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A. Fledderjohann

Publications and source records attributed to A. Fledderjohann.

18 recordsLinked to original sources
arXiv2009

Real space renormalization group approach to the 2d antiferromagnetic Heisenberg model

The low energy behaviour of the 2d antiferromagnetic Heisenberg model is studied in the sector with total spins $S=0,1,2$ by means of a renormalization group procedure, which generates a recursion formula for the interaction matrix $Δ_S^{(n+1)}$ of 4 neighbouring "$n$ clusters" of size $2^n\times 2^n$, $n=1,2,3,...$ from the corresponding quantities $Δ_S^{(n)}$. Conservation of total spin $S$ is implemented explicitly and plays an important role. It is shown, how the ground state energies $E_S^{(n+1)}$, $S=0,1,2$ approach each other for increasing $n$, i.e. system size. The most relevant couplings in the interaction matrices are generated by the transitions $ $ between the ground states $|S,m;n+1>$ ($m=-S,...,S$) on an $(n+1)$-cluster of size $2^{n+1}\times 2^{n+1}$, mediated by the staggered spin operator $S_q^*$

cond-mat.str-el↗
arXiv2009

Deconfinement phase transition in a two-dimensional model of interacting $2\times 2$ plaquettes

A two-dimensional model of interacting plaquettes is studied by means of the real space renormalization group approach. Interactions between the plaquettes are mediated solely by spin excitations on the plaquettes. Depending on the plaquette-plaquette coupling $J$, we find two regimes: "confinement" $J_c< J\leq 1$, where the singlet ground state forms an infinite ("confined") cluster in the thermodynamical limit. Here the singlet-triplet gap vanishes, which is the signature for long range spin-spin correlators. "deconfinement" $0\leq J< J_c$, where the singlet ground state "deconfines" - i.e. factorizes - into finite $n$-clusters of size $2^n\times 2^n$, with $n\leq n_c(J)$. Here the singlet-triplet gap is finite. The critical value turns out to be $J_c=0.473528..$.

cond-mat.str-el↗
arXiv2006

Formation of clusters in the two dimensional t-J model: The mechanism for phase separation

The emergence of phase separation is investigated in the framework of a 2D t-J model by means of a variational product ansatz, which covers the infinite lattice by two types of L x L clusters. Clusters of the first type are completely occupied with electrons, i.e. they carry maximal charge Q_e=L^2 and total spin 0, and thereby form the antiferromagnetic background. Holes occur in the second type of clusters -- called ``hole clusters''. They carry a charge Q_h 0.5) it turns out that hole clusters are occupied with an even number Q_h<L^2 of electrons and carry a total spin 0. For increasing αthe charge Q_h(α) of the hole clusters decreases.Some points on the boundary curve can be extracted from Q_h(α).

cond-mat.str-el↗
arXiv2005

Ferromagnetism in a hard-core boson model

The problem of ferromagnetism -- associated with a ground state with maximal total spin -- is discussed in the framework of a hard-core model, which forbids the occupancy at each site with more than one particle. It is shown that the emergence of ferromagnetism on finite square lattices crucially depends on the statistics of the particles. Fermions (electrons) lead to the well-known instabilities for finite hole densities, whereas for bosons (with spin) ferromagnetism appears to be stable for all hole densities.

cond-mat.str-el↗
arXiv2004

Formation of clusters in the ground state of the $t-J$ model on a two leg ladder

We investigate the ground state properties of the $t-J$ model on a two leg ladder with anisotropic couplings ($t,α=J/t$) along rungs and ($t',α'=J'/t'$) along legs. We have implemented a cluster approach based on 4-site plaqettes. In the strong asymmetric cases $α/α'\ll 1$ and $α'/α\ll 1$ the ground state energy is well described by plaquette clusters with charges $Q=2,4$. The interaction between the clusters favours the condensation of plaquettes with maximal charge -- a signal for phase separation. The dominance of Q=2 plaquettes explains the emergence of tightly bound hole pairs. We have presented the numerical results of exact diagonalization to support our cluster approach.

