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....

We investigate classical Heisenberg spins on the Shastry-Sutherland lattice and under an external magnetic field. A detailed study is carried out both analytically and numerically by means of classical Monte-Carlo simulations. Magnetization pseudo-plateaux are observed around 1/3 of the saturation magnetization for a range of values of the magnetic couplings. We show that the existence of the pseudo-plateau is due to an entropic selection of a particular collinear state. A phase diagram that shows the domains of existence of those pseudo-plateaux in the (h, T ) plane is obtained.

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We investigate the classical counterpart of an effective Hamiltonian for a strongly trimerized kagomé lattice. Although the Hamiltonian only has a discrete symmetry, the classical groundstate manifold has a continuous global rotational symmetry. Two cases should be distinguished for the sign of the exchange constant. In one case, the groundstate has a 120 • spin structure. To determine the transition temperature, we perform Monte-Carlo simulations and measure specific heat, the order parameter as well as the associated Binder cumulant. In the other case, the classical groundstates are macroscopically degenerate. A thermal order-by-disorder mechanism is predicted to select another 120 • spin-structure. A finite but very small transition temperature is detected by Monte-Carlo simulations using the exchange method.

We investigate a simple model of a frustrated classical spin chain coupled to adiabatic phonons under an external magnetic field. A thorough study of the magnetization properties is carried out both numerically and analytically. We show that already a moderate coupling with the lattice can stabilize a plateau at 1/3 of the saturation and discuss the deformation of the underlying lattice in this phase. We also study the transition to saturation where either a first or second order transition can occur, depending on the couplings strength.Comment: Submitted to Phys. Rev.