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     

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     

Density-matrix renormalization study of the Hubbard model [4]on a Bethe lattice

The half-filled Hubbard model on the Bethe lattice with coordination number z=3 is studied using the density-matrix renormalization group (DMRG) method. Ground-state properties such as the energy per site E, average local magnetization , its fluctuations and various spin correlation functions are determined as a function of the Coulomb interaction strength U/t. The local magnetic moments increase monotonically with increasing Coulomb repulsion U/t showing antiferromagnetic order between nearest neighbors []. At large U/t, is strongly reduced with respect to the saturation value 1/2 due to exchange fluctuations between nearest neighbors (NN) spins [ for ]. shows a maximum for U/t=2.4-2.9 that results from the interplay between the usual increase of with increasing U/t and the formation of important permanent moments at large U/t. While NN sites show antiferromagnetic spin correlations that increase with increasing Coulomb repulsion, the next NN sites are very weakly correlated over the whole range of U/t. The DMRG results are discussed and compared with tight-binding calculations for U=0, independent DMRG studies for the Heisenberg model and simple first-order perturbation estimates. Received 8 February 1999 and Received in final form 14 June 1999     

The statistical mechanics of turbo codes

The “turbo codes”, recently proposed by Berrou et al. [1] are written as a disordered spin Hamiltonian. It is shown that there exists a threshold such that for signal to noise ratios the error probability per bit vanishes in the thermodynamic limit, i.e. the limit of infinitely long sequences. The value of the threshold has been computed for two particular turbo codes. It is found that it depends on the code. These results are compared with numerical simulations. Received 14 March 2000 and Received in final form 17 July 2000     

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     

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     

Quasiclassical Hamiltonians for large-spin systems

We extend and apply a previously developed method for a semiclassical treatment of a system with large spin S. A multisite Heisenberg Hamiltonian is transformed into an effective classical Hamilton function which can be treated by standard methods for classical systems. Quantum effects enter in form of multispin interactions in the Hamilton function. The latter is written in the form of an expansion in powers of J/(TS), where J is the coupling constant. Main ingredients of our method are spin coherent states and cumulants. Rules and diagrams are derived for computing cumulants of groups of operators entering the Hamiltonian. The theory is illustrated by calculating the quantum corrections to the free energy of a Heisenberg chain which were previously computed by a Wigner-Kirkwood expansion. Received 5 May 1999 and received in final form 24 September 1999     

Quadrupolar order in the Heisenberg ferromagnet with the single-ion cubic anisotropy

The ground state properties of S =2 ferromagnets with isotropic Heisenberg exchange (J) and single-ion cubic anisotropy (D) are studied. The perturbation theory for is used to find an effective Hamiltonian up to the fourth order for 1, 2 and 3 dimensions. It is shown that in opposition to the MFA prediction there is the quadrupolar long range order at T = 0 in the non-magnetic state of the system without a quadrupolar type of interaction. The effect is a consequence of the quantum nature of the model. Received: 19 February 1998 / Accepted: 17 March 1998     

Local environment and electron correlation effects on the magnetic properties of clusters

The electronic and magnetic properties of clusters are investigated in the framework of the Hubbard model by treating electron correlations effects in a saddle-point slave-boson approximation. The size dependent single-particle spectrum is calculated using a third moment real-space expansion of the local density of states. Results for the magnetic moments, magnetic order, average number of double occupations and hopping renormalizations are given as a function of the local coordination number z, for different representative values of the Coulomb interaction strength U/t and band filling n. Several transitions between paramagnetic, ferromagnetic and antiferromagnetic behaviors are obtained as a function of z. The environment dependence of the magnetic behavior and of the degree of electron delocalization is analyzed. Advantages and limitations of the present approach are discussed. Received: 8 January 1998 / Revised: 22 June 1998 / Accepted: 6 August 1998     

Novel massive ground states of spin chains in a magnetic field

Novel massive quantum states appearing in spin chains under a strong magnetic field are discussed. These states lead to plateaus in magnetization curves. When the systems are axially symmetric and the field is applied parallel to the symmetry-axis, the phenomena are analogous to metal-insulator transitions. Striking features of the plateau phenomena - exactness and rationality - are explained as consequences the commensurability condition to the underlying lattice. The effects of the planar anisotropy are also discussed in detail. Received: 16 February 1998 / Revised: 20 April 1998 / Accepted: 30 April 1998     

