Publications (255)585.26 Total impact

Article: Hightemperature Expansion for Frustrated Magnets: Application to the J1J2 Model on the BCC Lattice
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ABSTRACT: We present the hightemperature expansion up to 11th order for the specific heat C and the uniform susceptibility χ0 and up to 9th order for the structure factor SQ of the frustrated spinhalf J1J2 Heisenberg model on the BCC lattice. We consider ferromagnetic as well as antiferromagnetic nearestneighbor exchange J1 and frustrating antiferromagnetic nextnearest neighbor exchange J2. We discuss the influence of frustration on the temperature dependence of these quantities. Furthermore, we use the HTE series to determine the critical temperature Tc as a function of the frustration parameter J2.  [Show abstract] [Hide abstract]
ABSTRACT: We quantify the stability of the formation of multipolar states against always present interchain couplings in quasionedimensional spin12 chain systems with a frustrating inchain J1J2 exchange, including parameter regimes that are of direct relevance to many edgeshared cuprate spinchain compounds. Three representative types of antiferromagnetic interchain coupling and the presence of uniaxial exchange anisotropy are considered. The magnetic phase diagrams are determined by density matrix renormalization group calculations and completed by very accurate analytic and numerical results for the nematic and the dipolar phases employing the hardcoreboson approach. We establish that a sizable interchain coupling has a strong influence on the possible instability of multipolar phases at high magnetic fields in the vicinity of the saturation fields in favor of the usual dipolar onemagnon phase. Moreover, skew interchain couplings strongly affect the pitch of spiral states. Our theoretical results bring to the fore candidate materials close to quantum nematic/triatic ordering.  [Show abstract] [Hide abstract]
ABSTRACT: Motivated by recent experiments on volborthite single crystals showing a wide 1/3magnetization plateau, we perform microscopic modeling by means of density functional theory (DFT) with the singlecrystal structural data as a starting point. Using DFT+U, we find four leading magnetic exchanges: antiferromagnetic J and J2, as well as ferromagnetic J' and J1. Simulations of the derived spin Hamiltonian show good agreement with the experiment. The 1/3plateau phase pertains to polarized magnetic trimers formed by strong J bonds. An effective J$\rightarrow\infty$ model shows a tendency towards condensation of magnon bound states preceding the plateau phase.  [Show abstract] [Hide abstract]
ABSTRACT: We apply the coupled cluster method to high orders of approximation and exact diagonalizations to study the groundstate properties of the triangularlattice spin$s$ Heisenberg antiferromagnet. We calculate the fundamental groundstate quantities, namely, the energy $e_0$, the sublattice magnetization $M_{\rm sub}$, the inplane spin stiffness $\rho_s$ and the inplane magnetic susceptibility $\chi$ for spin quantum numbers $s=1/2, 1, \ldots, s_{\rm max}$, where $s_{\rm max}=9/2$ for $e_0$ and $M_{\rm sub}$, $s_{\rm max}=4$ for $\rho_s$ and $s_{\rm max}=3$ for $\chi$. We use the data for $s \ge 3/2$ to estimate the leading quantum corrections to the classical values of $e_0$, $M_{\rm sub}$, $\rho_s$, and $\chi$. In addition, we study the magnetization process, the width of the 1/3 plateau as well as the sublattice magnetizations in the plateau state as a function of the spin quantum number $s$.  [Show abstract] [Hide abstract]
