arXiv subjects

Kai P. Schmidt

Publications and source records attributed to Kai P. Schmidt.

27 records · Page 2Linked to original sources

arXiv2005

Hardcore Magnons in the S=1/2 Heisenberg Model on the Square Lattice

We propose a versatile approach to treat commonly arising constraints. It is illustrated for interacting magnons of the Heisenberg antiferromagnet on a square lattice. For systems of $L\times L$ sites a non-perturbative continuous unitary transformation (CUT) is used to derive an effective Hamiltonian conserving the number of magnons. They are bosonic particles with a hardcore constraint which is captured by a local, repulsive interaction U. The limits $U\to\infty$ and $L\to\infty$ are achieved by extrapolation. The residual spin gap $Δ_1$ is smaller than 0.01J reflecting the gapless nature of the magnons. The one-magnon dispersion displays all known characteristics.

cond-mat.str-el↗

arXiv2005

Spectral Properties of Magnetic Excitations in Cuprate Two-Leg Ladder Systems

This article summarizes and extends the recent developments in the microscopic modeling of the magnetic excitations in cuprate two-leg ladder systems. The microscopic Hamiltonian comprises dominant Heisenberg exchange terms plus an additional four-spin interaction which is about five times smaller. We give an overview over the relevant energies like the one-triplon dispersion, the energies of two-triplon bound states and the positions of multi-triplon continua and over relevant spectral properties like spectral weights and spectral densities in the parameter regime appropriate for cuprate systems. It is concluded that an almost complete understanding of the magnetic excitations in undoped cuprate ladders has been obtained as measured by inelastic neutron scattering, inelastic light (Raman) scattering and infrared absorption.

cond-mat.str-el↗

arXiv2004

Spectral properties of the dimerized and frustrated $S=1/2$ chain

Spectral densities are calculated for the dimerized and frustrated S=1/2 chain using the method of continuous unitary transformations (CUTs). The transformation to an effective triplon model is realized in a perturbative fashion up to high orders about the limit of isolated dimers. An efficient description in terms of triplons (elementary triplets) is possible: a detailed analysis of the spectral densities is provided for strong and intermediate dimerization including the influence of frustration. Precise predictions are made for inelastic neutron scattering experiments probing the S=1 sector and for optical experiments (Raman scattering, infrared absorption) probing the S=0 sector. Bound states and resonances influence the important continua strongly. The comparison with the field theoretic results reveals that the sine-Gordon model describes the low-energy features for strong to intermediate dimerization only at critical frustration.

cond-mat.str-el↗

arXiv2004

High Order Perturbation Theory for Spectral Densities of Multi-Particle Excitations: S=1/2 Two-Leg Heisenberg Ladder

We present a high order perturbation approach to quantitatively calculate spectral densities in three distinct steps starting from the model Hamiltonian and the observables of interest. The approach is based on the perturbative continuous unitary transformation introduced previously. It is conceived to work particularly well in models allowing a clear identification of the elementary excitations above the ground state. These are then viewed as quasi-particles above the vacuum. The article focuses on the technical aspects and includes a discussion of series extrapolation schemes. The strength of the method is demonstrated for S=1/2 two-leg Heisenberg ladders, for which results are presented.

cond-mat.str-el↗

arXiv2003

The Structure of Operators in Effective Particle-Conserving Models

For many-particle systems defined on lattices we investigate the global structure of effective Hamiltonians and observables obtained by means of a suitable basis transformation. We study transformations which lead to effective Hamiltonians conserving the number of excitations. The same transformation must be used to obtain effective observables. The analysis of the structure shows that effective operators give rise to a simple and intuitive perspective on the initial problem. The systematic calculation of n-particle irreducible quantities becomes possible constituting a significant progress. Details how to implement the approach perturbatively for a large class of systems are presented.

cond-mat.str-el↗

arXiv2003

Excitations in one-dimensional S=1/2 quantum antiferromagnets

The transition from dimerized to uniform phases is studied in terms of spectral weights for spin chains using continuous unitary transformations (CUTs). The spectral weights in the S=1 channel are computed perturbatively around the limit of strong dimerization. We find that the spectral weight is concentrated mainly in the subspaces with a small number of elementary triplets (triplons), even for vanishing dimerization. So, besides spinons, triplons may be used as elementary excitations in spin chains. We conclude that there is no necessity to use fractional excitations in low-dimensional, undoped or doped quantum antiferromagnets.

cond-mat.str-el↗

arXiv2002

Thermodynamic Properties of Spin Ladders with Cyclic Exchange

By high temperature series expansion and exact complete diagonalization the magnetic susceptibility chi(T) and the specific heat C(T) of a two-leg S=1/2 ladder with cyclic (4-spin) exchange are computed. Both methods yield convincing results for not too small temperatures. We find that a small amount of cyclic exchange influences the thermodynamical properties significantly. Our results can serve as reliable basis for an efficient analysis of experimental data

cond-mat.str-el↗

arXiv2001

Multi-particle excitations and spectral densities in quantum spin-systems

The excitation spectrum of the 2-leg S=1/2 Heisenberg ladder is examined perturbatively. Using an optimally chosen continuous unitary transformation we expand the Hamiltonian and the Raman operator about the limit of isolated rungs leading to high order series expansions allowing to calculate spectral densities quantitatively. The 2-particle sector is examined for total momentum k=0. We show that triplet-triplet interaction gives rise to a band splitting.

cond-mat.str-el↗

arXiv2001

Raman Response in Antiferromagnetic Two-Leg S=1/2 Heisenberg Ladders

The Raman response in the antiferromagnetic 2-leg S=1/2 Heisenberg ladder is calculated for various couplings by continuous unitary transformations. For leg couplings above 80% of the rung coupling a characteristic 2-peak structure occurs with a point of zero intensity within the continuum. Experimental data for CaV_2O_5 and La_yCa_(14-y)Cu_24O_41 are analyzed and the coupling constants are determined. Evidence is found that the Heisenberg model is not sufficient to describe cuprate ladders. We argue that a cyclic exchange term is the appropriate extension.

cond-mat.str-el↗