In the quasi-one-dimensional antiferromagnets CsMnBr${}_{3}$ and RbMnBr${}_{3}$ the magnetization produced by an external magnetic field displays a much stronger dependence upon the direction of the field than expected from calculations done for a system of classical spins at zero temperature. By performing these calculations for a system at the temperature at which experiments were made it has been shown that thermal fluctuations may account for the observed anisotropy of the magnetization. We analyze here the role of quantum fluctuations. We find that the spin-wave approximation does not give meaningful results when applied to these systems and explain why this is so. We perform then density-matrix renormalization-group calculations, which show that the anisotropy is enhanced over its classical value by quantum fluctuations already at $T=0$.
In the quasi-one-dimensional antiferromagnets CsMnBr3 and RbMnBr3 the magnetization produced by an external magnetic field displays a much stronger dependence upon the direction of the field than expected from calculations done for a system of classical spins at zero temperature. By performing these calculations for a system at the temperature at which experiments were made it has been shown that thermal fluctuations may account for the observed anisotropy of the magnetization. We analyze here the role of quantum fluctuations. We find that the spin-wave approximation does not give meaningful results when applied to these systems and explain why this is so. We perform then density-matrix renormalization-group calculations, which show that the anisotropy is enhanced over its classical value by quantum fluctuations already at T=0.
We investigate one-dimensional S=1/2 and S=1 antiferromagnetic quantum-spin chains with easy-axis anisotropies in a transverse field. We calculate both the uniform magnetization and the staggered magnetization, using a variant of the density-matrix renormalization-group method. We find that the staggered magnetizations exhibit reentrant behavior as functions of the transverse field, where the competition between the classical N\'eel order and the quantum fluctuations plays an important role. We also discuss the critical behavior associated with the staggered magnetizations.
We study quantum ferrimagnets in one, two, and three dimensions by using a variety of methods and approximations. These include: (i) a treatment based on the spin coherent state path-integral formulation of quantum ferrimagnets by taking into account the leading order quantum and thermal fluctuations (ii) a field-theoretical (non-linear σ-model type) formulation of the special case of one-dimensional quantum ferrimagnets at zero temperature (iii) an effective description in terms of dimers and quantum rotors, and (iv) a quantum renormalization group study of ferrimagnetic Heisenberg chains. Some of the formalism discussed here can be used for a unified treatment of both ferromagnets and antiferromagnets in the semiclassical limit. We show that the low (high) energy effective Hamiltonian of a (S_1, S_2) Heisenberg ferrimagnet is a ferromagnetic (antiferromagnetic) Heisenberg model. We also study the phase diagram of quantum ferrimagnets in the presence of an external magnetic field h (hc1<h<hc2) and show that the low- and the high-field phases correspond respectively to the classical Néel and the fully polarized ferromagnetic states. We also calculate the transition temperature for the Berezinskii-Kosterlitz-Thouless phase transition in the special case of two-dimensional quantum ferrimagnets.
The T=0 dynamical properties of the one-dimensional (1D) s=21 Heisenberg antiferromagnet in a uniform magnetic field are studied via the Bethe ansatz for cyclic chains of N sites. The ground state at magnetization 0<Mz<N/2, which can be interpreted as a state with 2Mz spinons or as a state of $N/2\ensuremath{-}{M}_{z}$ magnons, is reconfigured here as the vacuum for a different species of quasiparticles, the psinons and antipsinons. We investigate three kinds of quantum fluctuations, namely the spin fluctuations parallel and perpendicular to the direction of the applied magnetic field and the dimer fluctuations. The dynamically dominant excitation spectra are found to be sets of collective excitations composed of two quasiparticles excited from the psinon vacuum in different configurations. The Bethe ansatz provides a framework for (i) the characterization of the new quasiparticles in relation to the more familiar spinons and magnons, (ii) the calculation of spectral boundaries and densities of states for each continuum, (iii) the calculation of transition rates between the ground state and the dynamically dominant collective excitations, (iv) the prediction of line shapes for dynamic structure factors relevant for experiments performed on a variety of quasi-1D antiferromagnetic compounds, including KCuF3,Cu(C4H4N2)(NO3)2, and CuGeO3.
We study classical and quantum Heisenberg antiferromagnets with exchange anisotropy of XXZ-type and crystal field single-ion terms of quadratic and quartic form in a field.The magnets display a variety of phases, including the spin-flop (or, in the quantum case, spin-liquid) and biconical (corresponding, in the quantum lattice gas description, to supersolid) phases.Applying ground-state considerations, Monte Carlo and density matrix renormalization group methods, the impact of quantum effects and lattice dimension is analysed.Interesting critical and multicritical behaviour may occur at quantum and thermal phase transitions.