ABSTRACT: We use the spinrotationinvariant Green's function method as well as the hightemperature expansion to discuss the thermodynamic properties of the frustrated spin$S$ $J_{1}$$J_{2}$ Heisenberg magnet on the bodycentered cubic lattice. We consider ferromagnetic nearestneighbor bonds $J_1 < 0$ and antiferromagnetic nextnearestneighbor bonds $J_2 \ge 0$ and arbitrary spin $S$. We find that the transition point $J_2^c$ between the ferromagnetic ground state and the antiferromagnetic one is nearly independent of the spin $S$, i.e., it is very close to the classical transition point $J_2^{c,{\rm clas}}= \frac{2}{3}J_1$. At finite temperatures we focus on the parameter regime $J_2<J_2^c$ with a ferromagnetic groundstate. We calculate the Curie temperature $T_{C}(S,J_{2})$ and derive an empirical formula describing the influence of the frustration parameter $J_{2}$ and spin $S$ on $T_C$. We find that the Curie temperature monotonically decreases with increasing frustration $J_2$, where very close to $J_2^{c,{\rm clas}}$ the $T_C(J_2)$curve exhibits a fast decay which is well described by a logarithmic term $1/\textrm{log}(\frac{2}{3}J_1J_{2})$. To characterize the magnetic ordering below and above $T_C$, we calculate the spinspin correlation functions $\langle {\bf S}_{\bf 0} {\bf S}_{\bf R} \rangle$, the spontaneous magnetization, the uniform static susceptibility $\chi_0$ as well as the correlation length $\xi$. Moreover, we discuss the specific heat $C_V$ and the temperature dependence of the excitation spectrum. As approaching the transition point $J_2^c$ some unusual features were found, such as negative spinspin correlations at temperatures above $T_C$ even though the ground state is ferromagnetic or an increase of the spin stiffness with growing temperature. 
Article: Strongly correlated flatband systems: The route from Heisenberg spins to Hubbard electrons
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ABSTRACT: In this review we recapitulate the basic features of the flatband spin systems and briefly summarize earlier studies in the field. Main emphasis is made on recent developments which include results for both spin and electron flatband models. In particular, for flatband spin systems we highlight fielddriven phase transitions for frustrated quantum Heisenberg antiferromagnets at low temperatures, chiral flatband states, as well as the effect of a slight dispersion of a previously strictly flat band due to nonideal lattice geometry. For electronic systems, we discuss the universal lowtemperature behavior of several flatband Hubbard models, the emergence of groundstate ferromagnetism in the squarelattice TasakiHubbard model and the related Paulicorrelated percolation problem, as well as the dispersiondriven groundstate ferromagnetism in flatband Hubbard systems. Closely related studies and possible experimental realizations of the flatband physics are also described briefly. 
Article: Frustrated Heisenberg antiferromagnet on the honeycomb lattice: Spin gap and lowenergy parameters
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ABSTRACT: We use the coupled cluster method implemented to high orders of approximation to investigate the frustrated spin$\frac{1}{2}$ $J_{1}$$J_{2}$$J_{3}$ antiferromagnet on the honeycomb lattice with isotropic Heisenberg interactions of strength $J_{1} > 0$ between nearestneighbor pairs, $J_{2}>0$ between nextnearestneighbor pairs, and $J_{3}>0$ between nextnextneareastneighbor pairs of spins. In particular, we study both the groundstate (GS) and lowestlying triplet excitedstate properties in the case $J_{3}=J_{2} \equiv \kappa J_{1}$, in the window $0 \leq \kappa \leq 1$ of the frustration parameter, which includes the (tricritical) point of maximum classical frustration at $\kappa_{{\rm cl}} = \frac{1}{2}$. We present GS results for the spin stiffness, $\rho_{s}$, and the zerofield uniform magnetic susceptibility, $\chi$, which complement our earlier results for the GS energy per spin, $E/N$, and staggered magnetization, $M$, to yield a complete set of accurate lowenergy parameters for the model. Our results all point towards a phase diagram containing two quasiclassical antiferromagnetic phases, one with N\'{e}el order for $\kappa < \kappa_{c_{1}}$, and the other with collinear striped order for $\kappa > \kappa_{c_{2}}$. The results for both $\chi$ and the spin gap $\Delta$ provide compelling evidence for a quantum paramagnetic phase that is gapped over a considerable portion of the intermediate region $\kappa_{c_{1}} < \kappa < \kappa_{c_{2}}$, especially close to the two quantum critical points at $\kappa_{c_{1}}$ and $\kappa_{c_{2}}$. Each of our fully independent sets of results for the lowenergy parameters is consistent with the values $\kappa_{c_{1}} = 0.45 \pm 0.02$ and $\kappa_{c_{2}} = 0.60 \pm 0.02$, and with the transition at $\kappa_{c_{1}}$ being of continuous (and probably of the deconfined) type and that at $\kappa_{c_{2}}$ being of firstorder type. 
