Related papers: Exact Haldane mapping for all $S$ and super univer…
We introduce the concept of super universality in quantum Hall and spin liquids which has emerged from previous studies. It states that all the fundamental features of the quantum Hall effect are generically displayed as general topological…
The well known Haldane map from spin chains into the $O(3)$ non linear sigma model is generalized to the case of spin ladders. This map allows us to explain the different qualitative behaviour between even and odd ladders, exactly in the…
Using group theoretical methods we show for both the triangular and square lattices that in the continuum limit the antiferromagnetic order parameter lives on SO3 without respect of the initial lattice. For the antiferromagnetic chain we…
In the present paper we revisit the so-called Haldane limit, i.e. a particular continuum limit, which leads from a spin chain to a sigma model. We use the coherent state formulation of the path integral to reduce the problem to a…
This work studies the appearance of a Haldane gap in quasi one-dimensional antiferromagnets in the long wavelength limit, via the nonlinear $\sigma$-model. The mapping from the three-dimensional, integer spin Heisenberg model to the…
We review the basic properties of the Haldane phase in spin-1 Heisenberg antiferromagnetic chains, including its persistence in quasi-one-dimensional geometries. Using large-scale numerical simulations, we map out the phase diagram for a…
We investigate both numerically and analytically the behaviour of a spin-1 antiferromagnetic (AFM) isotropic Heisenberg chain in an external magnetic field. Extensive DMRG studies of chains up to N=80 sites extend previous analyses and…
The Heisenberg spin ladder is studied in the semiclassical limit, via a mapping to the nonlinear $\sigma$ model. Different treatments are needed if the inter-chain coupling $K$ is small, intermediate or large. For intermediate coupling a…
The antiferromagnetic Heisenberg model on a chain with nearest and next nearest neighbor couplings is mapped onto the $SO(3)$ nonlinear sigma model in the continuum limit. In one spatial dimension this model is always in its disordered…
We consider the two-dimensional $\rm O(3)$ non-linear sigma model with topological term using a lattice regularization introduced by Shankar and Read [Nucl.Phys. B336 (1990), 457], that is suitable for studying the strong coupling regime.…
We study quantum quenches in the $S=1$ Heisenberg spin chain and show that the dynamics can be described by the recently developed semi-semiclassical method based on particles propagating along classical trajectories but scattering quantum…
Microscopic models of quantum antiferromagnets are investigated on the basis of a mapping onto effective low energy hamiltonians. Lattice effects are carefully taken into account and their role is discussed. We show that the presence of an…
We review the non linear sigma model approach (NLSM) to spin chains and spin ladders, presenting new results. The generalization of the Haldane's map to ladders in the Hamiltonian approach, give rise to different values of the $\theta$…
The antiferromagnetic Heisenberg spin chain of odd spin $S$ is in the Haldane phase with several defining physical properties, such as thermodynamical ground-state degeneracy, symmetry-protected edge states, and nonzero string order…
We study both the static and dynamic properties of gapped, one-dimensional, Heisenberg, anti-ferromagnetic, spin chains at finite temperature through an analysis of the O(3) non-linear sigma model. Exploiting the integrability of this…
We have investigated Haldane's conjecture for the S=2 isotropic antiferromagnetic quantum spin chain with nearest-neighbor exchange J. Using a density matrix renormalization group algorithm for chains up to L=350 spins, we find in the…
We study a model of two weakly coupled isotropic spin-1/2 Heisenberg chains with an antiferromagnetic coupling along the chains. It is shown that the system always has a spectral gap. For the case of identical chains the model in the…
Infinite projected entangled pair states simulations of the $S=1$ bilinear-biquadratic Heisenberg model on the square lattice reveal an emergent Haldane phase in between the previously predicted antiferromagnetic and 3-sublattice…
By using Lanczos exact diagonalization and quantum Monte Carlo combined with stochastic analytic continuation, we study the dynamical properties of the $S=1$ antiferromagnetic Heisenberg chain with different strengths of bond disorder. In…
The two-dimensional Heisenberg spin-glass model is investigated by means of a semiclassical expansion around classical states. At leading order, we obtain an effective quadratic spin-wave Hamiltonian and study the localization properties of…