Low temperature thermodynamics of inverse square spin models in one dimension

We present a field-theoretic renormalization group calculation in two loop order for classical O(N)-models with an inverse square interaction in the vicinity of their lower critical dimensionality one. The magnetic susceptibility at low temperatures is shown to diverge like with a=(N-2)/(N-1) and . From a comparison with the exactly solvable Haldane-Shastry model we find that the same temperature dependence applies also to ferromagnetic quantum spin chains. Received: 20 February 1998 / Revised: 27 April 1998 / Accepted: 30 April 1998     

Charge correlations in the weakly doped t-J model calculated by projection technique

We study frequency- and wave-vector dependent charge correlations in weakly doped antiferromagnets using Mori-Zwanzig projection technique. The system is described by the two-dimensional t-J model. The ground state is expressed within a cumulant formalism which has been successfully applied to study magnetic properties of the weakly doped system. Within this approach the ground state contains independent spin-bag quasiparticles (magnetic polarons). We present results for the charge-density response function and for the optical conductivity at zero temperature for different values of t / J. They agree well with numerical results calculated by exact diagonalization techniques. The density response function for intermediate and large momenta shows a broad continuum on energy scales of order of several t whereas the optical conductivity for is dominated by low energy excitations (at 1.5-2J). We show that these weak-doping properties can be well understood by transitions between excited states of spin-bag quasiparticles. Received: 10 July 1997 / Revised: 19 March 1998 / Accepted: 3 April 1998     

A DMRG study of the -symmetric Heisenberg chain

The spin one-half Heisenberg chain with U q [ SU (2)] symmetry is studied via density-matrix renormalization. Ground-state energy and q-symmetric correlation functions are calculated for the non-Hermitian case with integer r. This gives bulk and surface exponents for (para)fermionic correlations in the related Ising and Potts models. The case of real q corresponding to a diffusion problem is treated analytically. Received: 18 February 1998 / Accepted: 17 March 1998     

First excitations of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice

We study the exact low energy spectra of the spin 1/2 Heisenberg antiferromagnet on small samples of the kagomé lattice of up to N=36 sites. In agreement with the conclusions of previous authors, we find that these low energy spectra contradict the hypothesis of Néel type long range order. Certainly, the ground state of this system is a spin liquid, but its properties are rather unusual. The magnetic () excitations are separated from the ground state by a gap. However, this gap is filled with nonmagnetic () excitations. In the thermodynamic limit the spectrum of these nonmagnetic excitations will presumably develop into a gapless continuum adjacent to the ground state. Surprisingly, the eigenstates of samples with an odd number of sites, i.e. samples with an unsaturated spin, exhibit symmetries which could support long range chiral order. We do not know if these states will be true thermodynamic states or only metastable ones. In any case, the low energy properties of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice clearly distinguish this system from either a short range RVB spin liquid or a standard chiral spin liquid. Presumably they are facets of a generically new state of frustrated two-dimensional quantum antiferromagnets. Received: 27 November 1997 / Accepted: 29 January 1998     

Phase transition in the Blume-Capel model with second neighbour interaction

A two dimensional antiferromagnetic spin-1 Ising model with negative next- nearest neighbour interaction (J ₂ <0) and under an external magnetic field is investigated by two methods: The mean-field theory and Finite-Size-Scaling based on transfer matrix (TMFSS) calculations. The ground state diagrams exhibit several new phases including frustrated ones. At finite temperature we obtain by these two methods quite rich phase diagrams, with several multicritical points. While Mean field approximation yields phase diagrams which are sometimes even qualitatively incorrect, accurate results are obtained from transfer matrix finite size scaling calculations. For a certain range of interaction parameters, the model is shown to violate the ordinary universality hypothesis. Received: 3 November 1997 / Revised: 31 March 1998 / Accepted: 7 April 1998     