We study the role of long-range dipolar interactions on antiferromagnetic spin chains, from the classical $S\ensuremath{\rightarrow}\ensuremath{\infty}$ limit to the deep quantum case S=1/2, including a transverse magnetic field. To this end, we combine different techniques such as classical energy minima, classical Monte Carlo, linear spin waves, bosonization, and density matrix renormalization group (DMRG). We find a phase transition from the already reported dipolar ferromagnetic region to an antiferromagnetic region for high enough antiferromagnetic exchange. Thermal and quantum fluctuations destabilize the classical order before reaching magnetic saturation in both phases, and also close to zero field in the antiferromagnetic phase. In the extreme quantum limit S=1/2, extensive DMRG computations show that the main phases remain present with transition lines to saturation significatively shifted to lower fields, in agreement with the bosonization analysis. The overall picture maintains a close analogy with the phase diagram of the anisotropic XXZ spin chain in a transverse field.
In this thesis we study spin systems in low dimension at zero temperature, analyzing their quantum phase transitions. In particular, we used a variational method and a linear spin wave theory for obtaining the approximate ground state. Firstly, we studied the order-disorder transitions of the quasi-one-dimensional isotropic antiferromagneticHeisenberg model of spin-1=2, dened on a square lattice with exchange interactions between nearest neighbors, J and J0. The latter interaction is responsible for onedimensional or two-dimensional behavior of the model namely, when it is zero and when it has a nonzero value, respectively. We obtained the staggered magnetizations of the antiferromagnetic and collinear antiferromagnetic phases. In the absence of exchange interactions between second neighbors, the collinear antiferromagnetic phase is obtained for J0 < 0. This model in the one-dimensional limit has a critical value for the ratio J0=J, where we have a phase transition of the order-disorder type. We founda critical value J0=J = 0, which corresponds to the value physically expected, and compare our results with the linear spin wave theory, that predicts a nonzero critical value. The variational method is also used in the study of the Heisenberg anisotropic model with frustration induced by the inclusion of exchange interactions between second neighbors J2. We renamed the exchange interactions of the rst neighbors J1 e J0 1 , so this model is known as J1 J0 1 J2. Furthermore, we include in this modelthe exchange anisotropy which follows the x and y components of the spin operators. Thus, the more general Hamiltonian presents the isotropic Heisenberg and Ising model limits for certain values of the anisotropy. With the goal to analyze the real role played by this anisotropy, we distinguish between rst and seconds neighbors by the labels 1and 2, respectively. We analyzed the staggered magnetization and the energies for the antiferromagnetic, collinear antiferromagnetic and quantum paramagnetic phase. From these analyzes, we observed quantum phase transitions for certain values of the exchange anisotropy and frustration parameter, the latter one given by the ratio J2=J1. The global phase diagram was also obtained for the cases where the rst and second neighbor exchange anisotropies are equal and where they dier from each other. In the rst case, we can observe the ordered phases, Néel and collinear antiferromagnetic, and between them a magnetically disordered phase. We checked the existence of a critical endpoint separating the three phases. In the second case, we note that the exchange anisotropy inuences the region of the disordered phase, aecting even the existence of the critical endpoint. Besides presenting, at certain intervals of the anisotropy, a behavior that was not expected a priori. We also analyze the quasi-one-dimensional behavior J01 ! 0, where the shape of the phase diagram is unchanged. We explore the degree of dimer formation via the dimerization parameter for some values of exchange anisotropy and obtain a higher degree of dimerization for the disordered phase in comparison with the ordered phases, as expected. We end this work with a generalization of the rst study without frustration in function only of the exchange anisotropy. As a challenge to the variational method, we study the more general J1 J0 1 J2 modelfor integer spin-1 without the exchange anisotropy and avoiding the unidimensional case. Dierent from what happens in the semi-integer spins case, we did not nd the disordered phase for integer spin S= 1. We note only a rst-order phase transition between the ordered phases. Finally, we return to the frustrated model with exchange anisotropies 1 and 2 to study the model from a perspective of linear spin wavetheory, in order to compare the results with those obtained via the variational method. A detailed analysis was performed based on the comparison between the two methods, which agreed qualitatively in all explored boundaries and even those behaviors that were not expected from the variational method were conrmed by the spin wave theory.This consistency of the results allowed us to get a dierent view of the role played by the exchange anisotropy when dierentiated for rst and second neighbors. If the anisotropies are considered equal they work only as a parameter that carries the model from the isotopic Heisenberg limit to the Ising model. However, when dierent, they promote disorder in the system.