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Magnetization processes of spin-1 2 Heisenberg ladders are studied using strong-coupling expansions, numerical diagonalization of finite systems and a bosonization approach. We find that the magnetization exhibits plateaux as a function of the applied field at certain rational fractions of the saturation value. Our main focus are ladders with 3 legs where plateaux with magnetization one third of the saturation value are shown to exist.

In this paper we continue and extend a systematic study of plateaux in magnetization curves of antiferromagnetic Heisenberg spin-1/2 ladders. We first review a bosonic field-theoretical formulation of a single XXZ-chain in the presence of a magnetic field, which is then used for an Abelian bosonization analysis of N weakly coupled chains. Predictions for the universality classes of the phase transitions at the plateaux boundaries are obtained in addition to a quantization condition for the value of the magnetization on a plateau. These results are complemented by and checked against strong-coupling expansions. Finally, we analyze the strongcoupling effective Hamiltonian for an odd number N of cylindrically coupled chains numerically. For N = 3 we explicitly observe a spin-gap with a massive spinon-type fundamental excitation and obtain indications that this gap probably survives the limit N → ∞.

The frustrated classical antiferromagnetic Heisenberg model with Dzyaloshinskii-Moriya (DM) interactions on the triangular lattice is studied under a magnetic field by means of semiclassical calculations and large-scale Monte Carlo simulations. We show that even a small DM interaction induces the formation of an Antiferromagnetic Skyrmion crystal (AF-SkX) state. Unlike what is observed in ferromagnetic materials, we show that the AF-SkX state consists of three interpenetrating Skyrmion crystals (one by sublattice), and most importantly, the AF-SkX state seems to survive in the limit of zero temperature. To characterize the phase diagram we compute the average of the topological order parameter which can be associated to the number of topological charges or Skyrmions. As the magnetic field increases this parameter presents a clear jump, indicating a discontinuous transition from a spiral phase into the AF-SkX phase, where multiple Bragg peaks coexist in the spin structure factor. For higher fields, a second (probably continuous) transition occurs into a featureless paramagnetic phase.

We analyze the thermal conductivity of anisotropic and frustrated spin-1/2 chains using analytical and numerical techniques. This includes mean-field theory based on the Jordan-Wigner transformation, bosonization, and exact diagonalization of systems with N ≤ 18 sites. We present results for the temperature dependence of the zero-frequency weight of the conductivity for several values of the anisotropy ∆. In the gapless regime, we show that the mean-field theory compares well to known results and that the low-temperature limit is correctly described by bosonization. In the antiferromagnetic and ferromagnetic gapped regime, we analyze the temperature dependence of the thermal conductivity numerically. The convergence of the finite-size data is remarkably good in the ferromagnetic case. Finally, we apply our numerical method and mean-field theory to the frustrated chain where we find a good agreement of these two approaches on finite systems. Our numerical data do not yield evidence for a diverging thermal conductivity in the thermodynamic limit in case of the antiferromagnetic gapped regime of the frustrated chain. Introduction -Transport properties of lowdimensional spin systems have attracted recently interest both from the experimental and theoretical side. A particular motivation comes from the observation that magnetic excitations of one-dimensional spin systems significantly contribute to the thermal conductivity which is manifest in many experiments on materials such as the spin-ladder system 1,2,3 (Sr,La,Ca) 14 Cu 24 O 41 and the spin-chain compounds SrCuO 2 and Sr 2 CuO 3 4 . Assuming elementary excitations to carry the thermal current and using a relaxation time ansatz for their kinetic equation one finds extremely large mean-free paths being, for example, of the order of 1000Å in La 5 Ca 9 Cu 24 O 41 2 . Although the magnitude of the mean-free path is currently an issue of intense discussion, the question arises whether heat transport in low-dimensional spin systems is ballistic, i.e., whether intrinsic scattering of magnetic excitations is ineffective to render the thermal conductivity finite. From the theoretical point of view this issue is related to the value of the so-called (thermal) Drude weight 5 D th which is the zero-frequency weight of the thermal conductivity κ. A nonzero value of D th corresponds to a diverging thermal conductivity. This scenario is trivially realized if the energy-current operator is a conserved quantity, which is the case for the spin-1/2 Heisenberg chain 5,6 . For a number of other models like the frustrated chain, the dimerized chains or the spin ladder the energy-current operator is not conserved and the question of nonzero D th is a challenging topic.In this paper, we establish various numerical and analytical techniques to analyze the thermal Drude weight and to compute the temperature dependence of D th (T ). We study the model Hamiltonian H = l h l with the local energy-density given by