Quantum rotors with regular frustration and the quantum Lifshitz point

We have discussed the zero-temperature quantum phase transition in n-component quantum rotor Hamiltonian in the presence of regular frustration in the interaction. The phase diagram consists of ferromagnetic, helical and quantum paramagnetic phase, where the ferro-para and the helical-para phase boundary meets at a multicritical point called a (d,m) quantum Lifshitz point where (d,m) indicates that the m of the d spatial dimensions incorporate frustration. We have studied the Hamiltonian in the vicinity of the quantum Lifshitz point in the spherical limit and also studied the renormalisation group flow behaviour using standard momentum space renormalisation technique (for finite n). In the spherical limit ()one finds that the helical phase does not exist in the presence of any nonvanishing quantum fluctuation for m =d though the quantum Lifshitz point exists for all d > 1+m/2, and the upper critical dimensionality is given by d _u = 3 +m/2. The scaling behaviour in the neighbourhood of a quantum Lifshitz point in d dimensions is consistent with the behaviour near the classical Lifshitz point in (d+z) dimensions. The dynamical exponent of the quantum Hamiltonian z is unity in the case of anisotropic Lifshitz point (d>m) whereas z=2 in the case of isotropic Lifshitz point (d=m). We have evaluated all the exponents using the renormalisation flow equations along-with the scaling relations near the quantum Lifshitz point. We have also obtained the exponents in the spherical limit (). It has also been shown that the exponents in the spherical model are all related to those of the corresponding Gaussian model by Fisher renormalisation. Received: 23 December 1997 / Received in final form: 6 January 1998 / Accepted: 7 January 1998     

Moment-volume instabilities in alloys with compositions around the C14 laves phase

We measured the thermal expansion and the specific heat of Ti_xFe_100-x alloys with x = 30.5, 32.5 and 35, all with hexagonal C14 laves phase structure (MgZn₂) like TiFe₂, and determine the temperature dependence of the magnetic contributions to the thermal expansion and the specific heat c_mag. For fixed composition and c mag ( T ) show the same type of behavior, demonstrating that both anomalies are of the same microscopic nature. They originate from moment-volume fluctuations (antiferromagnetic Invar-effect) as a comparison with total energy calculations as a function of atomic volume and moment for TiFe₂ reveals. Received: 26 January 1998 / Accepted: 17 April 1998     

On the incommensurate phase in modulated Heisenberg chains

Using the density matrix renormalization group method (DMRG) we calculate the magnetization of frustrated S=1/2 Heisenberg chains for various modulation patterns of the nearest neighbour coupling: commensurate, incommensurate with sinusoidal modulation and incommensurate with solitonic modulation. We focus on the order of the phase transition from the commensurate dimerized phase (D) to the incommensurate phase (I). It is shown that the order of the phase transition depends sensitively on the model. For the solitonic model in particular, a k-dependent elastic energy modifies the order of the transition. Furthermore, we calculate gaps in the incommensurate phase in adiabatic approximation. Received: 9 March 1998 / Accepted: 17 April 1998     

Bias and temperature dependence of the noise in a single electron transistor

Models generalizing the su (2) XX spin-chain were recently introduced. These XXC models also have an underlying su (2) structure. Their construction method is shown to generalize to the chains based on the fundamental representations of the A_m Lie algebras. Integrability of the new models is shown in the context of the quantum inverse scattering method. Their R-matrix is found and shown to yield a representation of the Hecke algebra. The diagonalization of the transfer matrices is carried out using the algebraic Bethe Ansatz. I comment on eventual generalizations and possible links to reaction-diffusion processes. Received: 24 June 1998 / Received in final form: 8 September 1998 / Accepted: 10 September 1998     

Twin-correlations in atoms

We discuss the possibility of preparing an atomic sample of atoms with minimum fluctuations in the difference between populations of two levels. A first scheme involves absorption of twin beams of light, and it presents a variant of a recent proposal for atomic spin squeezing within an excited state manifold [Kuzmich et al., Phys. Rev. Lett. 79, 4782 (1997)]. A second scheme involves atoms with two stable states, and we suggest that by use of quantum non-demolition detection and feed-back optical pumping, we may ensure a perfect agreement between the number of atoms in these two states. Received: 14 May 1998 / Revised: 10 August 1998 / Accepted: 8 October 1998     

