Symmetry breaking in Heisenberg antiferromagnets

We extend Griffith's theorem on symmetry breaking in quantum spin systems to the situation where the order operator and the Hamiltonian do not commute with each other. The theorem establishes that the existence of a long range order in a symmetric (non-pure) infinite-volume state implies the existence of a symmetry breaking in the state obtained by applying an infinitesimal symmetry-breaking field. The theorem is most meaningful when applied to a class of quantum antiferromagnets where the existence of a long range order has been proved by the Dyson-Lieb-Simon method. We also present a related theorem for the ground states. It is an improvement of the theorem by Kaplan, Horsch and von der Linden. Our lower bounds on the spontaneous staggered magnetization in terms of the long range order parameter take into account the symmetry of the system properly, and are likely to be saturated in general models.     

Quasiperiodic Heisenberg antiferromagnets in two dimensions

We describe some of the properties of 2d quantum quasiperiodic antiferromagnets as reported in studies that have been carried out in the last decade. Many results have been obtained for perfectly ordered as well as for disordered two dimensional bipartite quasiperiodic tilings. The theoretical methods used include spin wave theory, and renormalization group along with Quantum Monte Carlo simulations. These methods all show that the ground state of these unfrustrated antiferromagnets have Néel type order but with a highly complex spatial distribution of local staggered magnetization. The ground state properties, excitation energies and spatial dependence, structure factor, and local susceptibilities are presented and discussed. The effects of introducing geometrical disorder on the magnetic properties are discussed.     

Heat transport in low-dimensional Heisenberg antiferromagnets

In this paper we study thermal transport in the one-dimensional spin S=1 and the two dimensional spin S=1/2 Heisenberg antiferromagnets, using the modified spin wave theory and the Kubo linear response formalism, to calculate the thermal conductivity. The low-temperature thermal Drude weights, in both cases, are non-zero at finite temperature indicating a ballistic behavior.     

Apparent diamagnetism in quasi-two-dimensional Heisenberg antiferromagnets

We observed an apparent diamagnetism in representative quasi-two-dimensional Heisenberg canted antiferromagnets, (C_nH_2n+1NH₃)₂MnCl₄, indicating that the quasi-one-dimensionality is not essential for the apparent diamagnetism. The apparent diamagnetic response seems to be promoted by a thermal quenching and is characterized by a linear response to the applied magnetic field with a constant internal field.     

Topological entanglement entropy

We formulate a universal characterization of the many-particle quantum entanglement in the ground state of a topologically ordered two-dimensional medium with a mass gap. We consider a disk in the plane, with a smooth boundary of length L, large compared to the correlation length. In the ground state, by tracing out all degrees of freedom in the exterior of the disk, we obtain a marginal density operator rho for the degrees of freedom in the interior. The von Neumann entropy of rho, a measure of the entanglement of the interior and exterior variables, has the form S(rho) = alphaL - gamma + ..., where the ellipsis represents terms that vanish in the limit L --> infinity. We show that - gamma is a universal constant characterizing a global feature of the entanglement in the ground state. Using topological quantum field theory methods, we derive a formula for gamma in terms of properties of the superselection sectors of the medium.     

Critical temperatures of the anisotropic Heisenberg antiferromagnets

The first eight terms of the high temperature series expansions for the mean-square fluctuations of the magnetization variables are derived for the spin $\text{?}\text{1}\text{2}$ anisotropic Heisenberg antiferromagnets. The antiferromagnetic critical temperatures are determined for the s.c. and b.c.c. lattices.     

Quantum nonlinear sigma model for arbitrary spin Heisenberg antiferromagnets

We derive a quantum nonlinear sigma model (QNLSM) for quantum Heisenberg antiferromagnets (QHA) with arbitrary S (spin) values. A upper limit of the low temperature is naturally carried out for the reliability of the QNLSM. The S dependence of the effective coupling constant and the spin-wave velocity in the QNLSM are also obtained explicitly. The resulting spin-wave velocity for 2D spin-1/2 QHA highly concurs with the experimental data of high T(c) compound La(2)CuO(4). The predicted correlation lengths for 2D QHA and spin-gap magnitudes for 1D QHA also agrees with the accurate numerical results.     

Controllable entanglement sudden birth of Heisenberg spins

We investigate the Entanglement Sudden Birth (ESB) of two Heisenberg spins A and B. The third controller, qutrit C is introduced, which only has the Dzyaloshinskii-Moriya (DM) spin-orbit interaction with qubit B. We find that the DM interaction is necessary to induce the Entanglement Sudden Birth of the system qubits A and B, and the initial states of the system qubits and the qurit C are also important to control its Entanglement Sudden Birth.     

Controllable entanglement sudden birth of Heisenberg spins

We investigate the Entanglement Sudden Birth (ESB) of two Heisenberg spins A and B. The third controller, qutrit C is introduced, which only has the Dzyaloshinskii-Moriya (DM) spin-orbit interaction with qubit B. We find that the DM interaction is necessary to induce the Entanglement Sudden Birth of the system qubits A and B, and the initial states of the system qubits and the qurit C are also important to control its Entanglement Sudden Birth.     

Spin diffusion and relaxation in three-dimensional isotropic Heisenberg antiferromagnets

A theory is proposed for kinetic effects in isotropic Heisenberg antiferromagnets at temperatures above the Néel point. The scaling behavior of the generalized coefficient of spin diffusion and relaxation constant in the paramagnetic phase is studied in terms of the approximation of interacting modes. It is shown that the kinetic coefficients in an antiferromagnetic system are singular in the fluctuation region. The corresponding critical indices for diffusion and relaxation processes are calculated. The scaling dimensionality of the kinetic coefficients agrees with the predictions of dynamic similarity theory and a renormalization group analysis. The proposed theory can be used to study the momentum and frequency dependence of the kinetic parameters, and to determine the form of the scaling functions. The role of nonlocal correlations and spin-fluid effects in magnetic systems is discussed. Zh. éksp. Teor. Fiz. 112, 1816–1829 (November 1997)     

Quantum localization in bilayer Heisenberg antiferromagnets with site dilution

The field-induced antiferromagnetic ordering in systems of weakly coupled S = 1/2 dimers at zero temperature can be described as a Bose-Einstein condensation of triplet quasiparticles (singlet quasiholes) in the ground state. For the case of a Heisenberg bilayer, it is here shown how the above picture is altered in the presence of site dilution of the magnetic lattice. Geometric randomness leads to quantum localization of the quasiparticles or quasiholes and to an extended Bose-glass phase in a realistic disordered model. This localization phenomenon drives the system towards a quantum-disordered phase well before the classical geometric percolation threshold is reached.