arXiv subjects

J. Schulenburg

Publications and source records attributed to J. Schulenburg.

At least 37 records · Page 2Linked to original sources

arXiv2004

Ground state and low-lying excitations of the spin-1/2 XXZ model on the kagome lattice at magnetization 1/3

We study the ground state and low-lying excitations of the S=1/2 XXZ antiferromagnet on the kagome lattice at magnetization one third of the saturation. An exponential number of non-magnetic states is found below a magnetic gap. The non-magnetic excitations also have a gap above the ground state, but it is much smaller than the magnetic gap. This ground state corresponds to an ordered pattern with resonances in one third of the hexagons. The spin-spin correlation function is short ranged, but there is long-range order of valence-bond crystal type.

cond-mat.str-el↗

arXiv2004

Absence of magnetic order for the spin-half Heisenberg antiferromagnet on the star lattice

We study the ground-state properties of the spin-half Heisenberg antiferromagnet on the two-dimensional star lattice by spin-wave theory, exact diagonalization and a variational mean-field approach. We find evidence that the star lattice is (besides the \kagome lattice) a second candidate among the 11 uniform Archimedean lattices where quantum fluctuations in combination with frustration lead to a quantum paramagnetic ground state. Although the classical ground state of the Heisenberg antiferromagnet on the star exhibits a huge non-trivial degeneracy like on the \kagome lattice, its quantum ground state is most likely dimerized with a gap to all excitations. Finally, we find several candidates for plateaux in the magnetization curve as well as a macroscopic magnetization jump to saturation due to independent localized magnon states.

cond-mat.str-el↗

arXiv2004

The spin-half Heisenberg antiferromagnet on the square-kagomé lattice: Ground state and low-lying excitations

We discuss the ground state and the low-lying excitations of the spin-half Heisenberg antiferromagnet on the two-dimensional square-kagome lattice. This magnetic system belongs to the class of highly frustrated spin systems with an infinite non-trivial degeneracy of the classical ground state as it is known also for the Heisenberg antiferromagnet on the kagome and on the star lattice. The quantum ground state of the spin-half system is a quantum paramagnet likely with a finite spin gap and with a large number of non-magnetic excitations within this gap. The magnetization versus field curve shows plateaux as well as a macroscopic magnetization jump to saturation due to independent localized magnon states.

cond-mat.str-el↗

arXiv2004

Magnetization plateaus in frustrated antiferromagnetic quantum spin models

Plateaus can be observed in the zero-temperature magnetization curve of quantum spin systems at rational values of the magnetization. In one dimension, the appearance of a plateau is controlled by a quantization condition for the magnetization which involves the length of the local spin and the volume of a translational unit cell of the ground state. We discuss examples of geometrically frustrated quantum spin systems with large (in general unbounded) periodicities of spontaneous breaking of translational symmetry in the ground state. In two dimensions, we discuss the square, triangular and Kagome lattices using exact diagonalization (ED) for up to N=40 sites. For the spin-1/2 XXZ model on the triangular lattice we study the nature and stability region of a plateau at one third of the saturation magnetization. The Kagome lattice gives rise to particularly rich behaviour with several plateaus in the magnetization curve and a jump due to local magnon excitations just below saturation.

cond-mat.str-el↗

arXiv2003

Exact eigenstates and macroscopic magnetization jumps in strongly frustrated spin lattices

For a class of frustrated spin lattices including e.g. the 1D sawtooth chain, the 2D kagomé and checkerboard, as well as the 3D pyrochlore lattices we construct exact product eigenstates consisting of several independent, localized one-magnon states in a ferromagnetic background. Important geometrical elements of the relevant lattices are triangles being attached to polygons or lines. Then the magnons can be trapped on these polygons/lines. If the concentration of localized magnons is small they can be distributed randomly over the lattice. Increasing the number of localized magnons their distribution over the lattice becomes more and more regular and finally the magnons condensate in a crystal-like state. The physical relevance of these eigenstates emerges in high magnetic fields where they become groundstates of the system. As a result a macroscopic magnetization jump appears in the zero-temperature magnetization curve just below the saturation field. The height of the jump decreases with increasing spin quantum number and vanishes in the classical limit. Thus it is a true macroscopic quantum effect.

cond-mat.str-el↗

arXiv2003

Ground-state phases in a system of two competing square-lattice Heisenberg antiferromagnets