Long-range spin-pairing order and spin defects in quantum spin- $${1 \over 2}$$ ladders

For w-legged antiferromagnetic spin-1/2 Heisenberg ladders, a long-range spin pairing order can be identified which enables the separation of the space spanned by finite-range (covalent) valence-bond configurations into w +1 subspaces. Since every subspace has an equivalent counter subspace connected by translational symmetry, twofold degeneracy, breaking translational symmetry is found except for the subspace where the ground state of w = even belongs to. In terms of energy ordering, (non)degeneracy and the discontinuities introduced in the long-range spin pairing order by topological spin defects, the differences between even and odd ladders are explained in a general and systematic way. Received 19 July 1999 and Received in final form 8 October 1999     

Order by thermal disorder in 2D planar rotator model with dipolar interactions

The energy of a square planar rotator model of spins interacting via dipolar forces is minimized by infinite inequivalent configurations corresponding to spins arranged on four interpenetrating sublattices making angles , , , with a reference axis, being arbitrary. This infinite degeneracy of the ground state is accidental in nature and one expects that it is removed by thermal fluctuations in agreement with Monte Carlo simulation. Indeed we find that the elementary excitation energies which depend on lead to a free energy which is a function of with minima at and corresponding to columnar configurations. This selection of columnar configurations out of the infinite ground state manifold is an example of order by thermal disorder. Received 4 August 1998     

Numerical diagonalization analysis of the ground-state superfluid-localization transition in two dimensions

Ground state of the two-dimensional hard-core-boson system in the presence of the quenched random chemical potential is investigated by means of the exact-diagonalization method for the system sizes up to L=5. The criticality and the DC conductivity at the superfluid-localization transition have been controversial so far. We estimate, with the finite-size scaling analysis, the correlation-length and the dynamical critical exponents as and z=2, respectively. The AC conductivity is computed with the Gagliano-Balseiro formula, with which the resolvent (dynamical response function) is expressed in terms of the continued-fraction form consisting of Lanczos tri-diagonal elements. Thereby, we estimate the universal DC conductivity as . Received 19 August 1998     

Flow equations for electron-phonon interactions: phonon damping

We report Nuclear Magnetic Resonance studies of CeAuAl₃ and LaAuAl₃ at frequencies between 1.30 and 76.91 MHz and at temperatures from up to . CeAuAl₃ is a new heavy-electron compound which orders antiferromagnetically at . For the two inequivalent Al sites of CeAuAl₃, the transferred hyperfine couplings and are relatively small compared to those in other Ce compounds. The nuclear quadrupolar coupling constants e2qQ / h are 2.9 MHz and 7.8 MHz, respectively. We suggest that the magnetic structure of the ordered state below is of a simple spiral type with the ordered Ce moments arranged ferromagnetically within the ( ab ) planes of the tetragonal crystal lattice. Based on this magnetic structure we estimate a 25% reduction of the Ce moments, most likely due to Kondo screening. At high temperatures, in the paramagnetic state of CeAuAl₃, the spin-lattice relaxation rate T1 ^-1 is dominated by the fluctuations of the localised Ce moments. At , T1 ^-1 is , more than two orders of magnitude larger than for the reference compound LaAuAl₃. For temperatures lower than T1 ^-1 decreases as a function of ( T / H ) and below , displays a linear-in-T behaviour, strongly enhanced compared to the reference compound LaAuAl₃. Received: 5 May 1998 / Received in final form: 16 July 1998 / Accepted: 20 July 1998     

Anomalous magnetic behavior of superconducting thin films in small magnetic fields [4] close to the transition temperature

