arXiv subjects

J. Richter

Publications and source records attributed to J. Richter.

At least 127 records · Page 7Linked to original sources

arXiv2004

Green's-function theory of the Heisenberg ferromagnet in a magnetic field

We present a second-order Green's-function theory of the one- and two-dimensional S=1/2 ferromagnet in a magnetic field based on a decoupling of three-spin operator products, where vertex parameters are introduced and determined by exact relations. The transverse and longitudinal spin correlation functions and thermodynamic properties (magnetization, isothermal magnetic susceptibility, specific heat) are calculated self-consistently at arbitrary temperatures and fields. In addition, exact diagonalizations on finite lattices and, in the one-dimensional case, exact calculations by the Bethe-ansatz method for the quantum transfer matrix are performed. A good agreement of the Green's-function theory with the exact data, with recent quantum Monte Carlo results, and with the spin polarization of a $ν=1$ quantum Hall ferromagnet is obtained. The field dependences of the position and height of the maximum in the temperature dependence of the susceptibility are found to fit well to power laws, which are critically analyzed in relation to the recently discussed behavior in Landau's theory. As revealed by the spin correlation functions and the specific heat at low fields, our theory provides an improved description of magnetic short-range order as compared with the random phase approximation. In one dimension and at very low fields, two maxima in the temperature dependence of the specific heat are found. The Bethe-ansatz data for the field dependences of the position and height of the low-temperature maximum are described by power laws. At higher fields in one and two dimensions, the temperature of the specific heat maximum linearly increases with the field.

cond-mat.str-el↗

arXiv2004

Phase diagram of a frustrated mixed-spin ladder with diagonal exchange bonds

Using exact numerical diagonalization and the conformal field theory approach, we study the effect of magnetic frustrations due to diagonal exchange bonds in a system of two coupled mixed-spin $(1,{1/2})$ Heisenberg chains. It is established that relatively moderate frustrations are able to destroy the ferrimagnetic state and to stabilize the critical spin-liquid phase typical for half-integer-spin antiferromagnetic Heisenberg chains. Both phases are separated by a narrow but finite region occupied by a critical partially-polarized ferromagnetic phase.

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

Study of an Antiferromagnetic Sawtooth Chain with Spin-1/2 and Spin-1 sites

We study the low-energy properties of a sawtooth chain with spin-1's at the bases of the triangles and spin-1/2's at the vertices of the triangles. The spins have Heisenberg antiferromagnetic interactions between nearest neighbors, with a coupling J_2 between a spin-1 and a spin-1/2, and a coupling J_1 = 1 between two spin-1's. Analysis of the exact diagonalization data for periodic chains containing up to N=12 unit cells shows that the ground state is a singlet for exchange couplings up to approximately J_2 = 3.8, whereas for larger J_2, the system exhibits a ferrimagnetic ground state characterized by a net ferromagnetic moment per unit cell of 1/2. In the region of small interactions J_2, the mixed spin sawtooth chain maps on to an effective isotropic spin model representing two weakly interacting and frustrated spin-1/2 Heisenberg chains composed of spin-1/2 sites at odd and even vertices respectively. Finally, we study the phenomenon of a macroscopic magnetization jump which occurs if a magnetic field is applied with a value close to the saturation field for J_2 = 2.

cond-mat.str-el↗

arXiv2003

Recursion method and one-hole spectral function of the Majumdar-Ghosh model

We consider the application of the recursion method to the calculation of one-particle Green's functions for strongly correlated systems and propose a new way how to extract the information about the infinite system from the exact diagonalisation of small clusters. Comparing the results for several cluster sizes allows us to establish those Lanczos coefficients that are not affected by the finite size effects and provide the information about the Green's function of the macroscopic system. The analysis of this 'bulk-related' subset of coefficients supplemented by alternative analytic approaches allows to infer their asymptotic behaviour and to propose an approximate analytical form for the 'terminator' of the Green's function continued fraction expansion for the infinite system. As a result, the Green's function acquires the branch cut singularity corresponding to the incoherent part of the spectrum. The method is applied to the spectral function of one-hole in the Majumdar-Ghosh model (the one-dimensional $ t-J-J^{\prime}$ model at $J^{\prime}/J=1/2$). For this model, the branch cut starts at finite energy $ω_0$, but there is no upper bound of the spectrum, corresponding to a linear increase of the recursion coefficients. Further characteristics of the spectral function are band gaps in the middle of the band and bound states below $ω_0$ or within the gaps. The band gaps arise due to the period doubling of the unit cell and show up as characteristic oscillations of the recursion coefficients on top of the linear increase.

cond-mat.str-el↗

arXiv2003

Dynamics of many-particle fragmentation in a Cellular Automaton model

A 3D Cellular Automaton model developed by the authors to deal with the dynamics of N-body interactions has been adapted to investigate the head-on collision of two identical bound clusters of particles, and the ensuing process of fragmentation. The range of impact energies is chosen low enough, to secure that a compound bound cluster can be formed. The model is devised to simulate the laboratory set-up of fragmentation experiments as monitored by 4pi detectors. The particles interact via a Lennard-Jones potential. At low impact energies the numerical experiments following the dynamics of the individual particles indicate a phase of energy sharing among all the particles of the compound cluster. Fragments of all sizes are then found to evaporate from the latter cluster. The cluster sizes, measured in our set-up by simulated 4pi detectors, conform to a power law of exponent around 2.6.

nucl-th↗

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

Magnetic phases of the mixed-spin $J_1-J_2$ Heisenberg model on a square lattice

We study the zero-temperature phase diagram and the low-energy excitations of a mixed-spin ($S_1>S_2$) $J_1-J_2$ Heisenberg model defined on a square lattice by using a spin-wave analysis, the coupled cluster method, and the Lanczos exact-diagonalization technique. As a function of the frustration parameter $J_2/J_1$ ($ >0$), the phase diagram exhibits a quantized ferrimagnetic phase, a canted spin phase, and a mixed-spin collinear phase. The presented results point towards a strong disordering effect of the frustration and quantum spin fluctuations in the vicinity of the classical spin-flop transition. In the extreme quantum system $(S_1,S_2)=(1,{1/2})$, we find indications of a new quantum spin state in the region $0.46< J_2/J_1<0.5$

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

Quantum Phase Transitions in Spin Systems

We discuss the influence of strong quantum fluctuations on zero-temperature phase transitions in a two-dimensional spin-half Heisenberg system. Using a high-order coupled cluster treatment, we study competition of magnetic bonds with and without frustration. We find that the coupled cluster treatment is able to describe the zero-temperature transitions in a qualitatively correct way, even if frustration is present and other methods such as quantum Monte Carlo fail.

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

Realistic description of electron-energy loss spectroscopy for One-Dimensional Sr$_2$CuO$_3$

We investigate the electron-energy loss spectrum of one-dimensional undoped CuO$_{3}$ chains within an extended multi-band Hubbard model and an extended one-band Hubbard model, using the standard Lanczos algorithm. Short-range intersite Coulomb interactions are explicitly included in these models, and long-range interactions are treated in random-phase approximation. The results for the multi-band model with standard parameter values agree very well with experimental spectra of Sr$_{2}$CuO$_{3}$. In particular, the width of the main structure is correctly reproduced for all values of momentum transfer. It is shown for both models that intersite Coulomb interactions mainly lead to an energy shift of the spectra. We find no evidence for enhanced intersite interactions in Sr$_{2}$CuO$_{3}$.

cond-mat.str-el↗