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G. Sierra

Publications and source records attributed to G. Sierra.

At least 37 records · Page 2Linked to original sources
arXiv2003

Log-periodic behavior of finite size effects in field theories with RG limit cycles

We compute the finite size effects in the ground state energy, equivalently the effective central charge c_{eff}, based on S-matrix theories recently conjectured to describe a cyclic regime of the Kosterlitz-Thouless renormalization group flows. The effective central charge has periodic properties consistent with renormalization group predictions. Whereas c_{eff} for the massive case has a singularity in the very deep ultra-violet, we argue that the massless version is non-singular and periodic on all length scales.

hep-th↗
arXiv2003

Russian Doll Renormalization Group, Kosterlitz-Thouless Flows, and the Cyclic sine-Gordon model

We investigate the previously proposed cyclic regime of the Kosterlitz-Thouless renormalization group (RG) flows. The period of one cycle is computed in terms of the RG invariant. Using bosonization, we show that the theory has $U_q (\hat{sl(2)})$ quantum affine symmetry, with $q$ {\it real}. Based on this symmetry, we study two possible S-matrices for the theory, differing only by overall scalar factors. We argue that one S-matrix corresponds to a continuum limit of the XXZ spin chain in the anti-ferromagnetic domain $Δ< -1$. The latter S-matrix has a periodicity in energy consistent with the cyclicity of the RG. We conjecture that this S-matrix describes the cyclic regime of the Kosterlitz-Thouless flows. The other S-matrix we investigate is an analytic continuation of the usual sine-Gordon one. It has an infinite number of resonances with masses that have a Russian doll scaling behavior that is also consistent with the period of the RG cycles computed from the beta-function. Closure of the bootstrap for this S-matrix leads to an infinite number of particles of higher spin with a mass formula suggestive of a string theory.

hep-th↗
arXiv2003

The elementary excitations of the BCS model in the canonical ensemble

We summarize previous works on the exact ground state and the elementary excitations of the exactly solvable BCS model in the canonical ensemble. The BCS model is solved by Richardson equations, and, in the large coupling limit, by Gaudin equations. The relationship between this two kinds of solutions are used to classiffy the excitations.

cond-mat.supr-con↗
arXiv2003

What are the elementary excitations of the BCS model in the canonical ensemble?

We have found the elementary excitations of the exactly solvable BCS model for a fixed number of particles. These turn out to have a peculiar dispersion relation, some of them with no counterpart in the Bogoliubov picture, and unusual counting properties related to an old conjecture made by Gaudin. We give an algorithm to count the number of excitations for each excited state and a graphical interpretation in terms of paths and Young diagrams. For large systems the excitations are described by an effective Gaudin model, which accounts for the finite size corrections to BCS.

cond-mat.supr-con↗
arXiv2002

Anderson transition in low-dimensional disordered systems driven by nonrandom long-range hopping

The single-parameter scaling hypothesis predicts the absence of delocalized states for noninteracting quasiparticles in low-dimensional disordered systems. We show analytically and numerically that extended states may occur in the one- and two-dimensional Anderson model with a nonrandom hopping falling off as some power of the distance between sites. The different size scaling of the bare level spacing and the renormalized magnitude of the disorder seen by the quasiparticles finally results in the delocalization of states at one of the band edges of the quasiparticle energy spectrum. The delocalized nature of those eigenstates is investigated by numerical diagonalization of the Hamiltonian and by the supersymmetric method for disorder averaging, combined with a renormalization group analysis.

cond-mat.dis-nn↗
arXiv2002

Large N limit of the exactly solvable BCS model: analytics versus numerics

We have studied the numerical solutions of Richardson equations of the BCS model in the limit of large number of energy levels at half-filling, and compare them with the analytic results derived by Gaudin and Richardson, which in turn leads to the standard BCS solution. We focus on the location and density of the roots, the eigenvalues of the conserved quantities, and the scaling properties of the total energy for the equally spaced and the two-level models.

cond-mat.supr-con↗
arXiv2002

Absence of weak localization in two-dimensional disordered Frenkel lattices

The standard one-parameter scaling theory predicts that all eigenstates in two-dimensional random lattices are weakly localized. We show that this claim fails in two-dimensional dipolar Frenkel exciton systems. The linear energy dispersion at the top of the exciton band, originating from the long-range inter-site coupling of dipolar nature, yields the same size-scaling law for the level spacing and the effective disorder seen by the exciton. This finally results in the delocalization of those eigenstates in the thermodynamic limit. Large scale numerical simulations allow us to perform a detailed multifractal analysis and to elucidate the nature of the excitonic eigenstates.

cond-mat.dis-nn↗
arXiv2001

Stripe Ansatzs from Exactly Solved Models

Using the Boltzmann weights of classical Statistical Mechanics vertex models we define a new class of Tensor Product Ansatzs for 2D quantum lattice systems, characterized by a strong anisotropy, which gives rise to stripe like structures. In the case of the six vertex model we compute exactly, in the thermodynamic limit, the norm of the ansatz and other observables. Employing this ansatz we study the phase diagram of a Hamiltonian given by the sum of XXZ Hamiltonians along the legs coupled by an Ising term. Finally, we suggest a connection between the six and eight-vertex Anisotropic Tensor Product Ansatzs, and their associated Hamiltonians, with the smectic stripe phases recently discussed in the literature.