We study a two-dimensional (2D) spin-half Heisenberg model related to the quasi 2D antiferromagnets (Ba,Sr)2Cu3O4Cl2 by means of exact diagonalization and spin-wave theory. The model consists of two inequivalent interpenetrating square-lattice Heisenberg antiferromagnets A and B. While the antiferromagnetic interaction JAA within the A subsystem is strong the coupling JBB within the B subsystem is much weaker. The coupling JAB between A and B subsystems is competing giving rise for interesting frustration effects. In dependence of the strength of JAB we find a collinear Neel phase, non-collinear states with zero magnetizations as well as canted and collinear ferrimagnetic phases with non-zero magnetizations. For not too large values of frustration JAB, which correpond to the situation in (Ba,Sr)2Cu3O4Cl2, we have Neel ordering in both subsystems A and B. In the classical limit these two Neel states are decoupled. Quantum fluctuations lead to a fluctuational coupling between both subsystems ('order from disorder') and select the collinear structure. For stronger JAB we find evidence for a novel spin state with coexisting Neel ordering in the A subsystem and disorder in the B subsystem.

cond-mat.str-el↗

arXiv2003

Spin-1/2 J1-J2 model on the body-centered cubic lattice

Using exact diagonalization (ED) and linear spin wave theory (LSWT) we study the influence of frustration and quantum fluctuations on the magnetic ordering in the ground state of the spin-1/2 J1-J2 Heisenberg antiferromagnet (J1-J2 model) on the body-centered cubic (bcc) lattice. Contrary to the J1-J2 model on the square lattice, we find for the bcc lattice that frustration and quantum fluctuations do not lead to a quantum disordered phase for strong frustration. The results of both approaches (ED, LSWT) suggest a first order transition at J2/J1 $\approx$ 0.7 from the two-sublattice Neel phase at low J2 to a collinear phase at large J2.

cond-mat.str-el↗

arXiv2002

Sequence of first-order quantum phase transitions in a frustrated spin half dimer-plaquette chain

We study the frustrated dimer-plaquette quantum spin chain for ferromagnetic dimer bonds. This quantum system undergoes a series of first-order ground-state phase transitions driven by frustration or by a magnetic field. We find that the different nature of the ground-state phases has a strong influence on the magnetization curve as well as the low-temperature thermodynamics. In particular, the magnetization curve exhibits plateaus and jumps, the number of which depends on the strength of frustration. The temperature dependence of the susceptibility may either show activated spin-gap behaviour for small frustration or Curie like paramagnetic behaviour for strong frustration.

cond-mat.str-el↗

arXiv2002

Macroscopic magnetization jumps due to independent magnons in frustrated quantum spin lattices

For a class of frustrated spin lattices including the kagome lattice we construct exact eigenstates consisting of several independent, localized one-magnon states and argue that they are ground states for high magnetic fields. If the maximal number of local magnons scales with the number of spins in the system, which is the case for the kagome lattice, the effect persists in the thermodynamic limit and gives rise to a macroscopic jump in the zero-temperature magnetization curve just below the saturation field. The effect decreases with increasing spin quantum number and vanishes in the classical limit. Thus it is a true macroscopic quantum effect.

cond-mat.str-el↗

arXiv2002

The spin-1/2 Heisenberg antiferromagnet on a 1/7-depleted triangular lattice: Ground-state properties

A linear spin-wave approach, a variational method and exact diagonlization are used to investigate the magnetic long-range order (LRO) of the spin-1/2 Heisenberg antiferromagnet on a two-dimensional 1/7-depleted triangular (maple leaf) lattice consisting of triangles and hexagons only. This lattice has z=5 nearest neighbors and its coordination number z is therefore between those of the triangular (z=6) and the kagome (z=4) lattices. Calculating spin-spin correlations, sublattice magnetization, spin stiffness, spin-wave velocity and spin gap we find that the classical 6-sublattice LRO is strongly renormalized by quantum fluctuations, however, remains stable also in the quantum model.

cond-mat.str-el↗

arXiv2001

Independent magnon states on magnetic polytopes

For many spin systems with constant isotropic antiferromagnetic next-neighbour Heisenberg coupling the minimal energies E_{min}(S) form a rotational band, i.e. depend approximately quadratically on the total spin quantum number S, a property which is also known as Lande interval rule. However, we find that for certain coupling topologies, including recently synthesised icosidodecahedral structures this rule is violated for high total spins. Instead the minimal energies are a linear function of total spin. This anomaly results in a corresponding jump of the magnetisation curve which otherwise would be a regular staircase.

cond-mat.mtrl-sci↗

arXiv2001

Infinite series of magnetization plateaus in the frustrated dimer-plaquette chain

