The exact expression derived by Bougourzi, Couture, and Kacir for the two-spinon contribution to the dynamic spin structure factor S(q, ) of the one-dimensional sϭ1/2 Heisenberg antiferromagnet at Tϭ0 is evaluated for direct comparison with finite-chain transition rates (Nр28) and an approximate analytical result previously inferred from finite-N data, sum rules, and Bethe ansatz calculations. The two-spinon excitations account for 72.89% of the total intensity in S(q, ). The singularity structure of the exact result is determined analytically and its spectral-weight distribution evaluated numerically over the entire range of the two-spinon continuum. The leading singularities of the frequency-dependent spin autocorrelation function, static spin structure factor, and q dependent susceptibility are determined via sum rules. The impact of the non-twospinon excitations on the integrated intensity, the susceptibility, the frequency moments, and the Euclidian time representation of S(q, ) is studied on the basis of finite-size data. ͓S0163-1829͑97͒00517-1͔

In the presence of a uniform field the one-dimensional spin-1 2 antiferromagnetic Heisenberg model develops zero frequency excitations at field-dependent 'soft mode' momenta. We determine three types of critical quantities, which we extract from the finite-size dependence of the lowest excitation energies, the singularities in the static structure factors and the infrared singularities in the dynamical structure factors at the soft mode momenta. We also compare our results with the predictions of conformal field theory.

We study numerically the dimerized Heisenberg model with frustration appropriate for the quasi-1D spin-Peierls compound CuGeO3. We present evidence for a bound state in the dynamical structure factor for any finite dimerization δ and estimate the respective spectral weight. For the homogeneous case (δ = 0) we show that the spin-wave velocity vs is renormalized by the n.n.n. frustration term α as vs = π/2 J(1 − bα) with b ≈ 1.12 78.20.Ls Quantum 1D spin systems may show a variety of instabilities. Of particular interest is the spin-Peierls (SP) phase due to residual magnetoelastic couplings [1], which leads to the opening of a gap in the spin excitation spectrum. The discovery [2] of the spin-Peierls transition below T SP = 14 K in an inorganic compound, CuGeO 3 , has attracted widespread attention.The spin-dynamics of CuGeO 3 is being studied intensively [3][4][5]. Above the spin-Peierls transition the onemagnon excitation spectrum, as measured by neutron scattering [6], forms a broad continuum. The form of the continuum is in good agreement with the continuum expected for one-dimensional antiferromagnetic Heisenberg chains [7]; it is also seen in the magnetic Raman spectrum [8,9]. The physics behind the continuum in the one-magnon excitation spectrum lies on the fact that the elementary excitations of the one-dimensional Heisenberg chain are spinons (also called solitons or Bloch walls), each magnon being made up of two solitons. The resulting "two-spinon" continuum has been seen experimentally also in other quasi-1D antiferromagnets [10].The exact form of the magnetic excitation spectrum in the dimerized state below T SP is still being investigated. A two-spinon continuum is observed [5,6] with large spectral weight at the lower edge. The dispersion of the lower edge has been used to extract the spin-wave velocity [3]. Muthukumar et al. have pointed out recently [9] that the experimental magnetic Raman intensity indicates a well defined magnon mode in the spin-Peierls state of CuGeO 3 and that the origin of this magnon could not be determined on the basis of the Raman scattering data obtained numerically for a single chain.The existence of a well defined magnon mode, i.e. a two-spinon bound state which splits of the continuum, has also been addressed recently by Uhrig and Schulz [11] within an RPA approach. A recent neutron scattering experiment [12], has been interpreted as indicative of such a bound-state.In this context it is an important question to address whether other techniques can shed light on the magnetic excitation spectrum of the dimerized Heisenberg model. Here we present data for the dynamical structure factor S(k, ω) obtained by applying the recursion method [13] to calculate the excitation spectrum of the hamiltonian given below. This approximate method in particular gives very accurate results for the low-lying excitaions. We find evidence for a bound-state for any dimerization δ > 0, independently of the amount of frustration α present. The finite-size corrections of the data is, for certa...