Article: Groundstate phase diagram of the XXZ spin s kagome antiferromagnet: A coupledcluster study
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ABSTRACT: We use the coupled cluster method to high orders of approximation in order to calculate the groundstate phase diagram of the XXZ spin$s$ kagome antiferromagnet with easyplane anisotropy, i.e. the anisotropy parameter $\Delta$ varies between $\Delta=1$ (isotropic Heisenberg model) and $\Delta=0$ ($XY$ model). We find that for the extreme quantum case $s=1/2$ the ground state is magnetically disordered in the entire region $0 \le \Delta \le 1$. For $s=1$ the ground state is disordered for $0.818 < \Delta \le 1$, it exhibits $\sqrt{3}\times\sqrt{3}$ magnetic longrange order for $0.281 < \Delta <0.818$, and $q=0$ magnetic longrange order for $0 \le \Delta < 0.281$. We confirm the recent result of Chernyshev and Zhitomirsky (Phys. Rev. Lett. 113, 237202 (2014)) that the selection of the ground state by quantum fluctuations is different for small $\Delta$ ($XY$ limit) and for $\Delta$ close to one (Heisenberg limit), i.e., $q=0$ magnetic order is favored over $\sqrt{3}\times\sqrt{3}$ for $0\le \Delta <\Delta_c$ and vice versa for $\Delta_c < \Delta \le 1$. We calculate $\Delta_c$ as a function of the spin quantum number $s$.  [Show abstract] [Hide abstract]
ABSTRACT: We consider the antiferromagnetic spin1/2 $XXZ$ Heisenberg model on a frustrated diamondchain lattice in a $z$ or $x$aligned external magnetic field. We use the strongcoupling approach to elaborate an effective description in the lowtemperature strongfield regime. The obtained effective models are spin1/2 $XY$ chains which are exactly solvable through the JordanWigner fermionization. We perform exactdiagonalization studies of the magnetization curves to test the quality of the effective description. The results may have relevance for the description of the azurite spinchain compound.  [Show abstract] [Hide abstract]
ABSTRACT: We investigate the antiferromagnetic canting instability of the spin1/2 kagome ferromagnet, as realized in the layered cuprates Cu$_3$Bi(SeO$_3)_2$O$_2$X (X=Br, Cl, and I). While the local canting can be explained in terms of competing exchange interactions, the direction of the ferrimagnetic order parameter fluctuates strongly even at short distances on account of frustration which gives rise to an infinite ground state degeneracy at the classical level. In analogy with the kagome antiferromagnet, the accidental degeneracy is fully lifted only by nonlinear 1/S corrections, rendering the selected uniform canted phase very fragile even for spins1/2, as shown explicitly by coupledcluster calculations. To account for the observed ordering, we show that the minimal description of these systems must include the microscopic DzyaloshinskyMoriya interactions, which we obtain from densityfunctional bandstructure calculations. The model explains all qualitative properties of the kagome francisites, including the detailed nature of the ground state and the anisotropic response under a magnetic field. The predicted magnon excitation spectrum and quantitative features of the magnetization process call for further experimental investigations of these compounds.  [Show abstract] [Hide abstract]
ABSTRACT: We use the coupled cluster method to high orders of approximation in order to calculate the groundstate energy, the groundstate magnetic order parameter, and the spin gap of the spin1/2 J_1J_2 model on the square lattice. We obtain values for the transition points to the magnetically disordered quantum paramagnetic phase of J_2^{c1}=0.454J_1 and J_2^{c2}= 0.588 J_1. The spin gap is zero in the entire parameter region accessible by our approach, i.e. for J_2 \le 0.49J_1 and J_2 > 0.58J_1. This finding is in favor of a gapless spinliquid or a nearcritical quantum paramagnetic ground state in this parameter regime.  [Show abstract] [Hide abstract]