We analyze the phase diagram of a system of spin-1/2 Heisenberg antiferromagnetic chains interacting through a zig-zag coupling, also called zig-zag ladders. Using bosonization techniques we study how a spin-gap or more generally plateaux in magnetization curves arise in different situations. While for coupled XXZ chains, one has to deal with a recently discovered chiral perturbation, the coupling term which is present for normal ladders is restored by an external magnetic field, dimerization or the presence of charge carriers. We then proceed with a numerical investigation of the phase diagram of two coupled Heisenberg chains in the presence of a magnetic field. Unusual behaviour is found for ferromagnetic coupled antiferromagnetic chains. Finally, for three (and more) legs one can choose different inequivalent types of coupling between the chains. We find that the three-leg ladder can exhibit a spin-gap and/or non-trivial plateaux in the magnetization curve whose appearance strongly depends on the choice of coupling.

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We study the one-particle von Neumann entropy of a system of N hard-core anyons on a ring. The entropy is found to have a clear dependence on the anyonic parameter which characterizes the generalized fractional statistics described by the anyons. This confirms the entanglement is a valuable quantity to investigate topological properties of quantum states. We derive the generalization to anyonic statistics of the Lenard formula for the one-particle density matrix of N hard-core bosons in the large N limit and extend our results by a numerical analysis of the entanglement entropy, providing additional insight into the problem under consideration.In recent years an intense research activity has been devoted to the study of entanglement in many-body states. Initially, this effort has been mostly motivated by the fact that quantum correlated many-body states, which appear in various solid-state models, can be valuable resources for information processing and quantum computation [1,2]. The theory of entanglement is now attracting even more attention because of its fundamental implication for the development of new efficient numerical methods for quantum systems [3,4,5] and for the characterization of quantum critical phases [6,7,8].Generally speaking, entanglement measures nonlocal properties of composite quantum systems and it can provide additional information to that obtained by investigating local observables or traditional correlation functions. In this respect entanglement might be a sensitive probe into the topological properties of quantum states. A particularly significant quantity is the entanglement entropy S A , which is defined in a bipartite system A ∪ B and quantified as the von Neumann entropy S A = −Trρ A ln ρ A associated to the reduced density matrix ρ A of a subsystem A. In two-dimensional systems a firm connection between topological order and entanglement entropy has been established in [9,10], where the entanglement entropy was defined by spatial partitioning. Recent studies on Laughlin states [11,12] have considered the entanglement entropy associated to particle partitioning [11,12]. Also in this case, the entanglement entropy turns out to reveal important aspects of the topological order in Laughlin States.The two-dimensional case is of particular interest due to the existence of models whose elementary excitations exhibit generalized fractional statistics. Anyons, the particles obeying such statistics, play a fundamental role in the description of the fractional quantum Hall effect [13]. Although this concept is essentially twodimensional, anyons can also occur in one-dimensional (1D) systems [14,15,16,17,18,19,20], where statistics and interactions are inextricable, leading to strong shortrange correlations. The 1D anyonic models have proven useful to study persistent charge and magnetic currents in 1D mesoscopic rings [15]. This possibility and their own pure theoretical interest lead us to investigate the effects of the anyonic statistics on the entanglement entropy in the present Letter....