arXiv subjects

I. Peschel

Publications and source records attributed to I. Peschel.

13 recordsLinked to original sources

arXiv2008

Entanglement in spin chains with gradients

We study solvable spin chains where either fields or couplings vary linearly in space and create a sandwich-like structure of the ground state. We find that the entanglement entropy between two halves of a chain varies logarithmically with the interface width. After quenching to a homogeneous critical system, the entropy grows logarithmically in time in the XX model, but quadratically in the transverse Ising chain. We explain this behaviour and indicate generalizations to other power laws.

cond-mat.stat-mech↗

arXiv2007

Entanglement evolution after connecting finite to infinite quantum chains

We study zero-temperature XX chains and transverse Ising chains and join an initially separate finite piece on one or on both sides to an infinite remainder. In both critical and non-critical systems we find a typical increase of the entanglement entropy after the quench, followed by a slow decay towards the value of the homogeneous chain. In the critical case, the predictions of conformal field theory are verified for the first phase of the evolution, while at late times a step structure can be observed.

cond-mat.stat-mech↗

arXiv2007

Evolution of entanglement after a local quench

We study free electrons on an infinite half-filled chain, starting in the ground state with a bond defect. We find a logarithmic increase of the entanglement entropy after the defect is removed, followed by a slow relaxation towards the value of the homogeneous chain. The coefficients depend continuously on the defect strength.

cond-mat.stat-mech↗

arXiv2001

Critical behaviour in parabolic geometries

We study two-dimensional systems with boundary curves described by power laws. Using conformal mappings we obtain the correlations at the bulk critical point. Three different classes of behaviour are found and explained by scaling arguments which also apply to higher dimensions. For an Ising system of parabolic shape the behaviour of the order at the tip is also found.

cond-mat.stat-mech↗

arXiv2001

Ising thin films with modulations and surface defects

Properties of magnetic films are studied in the framework of Ising models. In particular, we discuss critical phenomena of ferromagnetic Ising films with straight lines of magnetic adatoms and straight steps on the surface as well as phase diagrams of the axial next-nearest neighbour Ising (ANNNI) model for thin films exhibiting various spatially modulated phases.

cond-mat↗

arXiv2000

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.

cond-mat↗

arXiv1998

Density-matrix spectra for integrable models

The spectra which occur in numerical density-matrix renormalization group (DMRG) calculations for quantum chains can be obtained analytically for integrable models via corner transfer matrices. This is shown in detail for the transverse Ising chain and the uniaxial XXZ Heisenberg model and explains in particular their exponential character in these cases.

cond-mat.stat-mech↗

arXiv1998

A DMRG study of the q-symmetric Heisenberg chain

The spin one-half Heisenberg chain with $U_q[SU(2)]$ symmetry is studied via density-matrix renormalization. Ground-state energy and $q$-symmetric correlation functions are calculated for the non-hermitian case $q=\exp(iπ/(r+1))$ with integer $r$. This gives bulk and surface exponents for (para)fermionic correlations in the related Ising and Potts models. The case of real $q$ corresponding to a diffusion problem is treated analytically.

cond-mat.stat-mech↗

arXiv1997

Inhomogeneous Systems with Unusual Critical Behaviour

The phase transitions and critical properties of two types of inhomogeneous systems are reviewed. In one case, the local critical behaviour results from the particular shape of the system. Here scale-invariant forms like wedges or cones are considered as well as general parabolic shapes. In the other case the system contains defects, either narrow ones in the form of lines or stars, or extended ones where the couplings deviate from their bulk values according to power laws. In each case the perturbation may be irrelevant, marginal or relevant. In the marginal case one finds local exponents which depend on a parameter. In the relevant case unusual stretched exponential behaviour and/or local first order transitions appear. The discussion combines mean field theory, scaling considerations, conformal transformations and perturbation theory. A number of examples are Ising models for which exact results can be obtained. Some walks and polymer problems are considered, too.

cond-mat.stat-mech↗

arXiv1996

Length Scales and Power Laws in the Two-Dimensional Forest-Fire Model

We re-examine a two-dimensional forest-fire model via Monte-Carlo simulations and show the existence of two length scales with different critical exponents associated with clusters and with the usual two-point correlation function of trees. We check resp. improve previously obtained values for other critical exponents and perform a first investigation of the critical behaviour of the slowest relaxational mode. We also investigate the possibility of describing the critical point in terms of a distribution of the global density. We find that some qualitative features such as a temporal oscillation and a power law of the cluster-size distribution can nicely be obtained from such a model that discards the spatial structure.

cond-mat.stat-mech↗

arXiv1996

Matrix-Product States for a One-Dimensional Lattice Gas with Parallel Dynamics

The hopping motion of classical particles on a chain coupled to reservoirs at both ends is studied for parallel dynamics with arbitrary probabilities. The stationary state is obtained in the form of an alternating matrix product. The properties of one- and two-dimensional representations are studied in detail and a general relation of the matrix algebra to that of the sequential limit is found. In this way the general phase diagram of the model is obtained. The mechanism of the sequential limit, the formulation as a vertex model and other aspects are discussed.

cond-mat↗

arXiv1995

Critical Properties of the One-Dimensional Forest-Fire Model

The one-dimensional forest-fire model including lightnings is studied numerically and analytically. For the tree correlation function, a new correlation length with critical exponent ν~ 5/6 is found by simulations. A Hamiltonian formulation is introduced which enables one to study the stationary state close to the critical point using quantum-mechanical perturbation theory. With this formulation also the structure of the low-lying relaxation spectrum and the critical behaviour of the smallest complex gap are investigated numerically. Finally, it is shown that critical correlation functions can be obtained from a simplified model involving only the total number of trees although such simplified models are unable to reproduce the correct off-critical behaviour.

cond-mat↗

arXiv1994

Spectra of Quantum Chains without the Yang-Baxter Equation

We study one-dimensional reaction-diffusion models described by master equations and their associated two-state quantum Hamiltonians. By choosing appropriate rates, the equations of motion decouple into certain subsets. We solve the first subset which has a close relation to the problem of lattice electrons in an electric field. In this way we obtain $L (L - 1) + 1$ energy levels of a quantum chain with $L$ sites. The corresponding Hamiltonian depends on 7 parameters and does not look integrable using conventional methods. As an application, we compute the dynamical critical exponent of a new type of kinetic Ising model.

cond-mat↗