Effective Hubbard model for Zn-doped CuO2 plane

In the framework of the cell-perturbation method for the original p-d model an effective two-band Hubbard model for the CuO₂ plane with Zn impurities is derived. Zn impurities are modelled by Wannir oxygen one-hole states at vacant Cu sites. The model is based on the results of band structure calculations carried out within the local-density approximation. Further reduction to an extended t-J model shows a large ferromagnetic superexchange interaction between the Cu spin with the nearest virtual oxygen spin in the Zn cell. Received 17 November 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     

Vortices in quantum spin systems

We examine spin vortices in ferromagnetic quantum Heisenberg models with planar anisotropy on two-dimensional lattices. The symmetry properties and the time evolution of vortices built up from spin-coherent states are studied in detail. Although these states show a dispersion typical for wave packets, important features of classical vortices are conserved. Moreover, the results on symmetry properties provide a construction scheme for vortex-like excitations from exact eigenstates, which have a well-controlled time evolution. Our approach works for arbitrary spin length both on triangular and square lattices. Received 2 October 1998     

Monte-Carlo study of correlations in quantum spin chains at non-zero temperature

Antiferromagnetic Heisenberg spin chains with various spin values (S=1/2,1,3/2,2,5/2) are studied numerically with the quantum Monte-Carlo method. Effective spin S chains are realized by ferromagnetically coupling n=2S antiferromagnetic spin chains with S=1/2. The temperature dependence of the uniform susceptibility, the staggered susceptibility, and the static structure factor peak intensity are computed down to very low temperatures, . The correlation length at each temperature is deduced from numerical measurements of the instantaneous spin-spin correlation function. At high temperatures, very good agreement with exact results for the classical spin chain is obtained independent of the value of S. For the S=2 chain which has a gap , the correlation length and the uniform susceptibility in the temperature range are well predicted by the semi-classical theory of Damle and Sachdev. Received: 23 December 1997 / Revised and Accepted: 11 March 1998     

Off-diagonal long-range order in a supersymmetric integrable model of correlated electrons

A new model for correlated electrons is presented which is integrable in one-dimension. The symmetry algebra of the model is the Lie superalgebra gl(2|1) which depends on a continuous free parameter. This symmetry algebra contains the pairing algebra as a subalgebra which is used to show that the model exhibits Off-Diagonal Long-Range Order in any number of dimensions. Received: 9 December 1997 / Revised: 12 February 1998 / Accepted: 17 March 1998     

Ground-state landscape of J Ising spin glasses

Large numbers of ground states of two-dimensional Ising spin glasses with periodic boundary conditions in both directions are calculated for sizes up to 40². A combination of a genetic algorithm and Cluster-Exact Approximation is used. For each quenched realization of the bonds up to 40 independent ground states are obtained. For the infinite system a ground-state energy of e =-1.4015(3) is extrapolated. The ground-state landscape is investigated using a finite-size scaling analysis of the distribution of overlaps. The mean-field picture assuming a complex landscape describes the situation better than the droplet-scaling model, where for the infinite system mainly two ground states exist. Strong evidence is found that the ground states are not organized in an ultrametric fashion in contrast to previous results for three-dimensional spin glasses. Received 12 October 1998     

High-temperature series analysis of the p-state Potts glass model on d-dimensional hypercubic lattices

We analyze recently extended high-temperature series expansions for the “Edwards-Anderson” spin-glass susceptibility of the p-state Potts glass model on d-dimensional hypercubic lattices for the case of a symmetric bimodal distribution of ferro- and antiferromagnetic nearest-neighbor couplings . In these star-graph expansions up to order 22 in the inverse temperature , the number of Potts states p and the dimension d are kept as free parameters which can take any value. By applying several series analysis techniques to the new series expansions, this enabled us to determine the critical coupling K_c and the critical exponent of the spin-glass susceptibility in a large region of the two-dimensional (p,d)-parameter space. We discuss the thus obtained information with emphasis on the lower and upper critical dimensions of the model and present a careful comparison with previous estimates for special values of p and d. Received: 25 May 1998 / Revised and Accepted: 11 August 1998