On the evaluation of universal non-perturbative constants in O(N) sigma models

We investigate the relation between on-shell and zero-momentum non-perturbative quantities entering the parametrization of the two-point Green's function of two-dimensional non-linear O(N) sigma models. We present accurate estimates of ratios of mass-scales and renormalization constants, obtained by an analysis of the strong-coupling expansion of the two-point Green's function. These ratios allow to connect exact known on-shell results with typical zero-momentum lattice evaluations. Our results are supported by the 1/N-expansion.Comment: 10 pages, revte

Critical behavior of the correlation function of three-dimensional O(N) models in the symmetric phase

We present new strong-coupling series for O(N) spin models in three dimensions, on the cubic and diamond lattices. We analyze these series to investigate the two-point Green's function G(x) in the critical region of the symmetric phase. This analysis shows that the low-momentum behavior of G(x) is essentially Gaussian for all N from zero to infinity. This result is also supported by a large-N analysis.Comment: 3 pages, requires espcrc2.st

Topological susceptibility and string tension in CP(N-1) models

We investigate the features of ${\rm CP}^{N-1}$ models concerning confinement and topology. In order to study the approach to the large-$N$ asymptotic regime, we determine the topological susceptibility and the string tension for a wide range of values of $N$, in particular $N=4,10,21,41$. Quantitative agreement with the large-$N$ predictions is found for the ${\rm CP}^{20}$ and the ${\rm CP}^{40}$ models. Problems related to the measure of the topological susceptibility and the string tension on the lattice are discussed.Comment: Talk presented at the Lattice '92 Conference, Amsterdam. 6 pages, sorry, no figures included, if required we can send them by mai

Scaling and asymptotic scaling in two-dimensional CPN−1CP^{N-1} models

Two-dimensional $CP^{N-1}$ models are investigated by Monte Carlo methods on the lattice, for values of $N$ ranging from 2 to 21. Scaling and rotation invariance are studied by comparing different definitions of correlation length $\xi$. Several lattice formulations are compared and shown to enjoy scaling for $\xi$ as small as $2.5$. Asymptotic scaling is investigated using as bare coupling constant both the usual $\beta$ and $\beta_E$ (related to the internal energy); the latter is shown to improve asymptotic scaling properties. Studies of finite size effects show their $N$-dependence to be highly non-trivial, due to the increasing radius of the $\bar z z$ bound states at large $N$.Comment: 5 pages + 12 figures (PostScript), report no. IFUP-TH 46/9

1/N1/N Expansion of Two-Dimensional Models in the Scaling Region

The main technical and conceptual features of the lattice $1/N$ expansion in the scaling region are discussed in the context of a two-parameter two-dimensional spin model interpolating between $CP^{N-1}$ and $O(2N)$ $\sigma$ models, with standard and improved lattice actions. We show how to perform the asymptotic expansion of effective propagators for small values of the mass gap and how to employ this result in the evaluation of physical quantities in the scaling regime. The lattice renormalization group $\beta$ function is constructed explicitly and exactly to $O({1/N})$.Comment: 6 pages, report no. IFUP-TH 49/9

Universal quantum behaviors of interacting fermions in 1D traps: from few particles to the trap thermodynamic limit

We investigate the ground-state properties of trapped fermion systems described by the Hubbard model with an external confining potential. We discuss the universal behaviors of systems in different regimes: from few particles, i.e. in dilute regime, to the trap thermodynamic limit. The asymptotic trap-size (TS) dependence in the dilute regime (increasing the trap size l keeping the particle number N fixed) is described by a universal TS scaling controlled by the dilute fixed point associated with the metal-to-vacuum quantum transition. This scaling behavior is numerically checked by DMRG simulations of the one-dimensional (1D) Hubbard model. In particular, the particle density and its correlations show crossovers among different regimes: for strongly repulsive interactions they approach those of a spinless Fermi gas, for weak interactions those of a free Fermi gas, and for strongly attractive interactions they match those of a gas of hard-core bosonic molecules. The large-N behavior of systems at fixed N/l corresponds to a 1D trap thermodynamic limit. We address issues related to the accuracy of the local density approximation (LDA). We show that the particle density approaches its LDA in the large-l limit. When the trapped system is in the metallic phase, corrections at finite l are O(l^{-1}) and oscillating around the center of the trap. They become significantly larger at the boundary of the fermion cloud, where they get suppressed as O(l^{-1/3}) only. This anomalous behavior arises from the nontrivial scaling at the metal-to-vacuum transition occurring at the boundaries of the fermion cloud.Comment: 20 page

Adaptive Optimization of Wave Functions for Lattice Field Models

The accuracy of Green Function Monte Carlo (GFMC) simulations can be greatly improved by a clever choice of the approximate ground state wave function that controls configuration sampling. This trial wave function typically depends on many free parameters whose fixing is a non trivial task. Here, we discuss a general purpose adaptive algorithm for their non-linear optimization. As a non trivial application we test the method on the two dimensional Wess-Zumino model, a relativistically invariant supersymmetric field theory with interacting bosonic and fermionic degrees of freedom.Comment: 12 pages, 5 EPS figures, Contribution to the Proceedings of the "Quantum Monte Carlo" meeting (Trento, Italy, July 3-6, 2001

On the evaluation of the improvement parameter in the lattice Hamiltonian approach to critical phenomena

In lattice Hamiltonian systems with a quartic coupling $\gamma$, a critical value $\gamma^*$ may exist such that, when $\gamma=\gamma^*$, the leading irrelevant operator decouples from the Hamiltonian and the leading nonscaling contribution to renormalization-group invariant physical quantities (evaluated in the critical region) vanishes. The 1/N expansion technique is applied to the evaluation of $\gamma^*$ for the lattice Hamiltonian of vector spin models with O(N) symmetry. As a byproduct, systematic asymptotic expansions for the relevant lattice massive one-loop integrals are obtained.Comment: Conclusions clarified; 26 pages, 6 figures, RevTeX

Quantum transitions driven by one-bond defects in quantum Ising rings

We investigate quantum scaling phenomena driven by lower-dimensional defects in quantum Ising-like models. We consider quantum Ising rings in the presence of a bond defect. In the ordered phase, the system undergoes a quantum transition driven by the bond defect between a magnet phase, in which the gap decreases exponentially with increasing size, and a kink phase, in which the gap decreases instead with a power of the size. Close to the transition, the system shows a universal scaling behavior, which we characterize by computing, either analytically or numerically, scaling functions for the gap, the susceptibility, and the two-point correlation function. We discuss the implications of these results for the nonequilibrium dynamics in the presence of a slowly-varying parallel magnetic field h, when going across the first-order quantum transition at h=0.Comment: 5 page