arXiv subjects

A. Honecker

Publications and source records attributed to A. Honecker.

At least 91 records · Page 5Linked to original sources

arXiv2000

Lanczos Study of the S=1/2 Frustrated Square-Lattice Antiferromagnet in a Magnetic Field

We study the zero-temperature phase diagram of the frustrated square-lattice S=1/2 antiferromagnet in an external magnetic field numerically with the Lanczos algorithm. For strong frustration, we find disordered phases at high (and low) magnetic fields. Between these two disordered phases we find a plateau in the magnetization curve at half of the saturation magnetization which corresponds to a state with up-up-up-down (uuud) spin order. This and other considerations [cond-mat/0003343] suggest an unusual ordering scenario: There are an ordered phase with a spin gap (the plateau) and disordered magnetically gapless phases above and below. The transition to saturation is studied in further detail and problematic conclusions in earlier investigations of this region are pointed out.

cond-mat.str-el↗

arXiv2000

Field induced ordering in highly frustrated antiferromagnets

We predict that an external field can induce a spin order in highly frustrated classical Heisenberg magnets. We find analytically stabilization of collinear states by thermal fluctuations at a one-third of the saturation field for kagome and garnet lattices and at a half of the saturation field for pyrochlore and frustrated square lattices. This effect is studied numerically for the frustrated square-lattice antiferromagnet by Monte Carlo simulations for classical spins and by exact diagonalization for $S=1/2$. The field induced collinear states have a spin gap and produce magnetization plateaus.

cond-mat.str-el↗

arXiv2000

Doping-dependent magnetization plateaux in p-merized Hubbard chains

We study zero-temperature Hubbard chains with periodically modulated hopping at arbitrary filling n and magnetization m. We show that the magnetization curves have plateaux at certain values of m which depend on the periodicity p and the filling. At commensurate filling n a charge gap opens and then magnetization plateaux correspond to fully gapped situations. However, plateaux also arise in the magnetization curves at fixed n between the commensurate values and then the plateau-value of of m depends continuously on n and can thus also become irrational. In particular for the case of dimerized hopping (p=2) and fixed doping we find that a plateau appears at m=1-n. In this case, there is still a gapless mode on the plateau leading to thermodynamic behavior which is different from a completely gapped situation.

cond-mat.str-el↗

arXiv2000

A Spin-1/2 Model for CsCuCl_3 in an External Magnetic Field

CsCuCl_3 is a ferromagnetically stacked triangular spin-1/2 antiferromagnet. We discuss models for its zero-temperature magnetization process. The models range from three antiferromagnetically coupled ferromagnetic chains to the full three-dimensional situation. The situation with spin-1/2 is treated by expansions around the Ising limit and exact diagonalization. Further, weak-coupling perturbation theory is used mainly for three coupled chains which are also investigated numerically using the density-matrix renormalization group technique. We find that already the three-chain model gives rise to the plateau-like feature at one third of the saturation magnetization which is observed in magnetization experiments on CsCuCl_3 for a magnetic field perpendicular to the crystal axis. For a magnetic field parallel to the crystal axis, a jump is observed in the experimental magnetization curve in the region of again about one third of the saturation magnetization. In contrast to earlier spinwave computations, we do not find any evidence for such a jump with the model in the appropriate parameter region.

cond-mat.str-el↗

arXiv2000

Magnetization plateaux and jumps in a class of frustrated ladders: A simple route to a complex behaviour

We study the occurrence of plateaux and jumps in the magnetization curves of a class of frustrated ladders for which the Hamiltonian can be written in terms of the total spin of a rung. We argue on the basis of exact diagonalization of finite clusters that the ground state energy as a function of magnetization can be obtained as the minimum - with Maxwell constructions if necessary - of the energies of a small set of spin chains with mixed spins. This allows us to predict with very elementary methods the existence of plateaux and jumps in the magnetization curves in a large parameter range, and to provide very accurate estimates of these magnetization curves from exact or DMRG results for the relevant spin chains.