Using a specially designed SQUID magnetometer we measured the temperature dependence of the critical current density in a ring patterned thin film for magnetic fields parallel to the c-axis. In addition, the temporal relaxation of the remanent state as prepared by field cooling in an external field of 100 Oe at different temperatures is determined. The j c ( T ) data show a field-dependent anomalous kink close to T_c pointing to reduced dissipation with increasing temperature allowing to construct a corresponding H-T borderline. A similar behavior is observed for the normalized relaxation rate S ( T ) as extracted from the temporal behavior of the remanent state, which, at low temperatures, exhibits the expected increase for increasing T-values, while an anomalous decrease of S ( T ) is found for temperatures above 85 K. While the low-T regime is attributed to creep of 2D pinned single vortex lines, the high-T behavior is suggested to be dominated by collective motion with a more sluggish dynamics. This change in dynamics is also reflected by the activation barriers for flux creep U ( j ), which show a corresponding crossover in μ from 0.06 to 0.99. An additional scaling analysis of the E-j characteristics for according to vortex glass theory reveals quasi-2D collective creep behavior with . Received: 8 April 1998 / Revised: 15 July 1998 / Accepted: 2 September 1998     

On evaluation of transverse spin fluctuations in quantum magnets

A numerical method is described for evaluating transverse spin correlations in the random phase approximation. Quantum spin-fluctuation corrections to sublattice magnetization are evaluated for the antiferromagnetic ground state of the half-filled Hubbard model in two and three dimensions in the whole U/t range. Extension to the case of defects in the AF is also discussed for spin vacancies and low-U impurities. In the limit, the vacancy-induced enhancement in the spin fluctuation correction is obtained for the spin-vacancy problem in two dimensions, for vacancy concentration up to the percolation threshold. For low-U impurities, the overall spin fluctuation correction is found to be strongly suppressed, although surprisingly spin fluctuations are locally enhanced at the low-U sites. Received 27 April 1998 and Received in final form 13 August 1998     

Magnetic properties of the low dimensional spin system (VO)PO:ESR and susceptibility

Experimental results on magnetic resonance (ESR) and magnetic susceptibility are given for single crystalline (VO)₂P₂O₇. The crystal growth procedure is briefly discussed. The susceptibility is interpreted numerically using a model with alternating spin chains. We determine J =51 K and . Furthermore we find a spin gap of meV from our ESR measurements. Using elastic constants no indication of a phase transition forcing the dimerization is seen below 300 K. Received: 22 December 1997 / Accepted: 17 March 1998     

Unified quantum mechanical picture for confined spinons in dimerized and frustrated spin chains

A quantum mechanical picture is presented to describe the behavior of confined spinons in a variety of S =1/2 chains. The confinement is due to dimerization and frustration and it manifests itself as a nonlinear potential , centered at chain ends () or produced by modulation kinks (b > 1). The calculation extends to weak or zero frustration some previous ideas valid for spinons in strongly frustrated spin chains. The local magnetization patterns of the confined spinons are calculated. A (minimum) enhancement of the local moments of about 11/3 over a single S =1/2 is found. Estimates for excitation energies and binding lengths are obtained. Received: 8 May 1998 / Revised and Accepted: 12 August 1998     

Finite-size-scaling analyses of the chiral ordert in the Josephson-junction ladder with half a flux quantum per plaquette

Chiral order of the Josephson-junction ladder with half a flux quantum per plaquette is studied by means of the exact diagonalization method. We consider an extreme quantum limit where each superconductor grain (order parameter) is represented by S=1/2 spin. So far, the semi-classical case, where each spin reduces to a plane rotator, has been considered extensively. We found that in the case of S=1/2, owing to the strong quantum fluctuations, the chiral (vortex lattice) order becomes dissolved except in a region, where attractive intrachain and, to our surprise, repulsive interchain interactions both exist. On the contrary, for considerably wide range of parameters, the superconductor (XY) order is kept critical. The present results are regarded as a demonstration of the critical phase accompanying chiral-symmetry breaking predicted for frustrated XXZ chain field-theoretically. Received 20 February 2000