Exact ground states with deconfined gapless excitations for the three-leg spin-1/2 tube

We consider a spin-1/2 tube (a three-leg ladder with periodic boundary conditions) with a Hamiltonian given by two projection operators-one on the triangles and the other on the square plaquettes on the side of the tube-that can be written in terms of Heisenberg and four-spin ring exchange interactions. We identify 3 phases: (i)?for strongly antiferromagnetic exchange on the triangles, an exact ground state with a gapped spectrum can be given as an alternation of spin and chirality singlet bonds between nearest triangles; (ii)?for ferromagnetic exchange on the triangles, we recover the phase of the spin-3/2 Heisenberg chain; (iii)?between these two phases, a gapless incommensurate phase exists. We construct an exact ground state with two deconfined domain walls and a gapless excitation spectrum at the quantum phase transition point between the incommensurate and dimerized phases.     

Exact ground state of a spin ladder with a quantum phase transition

We introduce a spin ladder with Ising interactions along the legs and intrinsically frustrated Heisenberg-like ferromagnetic interactions on the rungs. The model is solved exactly in the subspaces relevant for the ground state by mapping to the quantum Ising model, and we show that a first order quantum phase transition separates the classical from quantum regime, with the spin correlations on the rungs being either ferromagnetic or antiferromagnetic, and different spin excitations in both regimes. The present case resembles the quantum phase transition found in the compass model in one and two dimensions.     

Resistivity peak values at the transition between fractional quantum hall states

Experimental data available in the literature for peak values of the diagonal resistivity in the transitions between the fractional quantum Hall states (ρ _xx ^max ) are compared with the theoretical predictions. It is found that the majority of the peak values are close to the theoretical values for two-dimensional systems with moderate mobilities. The text was submitted by the author in English.     

Non-equilibrium charge transport at a first-order phase transition

We have studied penetration of a charge density disturbance cause by a moving bubble wall in relativistic plasma, using the self-consistent field approximation. We have shown that the charge density as a function of distance from the wall has a power-law tail 1/z². We find that penetration of charge in plasma is most effective when the wall velocity is close to unity. However, for wall velocities u0.7, the effective, in the integral sense, penetration length is found to be essentially equal to the static Debye radius.     

Evolution of order and chaos across a first-order quantum phase transition

We study the evolution of the dynamics across a generic first-order quantum phase transition in an interacting boson model of nuclei. The dynamics inside the phase coexistence region exhibits a very simple pattern. A classical analysis reveals a robustly regular dynamics confined to the deformed region and well separated from a chaotic dynamics ascribed to the spherical region. A quantum analysis discloses regular bands of states in the deformed region, which persist to energies well above the phase-separating barrier, in the face of a complicated environment. The impact of kinetic collective rotational terms on this intricate interplay of order and chaos is investigated.     

Interfacial adsorption phenomena at a weakly first-order phase transition

We study the interfacial adsorption phenomena of the ferromagnetic five-state Potts model on the square lattice, whose transition is of weakly first-order, by using Monte Carlo simulations and finite-size scaling theory. It is shown that the net-adsorption has a finite-size effect according to the first-order phase transition even for systems much smaller than the bulk correlation length.     

Exact ground state of a frustrated integer-spin modified Shastry-Sutherland model

We propose a method to measure real-valued time series irreversibility which combines two different tools: the horizontal visibility algorithm and the Kullback-Leibler divergence. This method maps a time series to a directed network according to a geometric criterion. The degree of irreversibility of the series is then estimated by the Kullback-Leibler divergence (i.e. the distinguishability) between the inand outdegree distributions of the associated graph. The method is computationally efficient and does not require any ad hoc symbolization process. We find that the method correctly distinguishes between reversible and irreversible stationary time series, including analytical and numerical studies of its performance for: (i) reversible stochastic processes (uncorrelated and Gaussian linearly correlated), (ii) irreversible stochastic processes (a discrete flashing ratchet in an asymmetric potential), (iii) reversible (conservative) and irreversible (dissipative) chaotic maps, and (iv) dissipative chaotic maps in the presence of noise. Two alternative graph functionals, the degree and the degree-degree distributions, can be used as the Kullback-Leibler divergence argument. The former is simpler and more intuitive and can be used as a benchmark, but in the case of an irreversible process with null net current, the degree-degree distribution has to be considered to identify the irreversible nature of the series.     

Magnetic-field-induced phase transition in a two-dimensional quantum magnet with plaquette distortion

Magnetic field effect on the structure of the ground state of a two-dimensional quantum Heisenberg magnet is analyzed. A plaquette representation is used to solve the self-consistent problem and calculate the collective excitation spectrum in a magnetic field. Conditions are found for quantum transition between non-magnetic and oblique antiferromagnetic phases. The change in the ground state of the system is associated with disappearance of the gap in the spin excitation spectrum. Effects of frustration and magnetic field on the spectrum are analyzed. A phase diagram of stable singlet and magnetically ordered phases is presented.     

Unconventional state with two coexisting long-range orders for frustrated Heisenberg model at quantum phase transition

For the frustrated two-dimensional S=1/2 antiferromagnetic Heisenberg model close to quantum phase transition we consider the singlet ground states retaining both translational and SU(2) symmetry. Besides usually discussed checkerboard, spin-liquid and stripe states an unconventional state with two coexisting long-range orders appears to be possible at sufficiently large damping of spin excitations. The problem is treated in the frames of self-consistent spherically symmetric approach.     

