PACS. 71.10.Fd -Lattice fermion models. PACS. 75.40.Mg -Numerical simulation studies.Abstract. -We describe here the extension of the density matrix renormalization group algorithm to the case where the Hamiltonian has a non-Abelian global symmetry group. The block states transform as irreducible representations of the non-Abelian group. Since the representations are multi-dimensional, a single block state in the new representation corresponds to multiple states of the original density matrix renormalization group basis. We demonstrate the usefulness of the construction via the the one-dimensional Hubbard model as the symmetry group is enlargedIn past years, the density matrix renormalization group (DMRG) method [1] has been extensively used to study one and two dimensional strongly correlated electron systems [2]. This method became very popular when it was realized that it enabled a level of numerical accuracy for one dimensional systems that was not possible using other methods [3].One major drawback of DMRG is that calculations are performed in a subspace of purely Abelian symmetries, such as the U (1) symmetries of total particle number and the z component of the total spin. Thus one can only obtain a few states in different total particle number and z component of total spin sectors [4]. For models where ferromagnetism emerges the situation worsens, that is, to determine magnetization, a combination of methods must be employed which will artificially raise the energy of the higher spin state [5] within the chosen z component total spin sector.In recognizing the imperative need, to introduce a DMRG method which has a total spin quantum number naturally implemented, a number of unsuccessful attempts were previously made (e.g., for the spin 1 Heisenberg model [6] and t-t'-U model [7,8]). The most successful previous work on the application of non-trivial symmetries is the IRF-DMRG method introduced by Sierra and Nishino [9], whereby the vertex hamiltonian is first transformed into an interaction round a face hamiltonian [11], and then a variant of DMRG is applied to the IRF model. The IRF model can be chosen such that it explicitly factors out the global symmetry group. This technique has been successfully applied to the spin 1/2 Heisenberg chain and the XXZ chain with quantum group symmetry SU q (2) [9] and later, the spin 1 and spin 2 Heisenberg chains [10]. However, the IRF-DMRG method is complicated by the necessity c EDP Sciences

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The Kondo lattice model introduced in 1977 describes a lattice of localized magnetic moments interacting with a sea of conduction electrons. It is one of the most important canonical models in the study of a class of rare earth compounds, called heavy fermion systems, and as such has been studied intensively by a wide variety of techniques for more than a quarter of a century. This review focuses on the one dimensional case at partial band filling, in which the number of conduction electrons is less than the number of localized moments. The theoretical understanding, based on the bosonized solution, of the conventional Kondo lattice model is presented in great detail. This review divides naturally into two parts, the first relating to the description of the formalism, and the second to its application. After an all-inclusive description of the bosonization technique, the bosonized form of the Kondo

Using a non-Abelian density matrix renormalization group method we determine the phase diagram of the Kondo lattice model in one dimension, by directly measuring the magnetization of the ground state. This allowed us to discover a second ferromagnetic phase missed in previous approaches. The phase transitions are found to be continuous. The spin-spin correlation function is studied in detail, and we determine in which regions the large and small Fermi surfaces dominate. The importance of double-exchange ordering and its competition with Kondo singlet formation is emphasized in understanding the complexity of the model.

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