cond-mat.str-el↗

arXiv1999

Magnetic Properties of Zig-Zag Ladders

We analyze the phase diagram of a system of spin-1/2 Heisenberg antiferromagnetic chains interacting through a zig-zag coupling, also called zig-zag ladders. Using bosonization techniques we study how a spin-gap or more generally plateaux in magnetization curves arise in different situations. While for coupled XXZ chains, one has to deal with a recently discovered chiral perturbation, the coupling term which is present for normal ladders is restored by an external magnetic field, dimerization or the presence of charge carriers. We then proceed with a numerical investigation of the phase diagram of two coupled Heisenberg chains in the presence of a magnetic field. Unusual behaviour is found for ferromagnetic coupled antiferromagnetic chains. Finally, for three (and more) legs one can choose different inequivalent types of coupling between the chains. We find that the three-leg ladder can exhibit a spin-gap and/or non-trivial plateaux in the magnetization curve whose appearance strongly depends on the choice of coupling.

cond-mat.str-el↗

arXiv1999

A Comparative Study of the Magnetization Process of Two-Dimensional Antiferromagnets

Plateaux in the magnetization curves of the square, triangular and hexagonal lattice spin-1/2 XXZ antiferromagnet are investigated. One finds a zero magnetization plateau (corresponding to a spin-gap) on the square and hexagonal lattice with Ising-like anisotropies, and a plateau with one third of the saturation magnetization on the triangular lattice which survives a small amount of easy-plane anisotropy. Here we start with transfer matrix computations for the Ising limit and continue with series in the XXZ-anisotropy for plateau-boundaries using the groundstates of the Ising limit. The main focus is then a numerical computation of the magnetization curves with anisotropies in the vicinity of the isotropic situation. Finally, we discuss the universality class associated to the asymptotic behaviour of the magnetization curve close to saturation, as observed numerically in two and higher dimensions.

cond-mat.str-el↗

arXiv1998

A Strong-Coupling Approach to the Magnetization Process of Polymerized Quantum Spin Chains

Polymerized quantum spin chains (i.e. spin chains with a periodic modulation of the coupling constants) exhibit plateaux in their magnetization curves when subjected to homogeneous external magnetic fields. We argue that the strong-coupling limit yields a simple but general explanation for the appearance of plateaux as well as of the associated quantization condition on the magnetization. We then proceed to explicitly compute series for the plateau boundaries of trimerized and quadrumerized spin-1/2 chains. The picture is completed by a discussion how the universality classes associated to the transitions at the boundaries of magnetization plateaux arise in many cases from a first order strong-coupling effective Hamiltonian.

cond-mat.str-el↗

arXiv1998

Magnetization Plateaux in N-Leg Spin Ladders

In this paper we continue and extend a systematic study of plateaux in magnetization curves of antiferromagnetic Heisenberg spin-1/2 ladders. We first review a bosonic field-theoretical formulation of a single XXZ-chain in the presence of a magnetic field, which is then used for an Abelian bosonization analysis of N weakly coupled chains. Predictions for the universality classes of the phase transitions at the plateaux boundaries are obtained in addition to a quantization condition for the value of the magnetization on a plateau. These results are complemented by and checked against strong-coupling expansions. Finally, we analyze the strong-coupling effective Hamiltonian for an odd number N of cylindrically coupled chains numerically. For N = 3 we explicitly observe a spin-gap with a massive spinon-type fundamental excitation and obtain indications that this gap probably survives the limit N to infinity.

cond-mat.str-el↗

arXiv1997

Magnetization Curves of Antiferromagnetic Heisenberg Spin-1/2 Ladders

Magnetization processes of spin-1/2 Heisenberg ladders are studied using strong-coupling expansions, numerical diagonalization of finite systems and a bosonization approach. We find that the magnetization exhibits plateaux as a function of the applied field at certain rational fractions of the saturation value. Our main focus are ladders with 3 legs where plateaux with magnetization one third of the saturation value are shown to exist.

