arXiv subjects

Miguel A. Martin-Delgado

Publications and source records attributed to Miguel A. Martin-Delgado.

44 records · Page 3Linked to original sources

arXiv1996

Real-Space Renormalization Group Method Applied to Quantum Lattice Hamiltonians

I review recent work and some new results, performed in collaboration with G. Sierra, on the Real-Space Renormalization group method applied to quantum spin lattice systems mainly in spatial dimensions one and two, and to spin ladders which are somehow in between. The first part of these notes is devoted to non-interacting systems in 1D and 2D and the role played by the correlations between blocks. The second part comprises interacting systems in 1D, spin ladders and 2D using the standard BRG method.

cond-mat.stat-mech↗

arXiv1996

A Rotating-Valence-Bond scenario for the 2D Antiferromagnetic Heisenberg Model

We propose that the valence bonds forming the ground state of the 2D-AF Heisenberg model on a square lattice may rotate under the effect of the antiferromagnetic background. To test this idea we apply a real space renormalization group approach to construct a rotating-valence-bond ground state anstaz. Our results are analytic and valid for any value of the spin S of the AF-magnet, which allow us to perfom semiclassical expansions of the energy and the staggered magnetization.

cond-mat↗

arXiv1995

The Correlated Block Renormalization Group

We formulate the standard real-space renormalization group method in a way which takes into account the correlation between blocks. This is achieved in a dynamical way by means of operators which reflect the influence on a given block of its neighbours. We illustrate our method in the example of the tight-binding model in 1D and 2D for various types of boundary conditions.

cond-mat↗

arXiv1995

The Renormalization Group Method and Quantum Groups: the postman always rings twice

We review some of our recent results concerning the relationship between the Real-Space Renormalization Group method and Quantum Groups. We show this relation by applying real-space RG methods to study two quantum group invariant Hamiltonians, that of the XXZ model and the Ising model in a transverse field (ITF) defined in an open chain with appropriate boundary terms. The quantum group symmetry is preserved under the RG transformation except for the appearence of a quantum group anomalous term which vanishes in the classical case. This is called {\em the quantum group anomaly}. We derive the new qRG equations for the XXZ model and show that the RG-flow diagram obtained in this fashion exhibits the correct line of critical points that the exact model has. In the ITF model the qRG-flow equations coincide with the tensor product decomposition of cyclic irreps of $SU_q(2)$ with $q^4=1$.

hep-th↗

arXiv1995

Analytic Formulations of the Density Matrix Renormalization Group

We present two new analytic formulations of the Density Matrix Renormalization Group Method. In these formulations we combine the block renormalization group (BRG) procedure with Variational and Fokker-Planck methods. The BRG method is used to reduce the lattice size while the latter are used to construct approximate target states to compute the block density matrix. We apply our DMRG methods to the Ising Model in a transverse field (ITF model) and compute several of its critical properties which are then compared with the old BRG results.

cond-mat↗

arXiv1995

The Role of Boundary Conditions in the Real-Space Renormalization Group

We show that the failure of the real-space RG method in the 1D tight-binding model is not intrinsic to the method as considered so far but depends on the choice of boundary conditions. For fixed BC's the failure does happen. For free BC's we present a new analytical block RG-method which gives the exact ground state of the model and the correct $1/N^2$-law for the energy of the first excited state in the large $N$(size)-limit. We also give a reconstruction method for the wave-functions of the excited states.

cond-mat↗

arXiv1995

Real Space Renormalization Group Methods and Quantum Groups

We apply real-space RG methods to study two quantum group invariant Hamiltonians, that of the XXZ model and the Ising model in a transverse field defined in an open chain with appropiate boundary terms. The quantum group symmetry is preserved under the RG transformation except for the appearence of a quantum group anomalous term which vanishes in the classical case. We obtain correctly the line of critical XXZ models. In the ITF model the RG-flow coincides with the tensor product decomposition of cyclic irreps. of $SU_q(2)$ with $q^4=1$.

cond-mat↗

arXiv1995

Strongly Interacting Spinless Fermions in D=1 and 2 Dimensions: A Perturbative-Variational Approach

We propose a perturbative-variational approach to interacting fermion systems on 1D and 2D lattices at half-filling. We address relevant issues such as the existence of Long Range Order, quantum phase transitions and the evaluation of ground state energy. In 1D our method is capable of unveiling the existence of a critical point in the coupling constant at $(t/U)_c=0.7483$ as in fact occurs in the exact solution at a value of 0.5. In our approach this phase transition is described as an example of Bifurcation Phenomena in the variational computation of the ground state energy. In 2D the van Hove singularity plays an essential role in changing the asymptotic behaviour of the system for large values of $t/U$. In particular, the staggered magnetization for large $t/U$ does not display the Hartree-Fock law $(t/U) e^{-2 π\sqrt{t/U}}$ but instead we find the law $(t/U) e^{- \frac{π^2}{3} t/U}$. Moreover, the system does not exhibit bifurcation phenomena and thus we do not find a critical point separating a CDW state from a fermion "liquid" state.

cond-mat↗