cond-mat.str-el↗
arXiv2003

Charge density plateaux and insulating phases in the $t-J$ model with ladder geometry

We discuss the occurrence and the stability of charge density plateaux in ladder-like $t-J$ systems (at zero magnetization M=0) for the cases of 2- and 3-leg ladders. Starting from isolated rungs at zero leg coupling, we study the behaviour of plateaux-related phase transitions by means of first order perturbation theory and compare our results with Lanczos diagonalizations for $t-J$ ladders ($N=2\times 8$) with increasing leg couplings. Furthermore we discuss the regimes of rung and leg couplings that should be favoured for the appearance of the charge density plateaux.

cond-mat↗
arXiv2002

Instability of isolated triplet excitations on the Shastry-Sutherland lattice (SSL)

Configurations of singlets and triplets on the SSL have been proposed in the literature as variational ground states of the Shastry-Sutherland model at fixed magnetization M. We prove, that isolated triplet excitations on the SSL are unstable if the coupling alpha falls below a critical value alpha_c=2.0 (approx.). The instability should be visible in the compound SrCu_2(BO_3)_2 where a coupling alpha^*=1.48 is realized.

cond-mat↗
arXiv2002

Magnetic order in the Shastry-Sutherland model

The ground state properties of the Shastry-Sutherland model in the presence of an external field are investigated by means of variational states built up from unpaired spins (monomers) and singlet pairs of spins (dimers). The minimum of the energy is characterized by specific monomer-dimer configurations, which visualize the magnetic order in the sectors with fixed magnetization M=S/N. A change in the magnetic order is observed if the frustrating coupling alpha exceeds a critical value alpha_c(M), which depends on M. Special attention is paid to the ground state configurations at M=1/4, 1/6, 1/8.

cond-mat↗
arXiv2001

The magnetization process in the 2-dimensional J_1-J_2 model

We study the alpha = J_2/J_1-dependence of the magnetization process in the J_1-J_2 model on a square lattice with frustrating couplings J_2 along the diagonals. Perturbation expansions around alpha=J_2/J_1=0 and 1/alpha=0$ yield an adequate description of the magnetization curve in the antiferromagnetic and collinear antiferromagnetic phase, respectively. The transition from one phase to the other (0.5 < alpha < 0.7) leaves pronounced structures in the longitudinal and transverse structure factors at p=(pi,pi) and p=(0,pi).

cond-mat↗
arXiv2000

A numerical study of the formation of magnetisation plateaus in quasi one-dimensional spin-1/2 Heisenberg models

We study the magnetisation process of the one dimensional spin-1/2 antiferromagnetic Heisenberg model with modulated couplings over j=1,2,3 sites. It turns out that the evolution of magnetisation plateaus depends on j and on the wave number q of the modulation according to the rule of Oshikawa, et al. A mapping of two- and three-leg zig-zag ladders on one dimensional systems with modulated couplings yields predictions for the occurence of magnetization plateaus. The latter are tested by numerical computations with the DMRG algorithm.

cond-mat.str-el↗
arXiv1998

Soft modes, Gaps and Magnetization Plateaus in 1D Spin-1/2 Antiferromagnetic Heisenberg Models

We study the one-dimensional spin-1/2 model with nearest and next-to-nearest-neighbor couplings exposed to a homogeneous magnetic field $h_{3}$ and a dimer field with period $q$ and strength $δ$. The latter generates a magnetization plateau at $M=(1-q/π)/2$, which evolves with strength $δ$ of the perturbation as $δ^ε$, where $ε=ε(h_{3},α)$ is related to the $η$-exponent which describes the critical behavior of the dimer structure factor, if the perturbation is switched of ($δ=0$). We also discuss the appearance of magnetization plateaus in ladder systems with $l$ legs.

