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.     

The tensor renormalization group for pure and disordered two-dimensional lattice systems

The tensor renormalization group (TRG) is a powerful new approach for coarse-graining classical two-dimensional (2D) lattice Hamiltonians. It uses the intuitive framework of traditional position space renormalization group methods-analyzing flows in the space of Hamiltonian parameters-but can be systematically improved to yield thermodynamic properties at much higher precision. We present initial results demonstrating that the TRG can be generalized to quenched random systems, applying it to obtain the phase diagram of a bond-diluted triangular lattice Ising ferromagnet. This opens a variety of potential future applications, most prominently spin glasses.     

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.     

Functional renormalization group for quantized anharmonic oscillator

Functional renormalization group methods formulated in the real-time formalism are applied to the O(N) symmetric quantum anharmonic oscillator, considered as a 0 + 1 dimensional quantum field-theoric model, in the next-to-leading order of the gradient expansion of the one- and two-particle irreducible effective action. The infrared scaling laws and the sensitivity-matrix analysis show the existence of only a single, symmetric phase. The Taylor expansion for the local potential converges fast while it is found not to work for the field-dependent wavefunction renormalization, in particular for the double-well bare potential. Results for the gap energy for the bare anharmonic oscillator potential hint on improving scheme-independence in the next-to-leading order of the gradient expansion, although the truncated perturbation expansion in the bare quartic coupling provides strongly scheme-dependent results for the infrared limits of the running couplings.     

Electronic properties of disordered systems as derived by analytic continuation from renormalization group theory

The averaged single particle Green function for electrons moving in a gaussian random potential is calculated by analytic continuation from the order parameter susceptibility of a thermodynamic system with order parameter dimension O. New results are obtained and discussed.     

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.     

Nonequilibrium functional renormalization group for interacting quantum systems

We propose a nonequilibrium version of functional renormalization within the Keldysh formalism by introducing a complex-valued flow parameter in the Fermi or Bose functions of each reservoir. Our cutoff scheme provides a unified approach to equilibrium and nonequilibrium situations. We apply it to nonequilibrium transport through an interacting quantum wire coupled to two reservoirs and show that the nonequilibrium occupation induces new power law exponents for the conductance.     

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.     

Generalized renormalization group equation for systems of arbitrary symmetry

An exact renormalization group equation for the Ginzburg-Landau-Wilson functional of an arbitrary symmetry is obtained. The equation derived does not contain redundant operators which must be transformed away.     

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.     

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.     

Magnon renormalization in disordered ferromagnets

The renormalization of the magnon energies in disordered, isotropic ferromagnets is investigated in the Hartree approximation. An expression equivalent to the Keffer-Loudon-Bloch renormalization factor is obtained by replacing products of normal mode expansion coefficients by their weighted sample averages. The results of self-consistent calculations of the renormalization factor and the magnetization are reported for dilute bond and amorphous ferromagnets.