Influence of strong single-ion anisotropy on phase states of 3D and 2D frustrated magnets

We investigated the influence of strong single-ion anisotropy, exceeding exchange interaction, and frustrated exchange interaction on spin-wave excitation spectra and phase states using the Hubbard operators’ technique, allowing the exact account of single-ion anisotropy. The results show that both the homogeneous phases (ferromagnetic and quadrupolar) and the spatially inhomogeneous phase (spiral structure) are possible in the 3D magnetic crystal. The region of existence of the spiral structure is considerably smaller than that in the analogues system, but with weak single-ion anisotropy. The situation is more complex in the 2D system; another spatially inhomogeneous state (the domain structure) can be realized in addition to the spiral magnetic structure. The phase diagrams for both the 3D and 2D systems were plotted.     

Simple empirical order parameter for a first-order quantum phase transition in atomic nuclei

A simple, empirical, easy-to-measure effective order parameter of a first-order phase transition in atomic nuclei is presented, namely, the ratio of the energies of the first excited 6+ and 0+ states, distinguishing between first- and second-order transitions, and taking on a special value in the critical region, as data in Nd-Dy show. In the large NB limit of the interacting boson approximation model, a repeating degeneracy between alternate yrast and successive 0+ states is found in the critical region around the line of a first-order phase transition, pointing to a possible underlying symmetry.     

Magnetic fluctuations at a field-induced quantum phase transition

We report an inelastic neutron-scattering study at the field-induced magnetic quantum phase transition of CeCu5.8Au0.2. The data can be described better by the spin-density-wave scenario than by a local quantum critical point, while the latter scenario was shown to be applicable to the zero-field concentration-tuned quantum phase transition in CeCu6-xAux for x=0.1. This constitutes direct microscopic evidence for a difference in the quantum fluctuation spectra at a magnetic quantum critical point driven by different tuning parameters.     

Valence bond ground states in a frustrated two-dimensional spin-1/2 Heisenberg antiferromagnet

We study a class of two-dimensional spin-1/2 Heisenberg antiferromagnets, introduced by Klein [1], in which the nearest-neighbor term is supplemented by next-nearest-neighbor pair and four-body interactions, producing additional frustration. For certain lattices, including e.g. the hexagonal lattice, we prove that any finite subset which admits a dimer covering has a ground state space spanned by valence bond states, each of which consists only of nearest-neighbor (dimer) singlet pairs. We also establish linear independence of these valence bond states. The possible relevance to resonating-valence-bond theories of high-temperature superconductors is briefly discussed. In particular, our results apply both to regular subsets of the lattice and to subsets with static holes.Work supported in part by N.S.F. Postdoctoral Research FellowshipsWork supported by N.S.F. Grant No. DMR-83-18051     

Possible phase transition of anisotropic frustrated Heisenberg model at finite temperature

The frustrated spin-1/2 J_1a–J_1b–J₂ antiferromagnet with anisotropy on the two-dimensional square lattice was investigated, where the parameters J_1aand J_1b represent the nearest neighbor exchanges and along the x and y directions, respectively. J₂ represents the next-nearest neighbor exchange. The anisotropy includes the spatial and exchange anisotropies. Using the double-time Green’s function method, the effects of the interplay of exchanges and anisotropy on the possible phase transition of the Néel state and stripe state were discussed. Our results indicated that, in the case of anisotropic parameter 0≤η<1, the Néel and stripe states can exist and have the same critical temperature as long as J₂ = J_1b/2. Under such parameters, a first-order phase transformation between the Néel and stripe states can occur below the critical point. For J₂ ≠J_1b/2, our results indicate that the Néel and stripe states can also exist, while their critical temperatures differ. When J₂>J_1b/2, a first-order phase transformation between the two states may also occur. However, for J₂<J_1b/2, the Néel state is always more stable than the stripe state.     

Growth of clusters in a first-order phase transition

The results of computer simulations of phase separation kinetics in a binary alloy quenched from a high temperature are analyzed in detail, using the ideas of Lifshitz and Slyozov. The alloy was modeled by a three-dimensional Ising model with Kawasaki dynamics. The temperature after quenching was 0.59T _c, whereT _c is the critical temperature, and the concentration of minority atoms was=0.075, which is about five times their largest possible single-phase equilibrium concentration at that temperature. The time interval covered by our analysis goes from about 1000 to 6000 attempted interchanges per site. The size distribution of small clusters of minority atoms is fitted approximately byc ₁(1-)³ w(t),c ₁ (1–)⁴ Q _l w(t)^l(2l10); wherec _l is the concentration of clusters of sizel;Q ₂,...,Q ₁₀ are known constants, the cluster partition functions;t is the time; andw(t)=0.015(1+7.17t ^–1/3). The distribution of large clusters (l20) is fitted approximately by the type of distribution proposed by Lifshitz and Slyozov,c _l ,(t)=–(d/dl) [lnt+p (l/t)], where is a function given by those authors and is defined by(x)=C _o e–x-C ₁ e ^–4x/3-C ₂ e ^–5x/3;C ₀,C ₁,C ₂ are constants determined by considering how the total number of particles in large clusters changes with time.Supported by the U.S. Air Force Office of Scientific Research under Grant No. 78-3522 and by the U.S. Department of Energy under Contract No. EY-76-C-02-3077*000.