Real-space renormalization group for two-dimensional quantum spin systems

A generalization of the Niemeijer and Van Leeuwen real-space renormalization group method for quantum lattice spin systems is presented. A proposed rotationally invariant transformation which preserves the symmetry of the spin space is applied to several quantum systems on a triangular lattice. For the spin-1/2XY-model in both first- and second-order cumulant expansions a nontrivial fixed point exists, giving in the best approximation a critical interactionK _XY ^c =0.453 and critical exponent =1.65. A method of the reduction of the generalized arbitrary spin anisotropic Heisenberg model to the spin-half model is presented.     

Real-space renormalization group for directed percolation system

We use the recently proposed real-space renormalization group method to study the critical behavior of directed percolation system in two dimensions. The correlation length exponents and are found to be 1.76 and 1.15. These results are in good agreements with the best known values.     

Real-space renormalization group for gases of topological excitations

We report a block and a decimation real-space renormalization group technique to study the critical behavior of Coulomb and Yukawa two-dimensional gases.     

Electronic structure of strongly correlated systems emerging from combining path-integral renormalization group with the density-functional approach

A new scheme of first-principles computation for strongly correlated electron systems is proposed. This scheme starts from the local-density approximation (LDA) at high-energy band structure, while the low-energy effective Hamiltonian is constructed by a downfolding procedure using combinations of the constrained-LDA and the GW method. The obtained low-energy Hamiltonian is solved by the path-integral renormalization-group method, where spatial and dynamical fluctuations are fully considered. An application to Sr2VO4 shows that the scheme is powerful in agreement with experimental results. It further predicts a nontrivial orbital-stripe order.     

A direct renormalization group approach for the excluded volume problem

We propose a position-space renormalization group approach for the excluded volume problem in a square lattice by considering percolating self-avoiding paths in ab×b cell, whereb=2,3,4: Two ways of counting the paths are presented. The values obtained for the exponentv converge respectively to 0.731 and 0.720, close to the usually accepted valuev=0.75. Comments on the relation between percolation and self-avoiding walks are made.Work supported by Brazilian Agencies FINEP, CNPq and CNRS, France     

A direct renormalization group approach for the excluded volume problem

We propose a position-space renormalization group approach for the excluded volume problem in a square lattice by considering “percolating” self-avoiding paths in ab×b cell, whereb=2,3,4: Two ways of counting the paths are presented. The values obtained for the exponentv converge respectively to 0.731 and 0.720, close to the usually accepted valuev=0.75. Comments on the relation between percolation and self-avoiding walks are made.     

Real-space renormalization group for Langevin dynamics in absence of translational invariance

A novel exact dynamical real-space renormalization group for a Langevin equation derivable from a Euclidean Gaussian action is presented. It is demonstrated rigorously that an algebraic temporal law holds for the Green function on arbitrary structures of infinite extent. In the case of fractals it is shown on specific examples that two different fixed points are found, at variance with periodic structures. Connection with the growth dynamics of interfaces is also discussed.     

Migdal renormalization group approach to quantum spin systems

The Migdal RG approximation is extended to quantum spin systems such as the Heisenberg and XY-models. This yields the non-existence of phase transition in the two-dimensional Heisenberg model. The phase transition of the two-dimensional XY-model is also studied.     

量子多体系统的线性张量重正化群方法

文章简述了数值重正化群方法的历史发展,包括威耳逊（Wilson）的数值重正化群算法,S.R.White的密度矩阵重正化群方法,以及近期迅速发展的处理强关联量子系统的几种张量网络态与张量网络算法.在此基础上,文章重点介绍了作者最近提出的用于研究量子多体系统热力学性质的线性张量重正化群方法,以及该方法在一维和二维量子系统中的应用.     

量子多体系统的线性张量重正化群方法

文章简述了数值重正化群方法的历史发展,包括威耳逊（Wilson）的数值重正化群算法,S.R.White的密度矩阵重正化群方法,以及近 期迅速发展的处理强关联量子系统的几种张量网络态与张量网络算法.在此基础上,文章重点介绍了作者最近提出的用于研究量子多体系统热 力学性质的线性张量重正化群方法,以及该方法在一维和二维量子系统中的应用.     

Density matrix renormalization group approach for many-body open quantum systems

The density matrix renormalization group (DMRG) approach is extended to complex-symmetric density matrices characteristic of many-body open quantum systems. Within the continuum shell model, we investigate the interplay between many-body configuration interaction and coupling to open channels in case of the unbound nucleus (7)He. It is shown that the extended DMRG procedure provides a highly accurate treatment of the coupling to the nonresonant scattering continuum.     

Similarity renormalization group for few-body systems

Internucleon interactions evolved via flow equations yield soft potentials that lead to rapid variational convergence in few-body systems.     

Real-space renormalization group investigation of pure and disordered mixed spin Ising models ond-dimensional lattices

The mixed spin Ising model (spins =1/2 andS=1) ond-dimensional hypercubic lattices with nearest-neighbour exchange interactions is studied via a renormalization group transformation in position space. The phase diagrams in (L, K) space, i.e. in dependence of the bilinear (K) and the biquadratic (L) interaction coefficients, are qualitatively different ford=2 andd>2. For any dimensiond however it is found that all transitions are of second order. At zero-temperature (K=,L=), the ferromagnetic order disappears at (L/K)₀=2, which does not depend ond. Using an extension of this real-space renormalization group analysis we study the two-dimensional random disordered version of the above model.L is kept homogeneous and the bilinear interactionsK _ij are assumed to be independent random variables with distributionP(K _ij )=p(K _ij –K)+(1–p)(K _ij –K); whereK>0. The phase diagrams for different values ofp are obtained. At zero temperature, it is found that in the bond diluted model (=0) the value (L/K)₀ depends continuously onp, whereas in the random ±K interactions (=–1) (L/K)₀ is unique and does not depend onp.Supported by the agreement of cooperation between the DFGW. Germany and the CNR-Maroc     

Numerical renormalization group for continuum one-dimensional systems

We present a renormalization group (RG) procedure which works naturally on a wide class of interacting one-dimension models based on perturbed (possibly strongly) continuum conformal and integrable models. This procedure integrates Wilson's numerical renormalization group with Zamolodchikov's truncated conformal spectrum approach. The key to the method is that such theories provide a set of completely understood eigenstates for which matrix elements can be exactly computed. In this procedure the RG flow of physical observables can be studied both numerically and analytically. To demonstrate the approach, we study the spectrum of a pair of coupled quantum Ising chains and correlation functions in a single quantum Ising chain in the presence of a magnetic field.     

Mean field like renormalization group for disordered systems

Mean field results for small clusters of spins are combined with renormalization group ideas to give a new approximate scheme for the study of disordered systems. Dilute, random fields and random bonds Ising systems on a d-dimensional hypercubic lattice are analyzed with this new scheme.