Application of the numerical renormalization group method to the hubbard model in infinite dimensions (original) (raw)
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Real-space renormalization-group study of the Hubbard model: A modified scheme
Physical Review B, 1998
We present the real-space block renormalization group equations for fermion systems described by a Hubbard Hamiltonian on a triangular lattice with hexagonal blocks. The conditions that keep the equations from proliferation of the couplings are derived. Computational results are presented including the occurrence of a first-order metal-insulator transition at the critical value of U/t ≈ 12.5.
Renormalized pseudoparticle description of the one-dimensional Hubbard model thermodynamics
Physical Review B, 1991
It is shown that the Hubbard chain in a magnetic field of arbitrary strength H can be treated as a liquid of interacting pseudoparticles which at T = 0 has only forward scattering. The excitation spectra can be understood in terms of particle-hole processes in the pseudoparticle renormalized bands. Within this framework, we are able to study in detail the low-temperature thermodynamics of the Hubbard model. Explicit expressions for the specific heat c, for a nearly half-filled band and for values of the magnetic field close to the ferromagnetic saturated state are derived. The renormalized charge and spin masses which regulate the crossover regime to the exponential behavior of several physical quantities close to the metal-insulator and ferromagnetic transitions, respectively, are calculated.
Real-space renormalization group study of the Hubbard model on a non-bipartite lattice
International Journal of Molecular Sciences, 2002
We present the real-space block renormalization group equations for fermion systems described by a Hubbard Hamiltonian on a triangular lattice with hexagonal blocks. The conditions that keep the equations from proliferation of the couplings are derived. Computational results are presented including the occurrence of a first-order metal-insulator transition at the critical value of U/t ≈ 12.5.
Exact Diagonalization Approach for the infinite D Hubbard Model
1993
We present a powerful method for calculating the thermodynamic properties of the Hubbard model in infinite dimensions, using an exact diagonalization of an Anderson model with a finite number of sites. At finite temperatures, the explicit diagonalization of the Anderson Hamiltonian allows the calculation of Green's functions with a resolution far superior to that of Quantum Monte Carlo calculations. At zero temperature, the Lanczòs method is used and yields the essentially exact zero-temperature solution of the model, except in a region of very small frequencies. Numerical results for the halffilled case in the paramagnetic phase (quasi-particle weight, self-energy, and also real-frequency spectral densities) are presented.
Physical Review X, 2015
Numerical results for ground state and excited state properties (energies, double occupancies, and Matsubara-axis self energies) of the single-orbital Hubbard model on a two-dimensional square lattice are presented, in order to provide an assessment of our ability to compute accurate results in the thermodynamic limit. Many methods are employed, including auxiliary field quantum Monte Carlo, bare and bold-line diagrammatic Monte Carlo, method of dual fermions, density matrix embedding theory, density matrix renormalization group, dynamical cluster approximation, diffusion Monte Carlo within a fixed node approximation, unrestricted coupled cluster theory, and multireference projected Hartree-Fock. Comparison of results obtained by different methods allows for the identification of uncertainties and systematic errors. The importance of extrapolation to converged thermodynamic limit values is emphasized. Cases where agreement between different methods is obtained establish benchmark results that may be useful in the validation of new approaches and the improvement of existing methods. arXiv:1505.02290v1 [cond-mat.str-el] 9 May 2015
Journal of Physics A: Mathematical and General, 2003
The density matrix renormalization group (DMRG) method and its applications to finite temperatures and two-dimensional systems are reviewed. The basic idea of the original DMRG method, which allows precise study of the ground state properties and low-energy excitations, is presented for models which include long-range interactions. The DMRG scheme is then applied to the diagonalization of the quantum transfer matrix for one-dimensional systems, and a reliable algorithm at finite temperatures is formulated. Dynamic correlation functions at finite temperatures are calculated from the eigenvectors of the quantum transfer matrix with analytical continuation to the real frequency axis. An application of the DMRG method to twodimensional quantum systems in a magnetic field is demonstrated and reliable results for quantum Hall systems are presented.
Two-loop functional renormalization group approach to the one- and two-dimensional Hubbard model
Physical Review B, 2009
We consider the application of the two-loop functional renormalization-group (fRG) approach to study the low-dimensional Hubbard model. This approach accounts for both, the universal and non-universal contributions to the RG flow. While the universal contributions were studied previously within the field-theoretical RG for the one-dimensional Hubbard model with linearized electronic dispersion and the two-dimensional Hubbard model with flat Fermi surface, the nonuniversal contributions to the flow of the vertices and susceptibilities appear to be important at large momenta scales. The two-loop fRG approach is also applied to the two-dimensional Hubbard model with a curved Fermi surface and the van Hove singularities near the Fermi level. The vertices and susceptibilities in the end of the flow of the two-loop approch are suppressed in comparison with both the one-loop approach with vertex projection and the modified one-loop approach with corrected vertex projection errors. The results of the two-loop approach are closer to the results of one-loop approach with the projected vertices, the difference of the results of one-and two-loop fRG approaches decreases when going away from the van Hove band filling. The quasiparticle weight remains finite in two dimensions at not too low temperatures above the paramagnetic ground state.
Journal of Physics: Condensed Matter, 1999
We have studied the Hubbard model with bond-charge interaction on a triangular lattice for a half-filled band. At the point of particle-hole symmetry the model could be analyzed in detail in two opposite regimes of the parameter space. Using a real space renormalization group we calculate the ground state energy and the local moment over the whole parameter space. The RG results obey the exact results in the respective limits. In the intermediate region of the parameter space the RG results clearly show the effects of the non-bipartite geometry of the lattice as well as the absence of symmetry in the reversal of the sign of the hopping matrix element.
High-temperature Thermodynamics of the Hubbard Model
Australian Journal of Physics, 1993
Recently derived 10th-order high-temperature expansions for the Hubbard model are used to obtain the ferromagnetic susceptibility and specific heat at high temperatures. Numerical results are obtained for the simple cubic and face-centred cubic lattices by using Pade approximants to sum the series. The results are compared with two solvable limiting cases, namely the non-interacting limit U = 0 and the strongly-correlated or atomic limit t = O.
Finite size scaling approach to the 1D Hubbard model
Journal of Physics A: Mathematical and General, 1984
Finite size scaling is applied to the one-dimensional Hubbard model with the half filled energy band, at zero temperature. It is shown that, even for the scaling between small blocks of four, six and eight atoms, the essential singularity of the weak coupling limit is reproduced with remarkable accuracy, the error being less than 1 YO for the exponent and a few percent for the multiplicative constant. The results are discussed in comparison with the quantum renormalisation group approach, which fails to give the right exponent, and the advantages of the present method are pointed out.