The quantum phase transition induced by an external magnetic field in a dimerized spin crystal from its singlet ground state to an antiferromagnetic ordered state is examined under the assumption that the exchange interaction is antiferromagnetic, both within dimers and between them. It is shown that during this transition the magnetic polarization of the ions within a dimer and, therefore, of the dimers as a whole, is critical. The orientations and projections of the spin vectors in the magnetically ordered phase depend on the applied magnetic field, while the magnetic susceptibility of this essentially quantum phase remains (similarly to the case of a classical Neel antiferromagnet) constant as the spins of the magnetic sublattices undergo reorientation.
We study the
S=1/2 Heisenberg antiferromagnet on a square lattice with nearest-neighbor and plaquette four-spin exchanges [introduced by A. W. Sandvik, Phys. Rev. Lett. 98, 227202 (2007).] This model undergoes a quantum phase transition from a spontaneously dimerized phase to N\'eel order at a critical coupling. We show that as the critical point is approached from the dimerized side, the system exhibits strong fluctuations in the dimer background, reflected in the presence of a low-energy singlet mode, with a simultaneous rise in the triplet quasiparticle density. We find that both singlet and triplet modes of high density condense at the transition, signaling restoration of lattice symmetry. In our approach, which goes beyond mean-field theory in terms of the triplet excitations, the transition appears sharp; however since our method breaks down near the critical point, we argue that we cannot make a definite conclusion regarding the order of the transition.
We investigate a simple model antiferromagnet which shows a Quantum Phase Transition between a conventional Neel antiferromagnetic phase and a dimerized ‘Valence Bond Solid’ phase. Both the critical temperature and the ground state magnetization in the Neel phase approach zero at the critical point, and are found to scale according to power laws, with exponents 0.5, as expected from general considerations. 1. Introduction The subject of Quantum Phase Transitions (QPT’s) in condensed matter systems remains a frontier area of research [1]. These are transitions, at temperature T = 0, in the nature of the ground state of a strongly correlated quantum system. At QPT’s large quantum fluctuations play the same role as do large thermal fluctuations at normal phase transitions, and analogous universal scaling laws are to be expected. In real materials QPT’s can be induced by pressure, by applied magnetic fields, or by disorder. Theoretical studies of QPT’s are largely based on various simplified models, particularly low dimensional antiferromagnets, where the system can be tuned through a QPT by varying a particular parameter g in the Hamiltonian. Most of the models hereto studied have been two-dimensional. Examples include antiferromagnets with strong and weak bonds, with or without frustration, and bilayer systems, where the QPT separates a conventional Neel antiferromagnetic phase from a dimerized phase with only short-range correlations and no magnetic order. In such systems the magnetic order present in the ground state does not extend to finite temperatures. In the present work we study a three-dimensional model where magnetic order persists to some critical temperature Tc(g). We expect Tc(g) to vanish as g → gc, and we are interested in comparing the vanishing of Tc with the vanishing of the ground state magnetization M0. The magnetization is expected to vanish as (gc – g) β , where the critical exponent β is expected to have the value 0.5, corresponding to a classical thermally driven transition in four spatial dimensions, which is mean-field like (with possible logarithmic corrections). Does Tc(g) scale with (gc – g) in the same way? 2. The model and results
Quantum phase transition from the N\'eel to the dimer states in an antiferromagnetic (AF) Heisenberg model on square lattice is studied. We introduce a control parameter $\ensuremath{\alpha}$ for the exchange coupling that connects the N\'eel $(\ensuremath{\alpha}=0)$ and the dimer $(\ensuremath{\alpha}=1)$ states. We employ the
CP1 representation of the
s=21 spin operator and integrate out the half of the
CP1 variables at odd sites to obtain a
CP1 nonlinear $\ensuremath{\sigma}$ model. The effective coupling constant is a function of $\ensuremath{\alpha}$, and at $\ensuremath{\alpha}=0$, the
CP1 model is in the ordered phase that corresponds to the N\'eel state of the AF Heisenberg model. A phase transition to the dimer state occurs at a certain critical value of ${\ensuremath{\alpha}}_{C}$ as $\ensuremath{\alpha}$ increases. In the N\'eel state, the dynamical composite U(1) gauge field in the
CP1 model is in a Higgs phase, and low-energy excitations are gapless spin waves. In the dimer phase, a confinement phase of the gauge theory with
s=1 excitations is realized. For the critical point, we argue that a deconfinement phase, which is similar to the Coulomb phase in three spatial dimensions, is realized and
s=21 spinons appear as low-energy excitations.
Using a combination of unbiased quantum Monte Carlo simulations and a decoupled dimer mean-field theory, we investigate the thermal and quantum phase transitions of the spin-1/2 Heisenberg model on the dimerized diamond lattice. We find that at sufficiently strong dimerization the system exhibits a quantum disordered ground state, in contrast to the antiferromagnetic phase stabilized at weak dimerization. We determine the quantum critical point and examine the thermodynamic responses in both regimes. The ratio for the critical interdimer (
Jc) to intradimer (
JD) coupling is obtained as
Jc/JD=0.3615(5). Our results show that the decoupled dimer mean-field theory well captures the competition between the local singlet formation and the antiferromagnetic ordering tendency, and thus provides an appropriate qualitative description of this three-dimensional quantum magnet, in contrast to the conventional mean-field decoupling. We also examine the differences in the ordering temperatures between the antiferromagnetic and the ferromagnetic spin-1/2 Heisenberg model on the diamond lattice based on quantum Monte Carlo simulations.
Using a combination of unbiased quantum Monte Carlo simulations and a decoupled dimer mean-field theory, we investigate the thermal and quantum phase transitions of the spin- 1 2 Heisenberg model on the dimerized diamond lattice. We find that at sufficiently strong dimerization the system exhibits a quantum disordered ground state, in contrast to the antiferromagnetic phase stabilized at weak dimerization. We determine the quantum critical point and examine the thermodynamic responses in both regimes. The ratio for the critical interdimer ( J c ) to intradimer ( J D ) coupling is obtained as J c / J D = 0.3615 ( 5 ) . Our results show that the decoupled dimer mean-field theory well captures the competition between the local singlet formation and the antiferromagnetic ordering tendency, and thus provides an appropriate qualitative description of this three-dimensional quantum magnet, in contrast to the conventional mean-field decoupling. We also examine the differences in the ordering temperatures between the antiferromagnetic and the ferromagnetic spin- 1 2 Heisenberg model on the diamond lattice based on quantum Monte Carlo simulations.
The orientation of the order parameter of quantum magnets can be used to store information in a dense and efficient way.Switching this order parameter corresponds to writing data.To understand how this can be done, we study a precessional reorientation of the sublattice magnetization in an (an)isotropic quantum antiferromagnet induced by an applied magnetic field.For this intriguing nonequilibrium issue, we introduce a description including the leading quantum and thermal fluctuations, namely time-dependent Schwinger boson mean-field theory, because this theory allows us to describe both ordered phases and the phases in between them, as is crucial for switching.An activation energy has to be overcome, requiring a minimum applied field h t that is given essentially by the spin gap.It can be reduced significantly for temperatures approaching the Néel temperature, facilitating switching.The time required for switching diverges when the field approaches h t , which is the signature of an inertia in the magnetization dynamics.The temporal evolution of the magnetization and of the energy reveals signs of dephasing.The switched state has lost a part of its coherence because the magnetic modes do not evolve in phase.