cond-mat.str-el↗
arXiv2001

Renormalization Group study of the Sliding Luttinger liquids

We derive the RG-flow equations of the sliding Luttinger liquid perturbed by charge-density-wave (CDW) and superconducting (SC) operators. Using them we study the phase diagram of an array of XXZ spin chains coupled by Ising terms. In the weak coupling regime we find a new class of non-gaussian and unstable fixed points whose existence is due to a balance between the CDW, SC and sliding Luttinger couplings.

cond-mat.supr-con↗
arXiv2000

A Density Matrix Renormalization Group study of Excitons in Dendrimers

We introduce the density matrix renormalization group (DMRG) method as an efficient computational tool for one-exciton approximations with off-diagonal disorder. This method allows us to reduce the computational effort by targetting only a few low-lying eigenstates at each statistical sampling, in contrast to the exact diagonalization methods that compute the whole spectrum. As an application of the method, we study excitons in two families of branched molecules called dendrimers using a recently introduced simple model. We compute the absortion peaks for these dendrimers varying their generation number $g$ and number of wedges $w$.

cond-mat.str-el↗
arXiv2000

Single-Block Renormalization Group: Quantum Mechanical Problems

We reformulate the density matrix renormalization group method (DMRG) in terms of a single block, instead of the standard left and right blocks used in the construction of the superblock. This version of the DMRG, which we call the puncture renormalization group (PRG), makes easy and natural the extension of the DMRG to higher dimensional lattices. To test numerically this proposal, we study several quantum mechanical models in one, two and three dimensions. In 1D the performance of the standard DMRG is much better than its PRG version, however for 2D models the PRG is more efficient than the DMRG in a variety of circumstances. In 3D the PRG performs also quite well.

cond-mat↗
arXiv1999

The Crossover from the Bulk to the Few-Electron limit in Ultrasmall Metallic Grains

We study the properties of ultrasmall metallic grains with sizes in the range of 20 up to 400 electrons. Using a particle-hole version of the DMRG method we compute condensation energies, spectroscopic gaps, pairing parameters and particle-hole probabilities of the ground state wave function. The results presented in this paper confirm that the bulk superconducting regime (large grains) and the fluctuation dominated regime (small grains) are qualitative different, but show that the crossover between them is very smooth with no signs of critical level spacings separating them. We compare our DMRG results with the exact ones obtained with the Richardson solution finding complete agreement. We also propose a simplified version of the DMRG wave function, called the Particle-Hole BCS ansatz, which agrees qualitatively with the DMRG solution and illustrates what is lacking in the PBCS wave function in order to describe correctly the crossover. Finally we present a new recursive method to compute norms and expectation values with the PBCS wave function.

cond-mat.supr-con↗
arXiv1999

Exact Study of the Effect of Level Statistics in Ultrasmall Superconducting Grains

The reduced BCS model that is commonly used for ultrasmall superconducting grains has an exact solution worked out long ago by Richardson in the context of nuclear physics. We use it to check the quality of previous treatments of this model, and to investigate the effect of level statistics on pairing correlations. We find that the ground state energies are on average somewhat lower for systems with non-uniform than uniform level spacings, but both have an equally smooth crossover from the bulk to the few-electron regime. In the latter, statistical fluctuations in ground state energies strongly depend on the grain's electron number parity.

cond-mat.supr-con↗
arXiv1999

The Recurrent Variational Approach applied to the Electronic Structure of Conjugated Polymers

In this note, first the Recurrent Variational Approach (RVA) is introduced by using as example a non-trivial spin-model, the spin-1/2 antiferromagnetic two-leg-ladder. Then, a first application of this scheme to the electronic structure of conjugated polymers is proposed. An analogy between the two-leg ladder and the dimerized chain described by the Extended Peierls-Hubbard Hamiltonian is underlined and comparisons are made with DMRG calculations. The proposed ansatz is useful to get some analytical insight and it is a good starting point for further improvements using the RVA.

cond-mat↗
arXiv1999

Matrix Product Approach to Conjugated Polymers

The Matrix Product method (MPM) has been used in the past to generate variational ansatzs of the ground state (GS) of spin chains and ladders. In this paper we apply the MPM to study the GS of conjugated polymers in the valence bond basis, exploiting the charge and spin conservation as well as the electron-hole and spin-parity symmetries. We employ the $U-V-δ$ Hamiltonian which is a simplified version of the PPP Hamiltonian. For several coupling constants $U$ and $V$ and dimerizations $δ$ we compute the GS energy per monomer which agrees within a $2%-4%$ accuracy with the DMRG results. We also show the evolution of the MP-variational parameters in the weak and strong dimerization regimes.

cond-mat.str-el↗
arXiv1999

A Density Matrix Renormalization Group Study of Ultrasmall Superconducting Grains

We apply the DMRG method to the BCS pairing Hamiltonian which describes ultrasmall superconducting grains. Our version of the DMRG uses the particle (hole) states around the Fermi level as the system block (environment). We observe a smooth logarithmic-like crossover between the few electron regime and the BCS-bulk regime.

cond-mat.supr-con↗