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Ingo Peschel

Publications and source records attributed to Ingo Peschel.

32 records · Page 2Linked to original sources
arXiv2005

Critical entanglement of XXZ Heisenberg chains with defects

We study the entanglement properties of anisotropic open spin one-half Heisenberg chains with a modified central bond. The entanglement entropy between the two half-chains is calculated with the density-matrix renormalization method (DMRG).We find a logarithmic behaviour with an effective central charge c' varying with the length of the system. It flows to one in the ferromagnetic region and to zero in the antiferromagnetic region of the model. In the XX case it has a non-universal limit and we recover previous results.

cond-mat.stat-mech↗
arXiv2005

Entanglement entropy with interface defects

We consider a section of a half-filled chain of free electrons and its entanglement with the rest of the system in the presence of one or two interface defects. We find a logarithmic behaviour of the entanglement entropy with constants depending continuously on the defect strength.

cond-mat.stat-mech↗
arXiv2004

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.

cond-mat.stat-mech↗
arXiv2002

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.

cond-mat↗
arXiv2001

Symmetry breaking and phase coexistence in a driven diffusive two-channel system

We consider classical hard-core particles moving on two parallel chains in the same direction. An interaction between the channels is included via the hopping rates. For a ring, the stationary state has a product form. For the case of coupling to two reservoirs, it is investigated analytically and numerically. In addition to the known one-channel phases, two new regions are found, in particular the one, where the total density is fixed, but the filling of the individual chains changes back and forth, with a preference for strongly different densities. The corresponding probability distribution is determined and shown to have an universal form. The phase diagram and general aspects of the problem are discussed.

cond-mat.stat-mech↗
arXiv2001

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.

cond-mat.stat-mech↗
arXiv2000

On Density-Matrix Spectra for Two-Dimensional Quantum Systems

For a two-dimensional system of coupled oscillators, the spectra of reduced density matrices can be obtained analytically. This provides an example where the features of these quantities, which are of central importance in numerical studies using the DMRG method, can be seen.

cond-mat.stat-mech↗
arXiv2000

Exactly solvable statistical model for two-way traffic

We generalize a recently introduced traffic model, where the statistical weights are associated with whole trajectories, to the case of two-way flow. An interaction between the two lanes is included which describes a slowing down when two cars meet. This leads to two coupled five-vertex models. It is shown that this problem can be solved by reducing it to two one-lane problems with modified parameters. In contrast to stochastic models, jamming appears only for very strong interaction between the lanes.

cond-mat.stat-mech↗
arXiv1999

Density Matrices for a Chain of Oscillators

We consider chains with an optical phonon spectrum and study the reduced density matrices which occur in density-matrix renormalization group (DMRG) calculations. Both for one site and for half of the chain, these are found to be exponentials of bosonic operators. Their spectra, which are correspondingly exponential, are determined and discussed. The results for large systems are obtained from the relation to a two-dimensional Gaussian model.

cond-mat.stat-mech↗
arXiv1996

A unified treatment of Ising model magnetizations

We show how the spontaneous bulk, surface and corner magnetizations in the square lattice Ising model can all be obtained within one approach. The method is based on functional equations which follow from the properties of corner transfer matrices and vertex operators and which can be derived graphically. In all cases, exact analytical expressions for general anisotropy are obtained. Known results, including several for which only numerical computation was previously possible, are verified and new results related to general anisotropy and corner angles are obtained.

cond-mat.stat-mech↗
arXiv1996

Casimir Terms and Shape Instabilities for Two-Dimensional Critical Systems

We calculate the universal part of the free energy of certain finite two- dimensional regions at criticality by use of conformal field theory. Two geometries are considered: a section of a circle ("pie slice") of angle ϕand a helical staircase of finite angular (and radial) extent. We derive some consequences for certain matrix elements of the transfer matrix and corner transfer matrix. We examine the total free energy, including non- universal edge free energy terms, in both cases. A new, general, Casimir instability toward sharp corners on the boundary is found; other new instability behavior is investigated. We show that at constant area and edge length, the rectangle is unstable against small curvature.

cond-mat↗
arXiv1995

On Matrix Product Ground States for Reaction-Diffusion Models

We discuss a new mechanism leading to a matrix product form for the stationary state of one-dimensional stochastic models. The corresponding algebra is quadratic and involves four different matrices. For the example of a coagulation-decoagulation model explicit four-dimensional representations are given and exact expressions for various physical quantities are recovered. We also find the general structure of $n$-point correlation functions at the phase transition.

cond-mat↗
arXiv1995

Solution of a One-Dimensional Reaction-Diffusion Model with Spatial Asymmetry

We study classical particles on the sites of an open chain which diffuse, coagulate and decoagulate preferentially in one direction. The master equation is expressed in terms of a spin one-half Hamiltonian $H$ and the model is shown to be completely solvable if all processes have the same asymmetry. The relaxational spectrum is obtained directly from $H$ and via the equations of motion for strings of empty sites. The structure and the solvability of these equations are investigated in the general case. Two phases are shown to exist for small and large asymmetry, respectively, which differ in their stationary properties.

cond-mat↗