ABSTRACT: We investigate ground states of $s$=1/2 Heisenberg antiferromagnets on the eleven twodimensional (2D) Archimedian lattices by using the coupled cluster method. Magnetic interactions and quantum fluctuations play against each other subtly in 2D quantum magnets and the magnetic ordering is thus sensitive to the features of lattice topology. Archimedean lattices are those lattices that have 2D arrangements of regular polygons and they often build the underlying magnetic lattices of insulating quasitwodimensional quantum magnetic materials. Hence they allow a systematic study of the relationship between lattice topology and magnetic ordering. We find that the Archimedian lattices fall into three groups: those with semiclassical magnetic groundstate longrange order, those with a magnetically disordered (cooperative quantum paramagnetic) ground state, and those with a fragile magnetic order. The most relevant parameters affecting the magnetic ordering are the coordination number and the degree of frustration present.  [Show abstract] [Hide abstract]
ABSTRACT: We investigate a mechanism to establish groundstate ferromagnetism in flatband Hubbard systems based on a kind of {\it orderfromdisorder} effect driven by dispersion. As a paradigm we consider a frustrated diamond chain, where for ideal diamond geometry the lowest oneelectron band is flat, but the ground state remains paramagnetic for arbitrary onsite repulsion $U$. We focus on half filling of the flat band. By using numerical and analytical arguments we present the groundstate phase diagram for a distorted diamond chain, i.e., the former flat band becomes dispersive. Driven by the interplay of dispersion and interaction the ground state is ferromagnetic if the interaction exceeds a critical value $U_c$.  [Show abstract] [Hide abstract]
ABSTRACT: We investigate the spin1/2 Heisenberg model on the delta chain (sawtooth chain) with ferromagnetic nearestneighbor and antiferromagnetic nextneighbor interactions. For a special ratio between these interactions there is a class of exact ground states formed by localized magnons and the ground state is macroscopically degenerate with a large residual entropy per spin $s_0=\frac{1}{2}\ln 2$. An important feature of this model is a sharp decrease of the gaps for excited states with an increase of the number of magnons. These excitations give an essential contribution to the lowtemperature thermodynamics. The behavior of the considered model is compared with that of the delta chain with both antiferromagnetic interactions.  [Show abstract] [Hide abstract]
ABSTRACT: The spin1/2 alternating Heisenberg chain system Na$_3$Cu$_2$SbO$_6$ features two relevant exchange couplings: $J_{1a}$ within the structural Cu$_2$O$_6$ dimers and $J_{1b}$ between the dimers. Motivated by the controversially discussed nature of $J_{1a}$, we perform extensive densityfunctionaltheory (DFT) calculations, including DFT+$U$ and hybrid functionals. Fits to the experimental magnetic susceptibility using hightemperature series expansions and quantum Monte Carlo simulations yield the optimal parameters $J_{1a}\!=\!217$ K and $J_{1b}\!=\!174$ K with the alternation ratio $\alpha=J_{1a}/J_{1b}\simeq1.25$. For the closely related system Na$_2$Cu$_2$TeO$_6$, DFT yields substantially enhanced $J_{1b}$, but weaker $J_{1a}$. The comparative analysis renders the buckling of the chains as the key parameter altering the magnetic coupling regime. By simulating the dispersion relations of the alternating chain model and comparing them to the inelastic neutron scattering data $[$Y. Miura et al., J. Phys. Soc. Jpn. 77, 104709 (2008)$]$, we obtain an unequivocal evidence for a ferromagnetic $J_{1a}$ in Na$_3$Cu$_2$SbO$_6$.  [Show abstract] [Hide abstract]
