Related papers: Worm Algorithm for CP(N-1) Model
The CP(N-1) model in 2D is an interesting toy model for 4D QCD as it possesses confinement, asymptotic freedom and a non-trivial vacuum structure. Due to the lower dimensionality and the absence of fermions, the computational cost for…
We exactly reformulate the lattice CP(N-1) spin model on a D dimensional torus as a loop model whose configurations correspond to the complete set of strong coupling graphs of the original system. A Monte Carlo algorithm is described and…
We construct an efficient cluster algorithm for ferromagnetic SU(N)-symmetric quantum spin systems. Such systems provide a new regularization for CP(N-1) models in the framework of D-theory, which is an alternative non-perturbative approach…
A worm algorithm is proposed for the two-dimensional spin glasses. The method is based on a low-temperature expansion of the partition function. The low-temperature configurations of the spin glass on square lattice can be viewed as strings…
D-theory provides an alternative lattice regularization of the (1+1)-d CP(N-1) quantum field theory. In this formulation the continuous classical CP(N-1) fields emerge from the dimensional reduction of discrete SU(N) quantum spins. In…
We present numerical results for 2-d CP(N-1) models at \theta=0 and \pi obtained in the D-theory formulation. In this formulation we construct an efficient cluster algorithm and we show numerical evidence for a first order transition for…
We present a new approach to path integral Monte Carlo (PIMC) simulations based on the worm algorithm, originally developed for lattice models and extended here to continuous-space many-body systems. The scheme allows for efficient…
Despite several attempts, no efficient cluster algorithm has been constructed for CP(N-1) models in the standard Wilson formulation of lattice field theory. In fact, there is a no-go theorem that prevents the construction of an efficient…
We present a Markov-chain Monte Carlo algorithm of "worm"type that correctly simulates the O(n) loop model on any (finite and connected) bipartite cubic graph, for any real n>0, and any edge weight, including the fully-packed limit of…
In order to check the validity and the range of applicability of the 1/N expansion, we performed numerical simulations of the two-dimensional lattice CP(N-1) models at large N, in particular we considered the CP(20) and the CP(40) models.…
We study the lattice O(2N) Gross-Neveu model with Wilson fermions in the fermion loop formulation. Employing a worm algorithm for an open fermionic string, we simulate fluctuating topological boundary conditions and use them to tune the…
An efficient algorithm is presented to simulate the O(N) loop model on the square lattice for arbitrary values of $N>0$. The scheme combines the worm algorithm with a new data structure to resolve both the problem of loop crossings and the…
We present a novel and open-source implementation of the worm algorithm, which is an algorithm to simulate Bose-Hubbard and sign-positive spin models using a path integral representation of the partition function. The code can deal with…
In order to develop fast inversion algorithms we have used overlap solvers in two dimensions. Lattice QED theory with U(1) group symmetry in two dimensional space-times dimensions has always been a testing ground for algorithms. By the…
The 2d CP(N-1) models share a number of features with QCD, like asymptotic freedom, a dynamically generated mass gap and topological sectors. They have been formulated and analysed successfully in the framework of the so-called D-theory,…
We propose a new decoder for "matchable'' qLDPC codes that uses a Markov Chain Monte Carlo algorithm - called the worm algorithm - to approximately compute the probabilities of logical error classes given a syndrome. The algorithm hence…
We present model predictions for the spectrum of $CP^{N-1}$ in a periodic box and use them to interpret the strong finite size effects observed in lattice simulations at medium values of $N$. The asymptotic scaling behaviour of alternative…
We discuss the implementation of a directed geometrical worm algorithm for the study of quantum link-current models. In this algorithm Monte Carlo updates are made through the biased reptation of a worm through the lattice. A directed…
Worm algorithms have been very successful with the simulation of sigma models with fixed length spins which result from scalar field theories in the limit of infinite quartic coupling lambda. Here we investigate closer their algorithmic…
We present a family of graphical representations for the O($N$) spin model, where $N \ge 1$ represents the spin dimension, and $N=1,2,3$ corresponds to the Ising, XY and Heisenberg models, respectively. With an integer parameter $0 \le \ell…