cond-mat.str-el↗

arXiv1997

Ghost Systems: A Vertex Algebra Point of View

Fermionic and bosonic ghost systems are defined each in terms of a single vertex algebra which admits a one-parameter family of conformal structures. The observation that these structures are related to each other provides a simple way to obtain character formulae for a general twisted module of a ghost system. The U(1) symmetry and its subgroups that underly the twisted modules also define an infinite set of invariant vertex subalgebras. Their structure is studied in detail from a W-algebra point of view with particular emphasis on Z_N-invariant subalgebras of the fermionic ghost system.

hep-th↗

arXiv1997

A Non-Perturbative Approach to the Random-Bond Ising Model

We study the N -> 0 limit of the O(N) Gross-Neveu model in the framework of the massless form-factor approach. This model is related to the continuum limit of the Ising model with random bonds via the replica method. We discuss how this method may be useful in calculating correlation functions of physical operators. The identification of non-perturbative fixed points of the O(N) Gross-Neveu model is pursued by its mapping to a WZW model.

hep-th↗

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↗

arXiv1995

A Perturbative Approach to the Chiral Potts Model

The massive high-temperature phase of the chiral Potts quantum chain is studied using perturbative methods. For the Z_3-chain we present high-temperature expansions for the groundstate energy and the dispersion relations of the two single-particle states as well as two-particle states at general values of the parameters. We also present a perturbative argument showing that a large class of massive Z_n-spin quantum chains have quasiparticle spectra with n-1 fundamental particles. It is known from earlier investigations that -at special values of the parameters- some of the fundamental particles exist only for limited ranges of the momentum. In these regimes our argument is not rigorous as one can conclude from a discussion of the radius of convergence of the perturbation series. We also derive correlation functions from a perturbative evaluation of the groundstate for the Z_3-chain. In addition to an exponential decay we observe an oscillating contribution. The oscillation length seems to be related to the asymmetry of the dispersion relations. We show that this relation is exact at special values of the parameters for general Z_n using a form factor expansion.

hep-th↗

arXiv1995

Coset Realization of Unifying W-Algebras

We construct several quantum coset W-algebras, e.g. sl(2,R)/U(1) and sl(2,R)+sl(2,R) / sl(2,R), and argue that they are finitely nonfreely generated. Furthermore, we discuss in detail their role as unifying W-algebras of Casimir W-algebras. We show that it is possible to give coset realizations of various types of unifying W-algebras, e.g. the diagonal cosets based on the symplectic Lie algebras sp(2n) realize the unifying W-algebras which have previously been introduced as `WD_{-n}'. In addition, minimal models of WD_{-n} are studied. The coset realizations provide a generalization of level-rank-duality of dual coset pairs. As further examples of finitely nonfreely generated quantum W-algebras we discuss orbifolding of W-algebras which on the quantum level has different properties than in the classical case. We demonstrate in some examples that the classical limit according to Bowcock and Watts of these nonfreely finitely generated quantum W-algebras probably yields infinitely nonfreely generated classical W-algebras.

hep-th↗

arXiv1994

Excitation Spectrum and Correlation Functions of the Z_3-Chiral Potts Quantum Spin Chain

We study the excitation spectrum and the correlation functions of the Z_3- chiral Potts model in the massive high-temperature phase using perturbation expansions and numerical diagonalization. We are mainly interested in results for general chiral angles but we consider also the superintegrable case. For the parameter values considered, we find that the band structure of the low- lying part of the excitation spectrum has the form expected from a quasiparticle picture with two fundamental particles. Studying the N-dependence of the spectrum, we confirm the stability of the second fundamental particle in a limited range of the momentum, even when its energy becomes so high that it lies very high up among the multiparticle scattering states. This is not a phenomenon restricted to the superintegrable line. Calculating a non-translationally invariant correlation function, we give evidence that it is oscillating. Within our numerical accuracy we find a relation between the oscillation length and the dip position of the momentum dispersion of the lightest particle which seems to be quite independent of the chiral angles.

hep-th↗