Decrease of correlations in two-dimensional models with continuous symmetry group

Senya B. Shlosman

Walter Metzner

The functional renormalization group is an ideal tool for dealing with the diversity of energy scales and competition of correlations in interacting Fermi systems. Starting point is an exact hierarchy of flow equations which yields the gradual evolution from a microscopic model Hamiltonian to the effective action as a function of a continuously decreasing energy cutoff. Suitable truncations of the hierarchy have recently led to powerful new approximation schemes. I review applications of the functional renormalization group to the two-dimensional Hubbard model and to one-dimensional Luttinger liquids with impurities.

Aroon O’Brien, Stephen D. Bartlett, Andrew C. Doherty +1 more

We use a simple real-space renormalization-group approach to investigate the critical behavior of the quantum Ashkin-Teller model, a one-dimensional quantum spin chain possessing a line of criticality along which critical exponents vary continuously. This approach, which is based on exploiting the on-site symmetry of the model, has been shown to be surprisingly accurate for predicting some aspects of the critical behavior of the quantum transverse-field Ising model. Our investigation explores this approach in more generality, in a model in which the critical behavior has a richer structure but which reduces to the simpler Ising case at a special point. We demonstrate that the correlation length critical exponent as predicted from this real-space renormalization-group approach is in broad agreement with the corresponding results from conformal field theory along the line of criticality. Near the Ising special point, the error in the estimated critical exponent from this simple method is comparable to that of numerically intensive simulations based on much more sophisticated methods, although the accuracy decreases away from the decoupled Ising model point.

I. L. Genkin, Z. N. Chumak, O. V. Chumak

P.I. Kuindersma

Oleg Borisenko, Vladimir Chelnokov, Vladimir Kushnir

We propose a modification of the Nightingale renormalization group for lattice spin and gauge models by combining it with the cluster decimation approximation.Essential ingredients of our approach are: 1) exact calculation of the partition and correlation function on a finite lattice strip; 2) preservation of the mass gap or the second moment correlation length, computed in the infinite strip length limit, on each decimation step.The method is applied for studying general two and three dimensional Z(N) models.A perfect agreement with exact results (whenever available) is found.An extension of the method to models with a continuous symmetry is briefly discussed.