ABSTRACT: Motivated by recent experiments on lowdimensional frustrated quantum magnets with competing nearestneighbor exchange coupling J1 and next nearestneighbor exchange coupling J2 we investigate the magnetic susceptibility of twodimensional J1J2 Heisenberg models with arbitrary spin quantum number s. We use exact diagonalization and hightemperature expansion up to order 10 to analyze the influence of the frustration strength J2/J1 and the spin quantum number s on the position and the height of the maximum of the susceptibility. The derived theoretical data can be used to get information on the ratio J2/J1 by comparing with susceptibility measurements on corresponding magnetic compounds.  [Show abstract] [Hide abstract]
ABSTRACT: We present the hightemperature expansion (HTE) up to 10th order of the specific heat C and the uniform susceptibility χ for Heisenberg models with arbitrary exchange patterns and arbitrary spin quantum number s. We encode the algorithm in a C++ program which allows to get explicitly the HTE series for concrete Heisenberg models. We apply our algorithm to pyrochlore ferromagnets and kagome antiferromagnets using several Padé approximants for the HTE series. For the pyrochlore ferromagnet we use the HTE data for χ to estimate the Curie temperature Tc as a function of the spin quantum number s. We find that Tc is smaller than that for the simple cubic lattice, although both lattices have the same coordination number. For the kagome antiferromagnet the influence of the spin quantum number s on the susceptibility as a function of renormalized temperature T /s(s + 1) is rather weak for temperatures down to T /s(s + 1) ∼ 0.3. On the other hand, the specific heat as a function of T /s(s + 1) noticeably depends on s. The characteristic maximum in C(T) is monotonously shifted to lower values of T /s(s + 1) when increasing s.  [Show abstract] [Hide abstract]
ABSTRACT: We consider the spin1/2 antiferromagnetic Heisenberg model on the twodimensional squarekagome lattice with almost dispersionless lowest magnon band. For a general exchange coupling geometry we elaborate lowenergy effective Hamiltonians which emerge at high magnetic fields. The effective model to describe the lowenergy degrees of freedom of the initial frustrated quantum spin model is the (unfrustrated) squarelattice spin1/2 $XXZ$ model in a $z$aligned magnetic field. For the effective model we perform quantum Monte Carlo simulations to discuss the lowtemperature properties of the squarekagome quantum Heisenberg antiferromagnet at high magnetic fields. We pay special attention to a magneticfield driven BerezinskiiKosterlitzThouless phase transition which occurs at low temperatures.  [Show abstract] [Hide abstract]
ABSTRACT: We consider a lattice of antiferromagnetically interacting equal spins that have a ferrimagnetic ground state. We show that a special arrangement of S=5/2 Fe$^{3+}$ ions in double perovskites AFe$_{1/2}$M$_{1/2}$O$_{3}$ exhibits the ferrimagnetic ordering below T_{fe} ~ 5.6J_1 (J_1/k_B ~ 50 K), which is close to room temperature. Small clusters of the same structure exhibit a superparamagnetic behavior at T < T_{fe}. The possibility of formation of such clusters explains the roomtemperature (superpara)magnetism in 3dmetal based oxides. 
Article: Numerical study of magnetization plateaux in the spin1/2 kagome Heisenberg antiferromagnet
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ABSTRACT: We clarify the existence of several magnetization plateaux for the kagome $S=1/2$ antiferromagnetic Heisenberg model in a magnetic field. Using approximate or exact localized magnon eigenstates, we are able to describe in a similar manner the plateau states that occur for magnetization per site $m=1/3$, 5/9, and 7/9 of the saturation value. These results are confirmed using largescale Exact Diagonalization on lattices up to 63 sites.
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4k  Citations  
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Institutions

19912015

OttovonGuerickeUniversität Magdeburg
 Institute of Theoretical Physics (ITP)
Magdeburg, SaxonyAnhalt, Germany


19912010

Technische Universität Dortmund
 Chair of Theoretical Physics I
Dortmund, North RhineWestphalia, Germany


19992007

Technische Universität Dresden
 Institut für theoretische Physik
Dresden, Saxony, Germany


2004

Universität Augsburg
Augsberg, Bavaria, Germany


2001

Universität Osnabrück
Osnabrück, Lower Saxony, Germany
