On the reduced density matrix for a chain of free electrons

The properties of the reduced density matrix describing an interval of N sites in an infinite chain of free electrons are investigated. A commuting operator is found for arbitrary filling and also for open chains. For a half filled periodic chain it is used to determine the eigenfunctions for the dominant eigenvalues analytically in the continuum limit. Relations to the critical six-vertex model are discussed.Comment: 8 pages, small changes, Equ.(24) corrected, final versio

Calculation of reduced density matrices from correlation functions

It is shown that for solvable fermionic and bosonic lattice systems, the reduced density matrices can be determined from the properties of the correlation functions. This provides the simplest way to these quantities which are used in the density-matrix renormalization group method.Comment: 4 page

On entanglement evolution across defects in critical chains

We consider a local quench where two free-fermion half-chains are coupled via a defect. We show that the logarithmic increase of the entanglement entropy is governed by the same effective central charge which appears in the ground-state properties and which is known exactly. For unequal initial filling of the half-chains, we determine the linear increase of the entanglement entropy.Comment: 11 pages, 5 figures, minor changes, reference adde

Ising films with surface defects

The influence of surface defects on the critical properties of magnetic films is studied for Ising models with nearest-neighbour ferromagnetic couplings. The defects include one or two adjacent lines of additional atoms and a step on the surface. For the calculations, both density-matrix renormalization group and Monte Carlo techniques are used. By changing the local couplings at the defects and the film thickness, non-universal features as well as interesting crossover phenomena in the magnetic exponents are observed.Comment: 8 pages, 12 figures included, submitted to European Physical Journal

Real-space renormalization group approach for the corner Hamiltonian

We present a real-space renormalization group approach for the corner Hamiltonian, which is relevant to the reduced density matrix in the density matrix renormalization group. A set of self-consistent equations that the renormalized Hamiltonian should satisfy in the thermodynamic limit is also derived from the fixed point of the recursion relation for the corner Hamiltonian. We demonstrate the renormalization group algorithm for the $S=1/2$ XXZ spin chain and show that the results are consistent with the exact solution. We further examine the renormalization group for the S=1 Heisenberg spin chain and then discuss the nature of the eigenvalue spectrum of the corner Hamiltonian for the non-integrable model.Comment: 7 page

One-dimensional Hubbard model at quarter filling on periodic potentials

Using the Hubbard chain at quarter filling as a model system, we study the ground state properties of highly doped antiferromagnets. In particular, the Hubbard chain at quarter filling is unstable against 2k_F- and 4k_F-periodic potentials, leading to a large variety of charge and spin ordered ground states. Employing the density matrix renormalization group method, we compare the energy gain of the ground state induced by different periodic potentials. For interacting systems the lowest energy is found for a 2k_F-periodic magnetic field, resulting in a band insulator with spin gap. For strong interaction, the 4k_F-periodic potential leads to a half-filled Heisenberg chain and thus to a Mott insulating state without spin gap. This ground state is more stable than the band insulating state caused by any non-magnetic 2k_F-periodic potential. Adding more electrons, a cluster-like ordering is preferred.Comment: 8 pages, 5 figures, accepted by Phys. Rev.

Density-Matrix Spectra of Solvable Fermionic Systems

We consider non-interacting fermions on a lattice and give a general result for the reduced density matrices corresponding to parts of the system. This allows to calculate their spectra, which are essential in the DMRG method, by diagonalizing small matrices. We discuss these spectra and their typical features for various fermionic quantum chains and for the two-dimensional tight-binding model.Comment: 12 pages and 9 figure

Phase Diagram of a 2D Vertex Model

Phase diagram of a symmetric vertex model which allows 7 vertex configurations is obtained by use of the corner transfer matrix renormalization group (CTMRG), which is a variant of the density matrix renormalization group (DMRG). The critical indices of this model are identified as $\beta = 1/8$ and $\alpha = 0$.Comment: 2 pages, 5 figures, short not

Wilson-like real-space renormalization group and low-energy effective spectrum of the XXZ chain in the critical regime

We present a novel real-space renormalization group(RG) for the one-dimensional XXZ model in the critical regime, reconsidering the role of the cut-off parameter in Wilson's RG for the Kondo impurity problem. We then demonstrate the RG calculation for the XXZ chain with the free boundary. Comparing the hierarchical structure of the obtained low-energy spectrum with the Bethe ansatz result, we find that the proper scaling dimension is reproduced as a fixed point of the RG transformation.Comment: 4 pages, 6 figures, typos corrected, final versio

Spectral Density of the Two-Impurity Anderson Model

We investigate static and dynamical ground-state properties of the two-impurity Anderson model at half filling in the limit of vanishing impurity separation using the dynamical density-matrix renormalization group method. In the weak-coupling regime, we find a quantum phase transition as function of inter-impurity hopping driven by the charge degrees of freedom. For large values of the local Coulomb repulsion, the transition is driven instead by a competition between local and non-local magnetic correlations. We find evidence that, in contrast to the usual phenomenological picture, it seems to be the bare effective exchange interactions which trigger the observed transition.Comment: 18 pages, 6 figures, submitted to J. Phys.:Condens. Matte