cond-mat.str-el↗
arXiv1998

Gap's in the antiferromagnetic Heisenberg model

We study the one-dimensional spin-1/2 antiferromagnetic Heisenberg model exposed to an external field, which is a superposition of a homogeneous field $h_{3}$ and a small periodic field of strength $h_{1}$. For the case of a transverse staggered field a gap opens, which scales with $h_{1}^{ε_{1}}$, where $ε_{1}=ε_{1}(h_{3})$ is given by the critical exponent $η_{1}(M(h_{3}))$ defined through the transverse structure factor of the model at $h_{1}=0$. For the case of a longitudinal periodic field with wave vector $q=π/2$ and strength $h_{q}$ a plateau is found in the magnetization curve at $M=1/4$. The difference of the upper- and lower magnetic field scales with $h_{3}^{u}-h_{3}^{l}\sim h_{q}^{ε_{3}}$, where $ε_{3}=ε_{3}(h_{3})$ is given by the critical exponent $η_{3}(M(h_{3}))$ defined through the longitudinal structure factor of the model at $h_{q}=0$.

cond-mat.str-el↗
arXiv1998

The 1D spin-1/2 AF-Heisenberg model in a staggered field

We investigate the scaling properties of the excitation energies and transition amplitudes of the one-dimensional spin-$1\over 2$ antiferromagnetic Heisenberg model exposed to an external perturbation. Two types of perturbations are discussed in detail: a staggered field and a dimerized field.

cond-mat.str-el↗
arXiv1997

From one to two dimensions in quantum spin systems

We study the first derivative of the staggered magnetization squared $dm^†(θ)^2/dθ$ and the second derivative $d^2e_0(θ)/dθ^2$ of the ground state energy per site. The parameter $θ$ controls the anisotropy between horizontal and vertical couplings in a two-dimensional (2D) spin-1/2 antiferromagnetic Heisenberg model. It is shown, that both derivatives diverge at $θ=1$, where the anisotropic 2D model reduces to the 1D model.

cond-mat↗
arXiv1997

Critical properties of 1-D spin 1/2 antiferromagnetic Heisenberg model

We discuss numerical results for the 1-D spin 1/2 antiferromagnetic Heisenberg model with next-to-nearest neighbour coupling and in the presence of an uniform magnetic field. The model develops zero frequency excitations at field dependent soft mode momenta. We compute critical quantities from finite size dependence of static structure factors.

cond-mat↗
arXiv1996

Magnon-magnon interactions in the Spin-Peierls compound CuGeO_3

In a magnetic substance the gap in the Raman spectrum, Delta_R, is approximatively twice the value of the neutron scattering gap, Delta_S, if the the magnetic excitations (magnons) are only weakly interacting. But for CuGeO_3 the experimentally observed ratio Delta_R/Delta_S is approximatively 1.49-1.78, indicating attractive magnon-magnon interactions in the quasi-1D Spin-Peierls compound CuGe_3. We present numerical estimates for Delta_R/Delta_S from exact diagonalization studies for finite chains and find agreement with experiment for intermediate values of the frustration parameter alpha. An analysis of the numerical Raman intensity leads us to postulate a continuum of two-magnon bound states in the Spin-Peierls phase. We discuss in detail the numerical method used, the dependence of the results on the model parameters and a novel matrix-element effect due to the dimerization of the Raman-operator in the Spin-Peierls phase.

cond-mat.str-el↗
arXiv1994

Thermal Conductivity Anisotropy in Superconducting $UPt_3$

Recent thermal conductivity measurements on $UPt_3$ single crystals by Lussier et al. indicate the existence of a strong b--c anisotropy in the superconducting state. We calculate the thermal conductivity in various unconventional candidate states appropriate for the $UPt_3$ ``B phase" and compare with experiment, specifically the $E_{2u}$ and $E_{1g}$ $(1,i)$ states predicted in some Ginzburg-Landau analyses of the phase diagram. For the simplest realizations of these states over spherical or ellipsoidal Fermi surfaces, the normalized $E_{2u}$ conductivity is found, surprisingly, to be completely isotropic. We discuss the effects of inelastic scattering and realistic Fermi surface anisotropy, and deduce constraints on the symmetry class of the $UPt_3$ ground state.

cond-mat↗