F. Ortolani

Quantum chemistry using the density matrix renormalization group

A new implementation of the density matrix renormalization group is presented for ab initio quantum chemistry. Test computations have been performed of the dissociation energies of the diatomics Be2, N2, HF. A preliminary calculation on the Cr2 molecule provides a new variational upper bound to the ground state energy.

The density matrix renormalization group method. Application to the PPP model of a cyclic polyene chain.

The density matrix renormalization group (DMRG) method introduced by White for the study of strongly interacting electron systems is reviewed; the method is variational and considers a system of localized electrons as the union of two adjacent fragments A,B. A density matrix ρ is introduced, whose eigenvectors corresponding to the largest eigenvalues are the most significant, the most probable states of A in the presence of B; these states are retained, while states corresponding to small eigenvalues of ρ are neglected. It is conjectured that the decreasing behavior of the eigenvalues is Gaussian. The DMRG method is tested on the Pariser-Parr-Pople Hamiltonian of a cyclic polyene (CH)N up to N=34. A Hilbert space of dimension 5.×1018 is explored. The ground state energy is 10−3 eV within the full CI value in the case N=18. The DMRG method compares favorably also with coupled cluster approximations. The unrestricted Hartree-Fock solution (which presents spin density waves) is briefly reviewed, and a compar...

Density matrix renormalization group study of dimerization of the Pariser–Parr–Pople model of polyacetilene

We apply the density matrix renormalization group method to the Pariser–Parr–Pople Hamiltonian and investigate the onset of dimerization. We deduce the parameters of the hopping term and the contribution of the σ bonds from ab initio calculations on ethylene. Denoting by Rij the C–C distances, we perform a variational optimization of the dimerization δ=(Ri,i+1−Ri−1,i)/2 and of the average bond length R0 for chains up to N=50 sites. The critical value of N at which the transition occurs is found to be between N=14 and N=18 for the present model. The asymptotic values for large N for R0 and δ are given by 1.408(3) A and 0.036(0) A.

On \(\mathsf{c = 1}\) critical phases in anisotropic spin-1 chains

Abstract.Quantum spin-1 chains may develop massless phases in presence of Ising-like and single-ion anisotropies. We have studied c = 1 critical phases by means of both analytical techniques, including a mapping of the lattice Hamiltonian onto an O(2) NL

Investigation of quantum phase transitions using multi-target DMRG methods

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Single-site entanglement at the superconductor-insulator transition in the Hirsch model

M, and a multi-target DMRG algorithm which allows for accurate calculation of excited states. We find excellent quantitative agreement with the theoretical predictions and conclude that a pure Gaussian model, without any orbifold construction, describes correctly the low-energy physics of these critical phases. This combined analysis indicates that the multicritical point at large single-ion anisotropy does not belong to the same universality class as the Takhtajan-Babujian Hamiltonian as claimed in the past. A link between string-order correlation functions and twisting vertex operators, along the c = 1 line that ends at this point, is also suggested.

Renyi entanglement entropies of descendant states in critical systems with boundaries: conformal field theory and spin chains

Abstract.In this paper we examine how the predictions of conformal invariance can be widely exploited to overcome the difficulties of the density-matrix renormalization group near quantum critical points. The main idea is to match the set of low-lying energy levels of the lattice Hamiltonian, as a function of the system’s size, with the spectrum expected for a given conformal field theory in two dimensions. As in previous studies this procedure requires an accurate targeting of various excited states. Here we discuss how this can be achieved within the DMRG algorithm by means of the recently proposed Thick-restart Lanczos method. As a nontrivial benchmark we use an anisotropic spin-1 Hamiltonian with special attention to the transitions from the Haldane phase. Nonetheless, we think that this procedure could be generally valid in the study of quantum critical phenomena.

Bound states and expansion dynamics of interacting bosons on a one-dimensional lattice

We investigate the transition to the insulating state in the one-dimensional Hubbard model with bond-charge interaction x (Hirsch model), at half-filling and T=0. By means of the density-matrix renormalization group algorithm the charge gap closure is examined by both standard finite-size scaling analysis and looking at singularities in the derivatives of single-site entanglement. The results of the two techniques show that a quantum phase transition takes place at a finite Coulomb interaction uc(x) for x≳0.5. The region 0 xc

Density-matrix renormalization-group simulation of the SU(3) antiferromagnetic Heisenberg model

We discuss the Renyi entanglement entropies of descendant states in critical one-dimensional systems with boundaries, that map to boundary conformal field theories in the scaling limit. We unify the previous conformal-field-theory approaches to describe primary and descendant states in systems with both open and closed boundaries. We provide universal expressions for the first two descendants in the identity family. We apply our technique to critical systems belonging to different universality classes with non-trivial boundary conditions that preserve conformal invariance, and find excellent agreement with numerical results obtained for finite spin chains. We also demonstrate that entanglement entropies are a powerful tool to resolve degeneracy of higher excited states in critical lattice models.

Incommmensurability and unconventional superconductor to insulator transition in the hubbard model with bond-charge interaction.

The expansion dynamics of bosonic gases in optical lattices has recently been the focus of increasing attention, both experimental and theoretical. We consider, by means of numerical Bethe ansatz, the expansion dynamics of initially confined wave packets of two interacting bosons on a lattice. We show that a correspondence between the asymptotic expansion velocities and the projection of the evolved wave function over the bound states of the system exists, clarifying the existing picture for such situations. Moreover, we investigate the role of the lattice in this kind of evolution.