Recent thermal conductivity measurements on UP t3 single crystals by Lussier et al. indicate the existence of a strong b{c anisotropy in the superconducting state. We calculate the thermal conductivity in various unconventional candidate states appropriate for the UP t3 \B phase" and compare with experiment, speci cally the E2u and E1g (1; i) states predicted in some GinzburgLandau analyses of the phase diagram. For the simplest realizations of these states over spherical or ellipsoidal Fermi surfaces, the normalized E2u conductivity is found, surprisingly, to be completely isotropic. We discuss the e ects of inelastic scattering and realistic Fermi surface anisotropy, and deduce constraints on the symmetry class of the UP t3 ground state.PACS Numbers: 74.70T,74.25FThe heavy fermion superconductor UPt 3 is now generally thought to be \unconventional", in the sense that the order parameter exhibits a lower symmetry than that of the Fermi surface. The principal evidence for this conclusion has been the observation of a nontrivial phase diagram for the system in applied magnetic eld and pressure. Earlier hints of unconventional behavior included transport and thermodynamic properties reported to vary as power laws in the temperature for T T c , as well as strong, temperature{dependent anisotropy in superconducting transport properties. 1] Current Ginzburg-Landau (GL) theories of the UPt 3 phase diagram attempt to explain the multiplicity of superconducting phases observed by assuming an order parameter corresponding to 1) a higher dimensional irreducible representation of the normal state symmetry group, weakly split by a symmetry{breaking eld; or 2) a mixture of two accidentally nearly degenerate representations. In most scenarios, the quartic terms in the GL free energy are chosen to reproduce, if possible, the expected nature of the low-temperature, low-eld UPt 3 "Bphase", characterized by a line of gap nodes in the hexagonal basal plane, and possibly point nodes along the caxis. The prejudice in favor of this structure arises from early tranport experiments. 1,2] Qualitatively speaking, these experiments support a picture in which there is, for T T c , a higher density of excited quasiparticles with wave vectors in the basal plane. Attempts to measure this anisotropy in other experiments have not been uniformly successful, however. For example, measurements of the London penetration depth L in geometries chosen to maximize currents along chosen directions found L (T ) T 2 with coe cients depending only weakly on direction. 3] A SR experiment reporting considerable anisotropy in the same quantity 4] may in fact have been dominated by extraneous e ects. 5] Explicit evidence in favor of strong gap anisotropy in the superconducting state involving measurements in di erent directions in the same sample is in fact rather limited. 1,6] The recent thermal conductivity measurements of Lussier et al. are therefore of considerable interest, both as hard qualitative evidence for anisotropy and for the opportunity to make q...

We study the one-dimensional spin-1/2 model with nearest and next-to-nearest-neighbor couplings exposed to a homogeneous magnetic field h3 and a dimer field with period q and strength δ. The latter generates a magnetization plateau at M = (1 − q/π)/2, which evolves with strength δ of the perturbation as δ ǫ , where ǫ = ǫ(h3, α) is related to the η-exponent which describes the critical behavior of the dimer structure factor, if the perturbation is switched of (δ = 0). We also discuss the appearance of magnetization plateaus in ladder systems with l legs.

We compute the energies and transition probabilities for low excitations in the one-dimensional antiferromagnetic spin- 1/2 Heisenberg model by means of the recursion method. We analyse finite-size effects in the Euclidean time ( tau -) representation and compare the resulting estimate for the thermodynamical limit with two parametrizations for the dynamical structure factors in the spectral ( omega -) representation.

We investigate the critical exponents η3(α, M ), η1(α, M ) associated with the singularities in the longitudinal and transverse structure factors of the one dimensional antiferromagnetic Heisenberg model with nearest (J1) and next to nearest (J2) neighbour coupling of relative strength α = J 2 J 1 and an external field B with magnetization M (B).

Abstract. We report on a systematic implementation of su(2) invariance for matrix product states (MPS) with concrete computations cast in a diagrammatic language. As an application we present a variational MPS study of a spin-1/2 quantum chain. For efficient computations we make systematic use of the su(2) symmetry at all steps of the calculations: (i) the matrix space is set up as a direct sum of irreducible representations, (ii) the local matrices with state-valued entries are set up as superposition of su(2) singlet operators, (iii) products of operators are evaluated algebraically by making use of identities for 3j and 6j symbols. The remaining numerical computations like the diagonalization of the associated transfer matrix and the minimization of the energy expectation value are done in spaces free of symmetry degeneracies. The energy expectation value is a strict upper bound of the true ground-state energy and yields definite conclusions about the accuracy of DMRG results reported in the literature. Furthermore, we present explicit results with accuracy better than 10 −4 for nearestand next-nearest neighbour spin correlators and for general dimer-dimer correlators in the thermodynamical limit of the spin-1 2 Heisenberg chain with frustration.