies for density matrix renormalization group algorithms on shared-memory systems
2003
Shared-memory parallelization (SMP) strategies for density matrix renormalization group (DMRG) algorithms enable the treatment of complex systems in solid state physics. We present two different approaches by which parallelization of the standard DMRG algorithm can be accomplished in an efficient way. The methods are illustrated with DMRG calculations of the two-dimensional Hubbard model and the one-dimensional Holstein-Hubbard model on contemporary SMP architectures. The parallelized code shows good scalability up to at least eight processors and allows us to solve problems which exceed the capability of sequential DMRG calculations.
Supersolid-superfluid phase separation in the extended Bose-Hubbard model
2021
Recent studies have suggested a new phase in the extended Bose-Hubbard model in one dimension at integer filling [1,2]. In this work, we show that this new phase is phase-separated into a supersolid and superfluid part, generated by mechanical instability. Numerical simulations are performed by means of the density matrix renormalization group algorithm in terms of matrix product states. In the phase-separated phase and the adjacent homogeneous superfluid and supersolid phases, we find peculiar spatial patterns in the entanglement spectrum and string-order correlation functions and show that they survive in the thermodynamic limit. In particular, we demonstrate that the elementary excitatio…
Exact Numerical Treatment of Finite Quantum Systems Using Leading-Edge Supercomputers
2005
Using exact diagonalization and density matrix renormalization group techniques a finite-size scaling study in the context of the Peierls-insulator Mott-insulator transition is presented. Program implementation on modern supercomputers and performance aspects are discussed.
Phase transitions in polymer blends and block copolymer melts: Some recent developments
2005
The classical concepts about unmixing of polymer blends (Flory-Huggins theory) and about mesophase ordering in block copolymers (Leibler's theory) are briefly reviewed and their validity is discussed in the light of recent experiments, computer simulations and other theoretical concepts. It is emphasized that close to the critical point of unmixing non-classical critical exponents of the Ising universality class are observed, in contrast to the classical mean-field exponents implied by the Flory-Huggins theory. The temperature range of this non-mean-field behavior can be understood by Ginzburg criteria. The latter are also useful to discuss the conditions under which the linearized (Cahn-li…
Infrared renormalization of two-loop integrals and the chiral expansion of the nucleon mass
2007
We describe details of the renormalization of two-loop integrals relevant to the calculation of the nucleon mass in the framework of manifestly Lorentz-invariant chiral perturbation theory using infrared renormalization. It is shown that the renormalization can be performed while preserving all relevant symmetries, in particular chiral symmetry, and that renormalized diagrams respect the standard power counting rules. As an application we calculate the chiral expansion of the nucleon mass to order O(q^6).
Proposal for a running coupling JIMWLK equation
2014
In the CGC framework the initial stages of a heavy ion collision at high energy are described as "glasma" field configurations. The initial condition for these evolving fields depends, in the CGC effective theory, on a probability distribution for color charges. The energy dependence of this distribution can be calculated from the JIMWLK renormalization group equation. We discuss recent work on a practical implementation of the running coupling constant in the Langevin method of solving the JIMWLK equation.
Domain Wall Renormalization Group Study of XY Model with Quenched Random Phase Shifts
2002
The XY model with quenched random disorder is studied by a zero temperature domain wall renormalization group method in 2D and 3D. Instead of the usual phase representation we use the charge (vortex) representation to compute the domain wall, or defect, energy. For the gauge glass corresponding to the maximum disorder we reconfirm earlier predictions that there is no ordered phase in 2D but an ordered phase can exist in 3D at low temperature. However, our simulations yield spin stiffness exponents $\theta_{s} \approx -0.36$ in 2D and $\theta_{s} \approx +0.31$ in 3D, which are considerably larger than previous estimates and strongly suggest that the lower critical dimension is less than thr…
Towards gauge coupling unification in left-right symmetric SU(3)c×SU(3)L×SU(3)R×U(1)X theories
2017
We consider the possibility of gauge coupling unification within the simplest realizations of the $\mathrm{SU}(3{)}_{\mathrm{c}}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(3{)}_{\mathrm{L}}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(3{)}_{\mathrm{R}}\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1{)}_{\mathrm{X}}$ gauge theory. We present a first exploration of the renormalization group equations governing the ``bottom-up'' evolution of the gauge couplings in a generic model with free normalization for the generators. Interestingly, we find that for a $\mathrm{SU}(3{)}_{\mathrm{c}}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(3{)}_{\mathrm{L}}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(…
The liquid-solid transition of hard discs: first-order transition or Kosterlitz-Thouless-Halperin-Nelson-Young scenario?
2002
We consider the question of whether a two-dimensional hard-disc fluid has a first-order transition from the liquid state to the solid state as in the three-dimensional melting-crystallization transition or whether one has two subsequent continuous transitions, from the liquid to the hexatic phase and then to the solid phase, as proposed by Kosterlitz, Thouless, Halperin, Nelson and Young (KTHNY). Monte Carlo (MC) simulations of the fluid that study the growth of the bond orientational correlation length, and of the crystal are discussed. The emphasis is on a recent consistency test of the KTHNY renormalization group (RG) scenario, where MC simulations are used to estimate the bare elastic c…