The dimer-plaquette chain undergoes a first order transition driven by frustration to an orthogonal dimer ground state. We analyze the magnetization curve in this orthogonal dimer regime. Besides of the recently found magnetization plateaus at m=1/4 and the m=1/2 we find an infinite sequence of plateaus between m=1/4 and m=1/2. These additional plateaus belong to magnetizations m(n)=n/(2n+2), where n is a positive integer number.

cond-mat.str-el↗

arXiv2001

Exact diagonalization of the S=1/2 XY ferromagnet on finite bcc lattices to estimate T=0 properties on the infinite lattice

In this paper finite bcc lattices are defined by a triple of vectors in two different ways - upper triangular lattice form and compact form. In Appendix A are lists of some 260 distinct and useful bcc lattices of 9 to 32 vertices. The energy and magnetization of the S = 1/2 XY ferromagnet have been computed on these bcc lattices in the lowest states for $S_z$ = 0, 1/2, 1 and 3/2. These data are studied statistically to fit the first three terms of the appropriate finite lattice scaling equations. Our estimates of the T = 0 energy and magnetization agree very well with spin wave and series expansion estimates.

cond-mat.str-el↗

arXiv2001

Ground state of the spin-1/2 Heisenberg antiferromagnet on an Archimedean 4-6-12 lattice

An investigation of the Néel Long Range Order (NLRO) in the ground state of antiferromagnetic Heisenberg spin system on the two-dimensional, uniform, bipartite lattice consisting of squares, hexagons and dodecagons is presented. Basing on the analysis of the order parameter and the long-distance correlation function the NLRO is shown to occur in this system. Exact diagonalization and variational (Resonating Valence Bond) methods are applied.

cond-mat.stat-mech↗

arXiv1998

Exact diagonalization of the S=1/2 Heisenberg antiferromagnet on finite bcc lattices to estimate properties on the infinite lattice

Here we generate finite bipartite body-centred cubic lattices up to 32 vertices. We have studied the spin one half Heisenberg antiferromagnet by diagonalizing its Hamiltonian on each of the finite lattices and hence computing its ground state properties. By extrapolation of these data we obtain estimates of the T = 0 properties on the infinite bcc lattice. Our estimate of the T = 0 energy agrees to five parts in ten thousand with third order spin wave and series expansion method estimates, while our estimate of the staggered magnetization agrees with the spin wave estimate to within a quarter of one percent.

cond-mat↗

arXiv1998

The antiferromagnetic spin 1/2 chain with competing dimers and plaquettes: Numerical versus exact results

We examine the ground state and the excitations of an one-dimensional Heisenberg spin 1/2 antiferromagnet with alternating dimers and four-spin plaquettes (dimer-plaquette chain). The properties of the system depend on the competing dimer and plaquette bonds. Several exact, exact-numerical and perturbational results are presented. We find that the system is gapped for all parameter values. For the latter one we find an effective S=1 Haldane like behaviour in the limit of dominating dimer bonds. The model considered is related to the recently found 1/5-depleted square-lattice Heisenberg system $CaV_4O_9$.

cond-mat↗

arXiv1997

Magnetic model for Ba_2Cu_3O_4Cl_2

Ba_2Cu_3O_4Cl_2 consists of two types of copper atoms, Cu(A) and Cu(B). We study the corresponding Heisenberg model with three antiferromagnetic couplings, J_AA, J_BB and J_AB. We find interesting frustration effects due to the coupling J_AB.

cond-mat.stat-mech↗

arXiv1997

Tight-binding parameters and exchange integrals of Ba_2Cu_3O_4Cl_2

Band structure calculations for Ba_2Cu_3O_4Cl_2 within the local density approximation (LDA) are presented. The investigated compound is similar to the antiferromagnetic parent compounds of cuprate superconductors but contains additional Cu_B atoms in the planes. Within the LDA, metallic behavior is found with two bands crossing the Fermi surface (FS). These bands are built mainly from Cu 3d_{x^2-y^2} and O 2p_{x,y} orbitals, and a corresponding tight-binding (TB) model has been parameterized. All orbitals can be subdivided in two sets corresponding to the A- and B-subsystems, respectively, the coupling between which is found to be small. To describe the experimentally observed antiferromagnetic insulating state, we propose an extended Hubbard model with the derived TB parameters and local correlation terms characteristic for cuprates. Using the derived parameter set we calculate the exchange integrals for the Cu_3O_4 plane. The results are in quite reasonable agreement with the experimental values for the isostructural compound Sr_2Cu_3O_4Cl_2.

cond-mat.str-el↗