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Alexander Weiße

Publications and source records attributed to Alexander Weiße.

11 recordsLinked to original sources
arXiv2021

Short-distance thermal correlations in the XXZ chain

Recent studies have revealed much of the mathematical structure of the static correlation functions of the XXZ chain. Here we use the results of those studies in order to work out explicit examples of short-distance correlation functions in the infinite chain. We compute two-point functions ranging over 2, 3 and 4 lattice sites as functions of the temperature and the magnetic field for various anisotropies in the massless regime $- 1 < Δ< 1$. It turns out that the new formulae are numerically efficient and allow us to obtain the correlations functions over the full parameter range with arbitrary precision.

cond-mat.str-el↗
arXiv2021

Fourth-neighbour two-point functions of the XXZ chain and the Fermionic basis approach

We give a descriptive review of the Fermionic basis approach to the theory of correlation functions of the XXZ quantum spin chain. The emphasis is on explicit formulae for short-range correlation functions which will be presented in a way that allows for their direct implementation on a computer. Within the Fermionic basis approach a huge class of stationary reduced density matrices, compatible with the integrable structure of the model, assumes a factorized form. This means that all expectation values of local operators and all two-point functions, in particular, can be represented as multivariate polynomials in only two functions $ρ$ and $ω$ and their derivatives with coefficients that are rational in the deformation parameter $q$ of the model. These coefficients are of `algebraic origin'. They do not depend on the choice of the density matrix, which only impacts the form of $ρ$ and $ω$. As an example we work out in detail the case of the grand canonical ensemble at temperature $T$ and magnetic field $h$ for $q$ in the critical regime. We compare our exact results for the fourth-neighbour two-point functions with asymptotic formulae for $h, T = 0$ and for finite $h$ and $T$.

cond-mat.stat-mech↗
arXiv2018

Zero is a resonance of every Schottky surface

For certain spectral parameters we find explicit eigenfunctions of transfer operators for Schottky surfaces. Comparing the dimension of the eigenspace for the spectral parameter zero with the multiplicity of topological zeros of the Selberg zeta function, we deduce that zero is a resonance of every Schottky surface.

math.SP↗
arXiv2014

Root systems, spectral curves, and analysis of a Chern-Simons matrix model for Seifert fibered spaces

We study a class of scalar, linear, non-local Riemann-Hilbert problems (RHP) involving finite subgroups of PSL(2,C). We associate to such problems a (maybe infinite) root system and describe the relevance of the orbits of the Weyl group in the construction of its solutions. As an application, we study in detail the large N expansion of SU(N) or SO(N) or Sp(2N) Chern-Simons partition function Z_N(M) of 3-manifolds M that are either rational homology spheres or more generally Seifert fibered spaces. It has a matrix model-like representation, whose spectral curve can be characterized in terms of a RHP as above. When pi_1(M) is finite (i.e. for manifolds M that are quotients of \mathbb{S}_{3} by a finite isometry group of type ADE), the Weyl group associated to the RHP is finite and the spectral curve is algebraic and can be in principle computed. We then show that the large $N$ expansion of Z_N(M) is computed by the topological recursion. This has consequences for the analyticity properties of SU/SO/Sp perturbative invariants of knots along fibers in $M$.

math-ph↗
arXiv2013

Divide and conquer the Hilbert space of translation-symmetric spin systems

Iterative methods that operate with the full Hamiltonian matrix in the untrimmed Hilbert space of a finite system continue to be important tools for the study of one- and two-dimensional quantum spin models, in particular in the presence of frustration. To reach sensible system sizes such numerical calculations heavily depend on the use of symmetries. We describe a divide-and-conquer strategy for implementing translation symmetries of finite spin clusters, which efficiently uses and extends the "sublattice coding" of H. Q. Lin. With our method, the Hamiltonian matrix can be generated on-the-fly in each matrix vector multiplication, and problem dimensions beyond 10^11 become accessible.

cond-mat.str-el↗
arXiv2011

On the theory of microwave absorption by the spin-1/2 Heisenberg-Ising magnet

We analyze the problem of microwave absorption by the Heisenberg-Ising magnet in terms of shifted moments of the imaginary part of the dynamical susceptibility. When both, the Zeeman field and the wave vector of the incident microwave, are parallel to the anisotropy axis, the first four moments determine the shift of the resonance frequency and the line width in a situation where the frequency is varied for fixed Zeeman field. For the one-dimensional model we can calculate the moments exactly. This provides exact data for the resonance shift and the line width at arbitrary temperatures and magnetic fields. In current ESR experiments the Zeeman field is varied for fixed frequency. We show how in this situation the moments give perturbative results for the resonance shift and for the integrated intensity at small anisotropy as well as an explicit formula connecting the line width with the anisotropy parameter in the high-temperature limit.

cond-mat.str-el↗
arXiv2009

Green-Function-Based Monte Carlo Method for Classical Fields Coupled to Fermions

Microscopic models of classical degrees of freedom coupled to non-interacting fermions occur in many different contexts. Prominent examples from solid state physics are descriptions of colossal magnetoresistance manganites and diluted magnetic semiconductors, or auxiliary field methods for correlated electron systems. Monte Carlo simulations are vital for an understanding of such systems, but notorious for requiring the solution of the fermion problem with each change in the classical field configuration. We present an efficient, truncation-free O(N) method on the basis of Chebyshev expanded local Green functions, which allows us to simulate systems of unprecedented size N.

cond-mat.stat-mech↗
arXiv2003

Mixed-phase description of colossal magnetoresistive manganites

In view of recent experiments, indicating the spatial coexistence of conducting and insulating regions in the ferromagnetic metallic phase of doped manganites, we propose a refined mixed-phase description. The model is based on the competition of a double-exchange driven metallic component and a polaronic insulating component, whose volume fractions and carrier concentrations are determined self-consistently by requiring equal pressure and chemical potential. The resulting phase diagram as well as the order of the phase transition are in very good agreement with measured data. In addition, modelling the resistivity of the mixed, percolative phase by a random resistor network, we obtain a pronounced negative magnetoresistance in the vicinity of the Curie temperature $T_C$.

cond-mat.str-el↗
arXiv2000

Lattice dynamical effects on the Peierls transition in one-dimensional metals and spin chains

The interplay of charge, spin and lattice degrees of freedom is studied for quasi-one-dimensional electron and spin systems coupled to quantum phonons. Special emphasis is put on the influence of the lattice dynamics on the Peierls transition. Using exact diagonalization techniques the ground-state and spectral properties of the Holstein model of spinless fermions and of a frustrated Heisenberg model with magneto-elastic coupling are analyzed on finite chains. In the non-adiabatic regime a (T=0) quantum phase transition from a gapless Luttinger-liquid/spin-fluid state to a gapped dimerized phase occurs at a nonzero critical value of the electron/spin-phonon interaction. To study the nature of the spin-Peierls transition at finite temperatures for the infinite system, an alternative Green's function approach is applied to the magnetostrictive XY model. With increasing phonon frequency the structure factor shows a remarkable crossover from soft-mode to central-peak behaviour. The results are discussed in relation to recent experiments on $\rm CuGeO_3$.

cond-mat.str-el↗