Quantum phase transitions in the transverse 1-D Ising model with four-spin interactions (original) (raw)
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Quantum phase transitions in the transverse one-dimensional Ising model with four-spin interactions
Physical Review B, 2006
In this work we investigate the quantum phase transitions at zero temperature of the one-dimensional transverse Ising model with an extra term containing four-spin interactions. The competition between the energy couplings of the model leads to an interesting zero-temperature phase diagram. We use a modified Lanczos method to determine the ground state and the first excited state energies of the system, with sizes of up to 20 spins. We apply finite size scaling to the energy gap to obtain the boundary region where ferromagnetic to paramagnetic transition takes place. We also find the critical exponent associated with the correlation length. We find a degenerate ͗3,1͘ phase region. The first-order transition boundary between this phase and the paramagnetic phase is determined by analyzing the behavior of the transverse spin susceptibility as the system moves from one region to the other.
Temperature effects on the dynamics of the 1-D transverse Ising model with four-spin interactions
Physica A-statistical Mechanics and Its Applications - PHYSICA A, 2004
The dynamics of one-dimensional quantum spin systems has been a long standing theoretical and experimental problem. Among them, the transverse Ising model with multi-spin interactions, regarded as one of the simplest with non-trivial dynamics, has attracted considerable interest in recent years. We investigate the temperature effects on the dynamics of the transverse Ising model with four-spin interactions. The model is relevant to the physics of poly(vinylidene fluoride-trifluoroethylene)[P(VDF-TrFE)] copolymers. We determine the time-dependent correlation function and spectral density for all temperatures for cases where the transverse field B is less, equal or greater than the four-spin coupling J. Our calculations were done with rings of up to 11 spins. However the results presented are also valid in the thermodynamic limit. We find that the time-dependent correlation function in general has oscillatory behavior when the transverse field is stronger than the coupling energy. On ...
Quantum phase transitions in a chain with two- and four-spin interactions in a transverse field
Physical review. E, Statistical, nonlinear, and soft matter physics, 2014
We use entanglement entropy and finite-size scaling methods to investigate the ground-state properties of a spin-1/2 Ising chain with two-spin (J(2)) and four-spin (J(4)) interactions in a transverse magnetic field (B). We concentrate our study on the unexplored critical region B=1 and obtain the phase diagram of the model in the (J(4)-J(2)) plane. The phases found include ferromagnetic (F), antiferromagnetic (AF), as well as more complex phases involving spin configurations with multiple periodicity. The system presents both first- and second-order transitions separated by tricritical points. We find an unusual phase boundary on the semi-infinite segment (J(4)<-1,J(2)=0) separating the F and AF phases.
Physical Review B, 2002
We apply a finite-size scaling approach to the one-dimensional spin-1/2 Ising model with nearest-and next-nearest-neighbor interactions in the presence of a transverse magnetic field. By using the scaling behavior of the energy gap we are able not only to determine the ferromagnetic-paramagnetic transition line at zero absolute temperature but also to compute the corresponding critical exponent. A comparison with other approaches is made, and aside for small discrepancies likely to occur at the thermodynamic limit, we believe that the present results are quite close to the unknown exact ones.
Quantum phase transitions in alternating transverse Ising chains: Analytical and numerical results
Physical Review B, 2002
This chapter is devoted to a discussion of quantum phase transitions in regularly alternating spin-1 2 Ising chain in a transverse field. After recalling some generally-known topics of the classical (temperature-driven) phase transition theory and some basic concepts of the quantum phase transition theory I pass to the statistical mechanics calculations for a one-dimensional spin-1 2 Ising model in a transverse field, which is the simplest possible system exhibiting the continuous quantum phase transition. The essential tool for these calculations is the Jordan-Wigner fermionization. The latter technique being completed by the continued fraction approach permits to obtain analytically the thermodynamic quantities for a "slightly complicated" model in which the intersite exchange interactions and on-site fields vary regularly along a chain. Rigorous analytical results for the ground-state and thermodynamic quantities, as well as exact numerical data for the spin correlations computed for long chains (up to a few thousand sites) demonstrate how the regularly alternating bonds/fields effect the quantum phase transition. I discuss in detail the case of period 2, swiftly sketch the case of period 3 and finally summarize emphasizing the effects of periodically modulated Hamiltonian parameters on quantum phase transitions in the transverse Ising chain and in some related models.
Quantum simulation and phase diagram of the transverse-field Ising model with three atomic spins
2010
We perform a quantum simulation of the Ising model with a transverse field using a collection of three trapped atomic ion spins. By adiabatically manipulating the Hamiltonian, we directly probe the ground state for a wide range of fields and form of the Ising couplings, leading to a phase diagram of magnetic order in this microscopic system. The technique is scalable to much larger numbers of trapped ion spins, where phase transitions approaching the thermodynamic limit can be studied in cases where theory becomes intractable.
Phase diagrams of a spin-1 Ising system with competing short- and long-range interactions
Physical review. E, Statistical, nonlinear, and soft matter physics, 2015
We have studied the phase diagrams of the one-dimensional spin-1 Blume-Capel model with anisotropy constant D, in which equivalent-neighbor ferromagnetic interactions of strength -J are superimposed on nearest-neighbor antiferromagnetic interactions of strength K. A rich critical behavior is found due to the competing interactions. At zero temperature two ordered phases exist in the D/J-K/J plane, namely the ferromagnetic (F) and the antiferromagnetic one (AF). For lower values of D/J(D/J<0.25) these two ordered phases are separated by the point K_{c}=0.25J. For 0.25<D/J≤0.50, the paramagnetic phase P emerges in a region separated between the lines determined by D/J=0.5-K/J and D/J=K/J. For D/J>0.5, only phases AF and F exist and are separated by a line given by D/J=K/J. At finite temperatures, we found that the ferromagnetic region of the phase diagram in the k_{B}T/J-D/J plane is enriched by another ferromagnetic phase F^{^{'}} above a first-order line for 0.195<K/...
Kinetic phase transition in the mixed-spin Ising model
Brazilian Journal of Physics, 2004
In this work we studied a ferromagnetic mixed-spin Ising model including a single ion crystal-field term. The model system consists of two interpenetrating sublattices with spins σ = 1/2 and S = 1. The spins σ = 1/2 occupy the sites of one sublattice, their nearest-neighbours are spins S on the other sublattice, and vice versa. The system is in contact with a heat bath, the spins flipping according to the Metropolis transition rate and, at the same time, subject to an external flow of energy, which is simulated by a two-spin flip process. The model is studied via the dynamical pair approximation and through Monte Carlo simulations. We have determined the phase diagram of the model in the plane crystal-field D versus competition parameter p. The parameter p accounts for the competition between the one-and two-spin flip processes. In the pair approximation, the phase diagram, at high temperatures, present three phases separated by two transition lines: a continuous transition line between the ferromagnetic and paramagnetic phases, and a first-order transition line between the paramagnetic and antiferromagnetic phases. However, Monte Carlo simulations predict the same topology for the phase diagram as the pair approximation, but all the transition lines are continuous for any value of the temperature.
Physical Review Letters, 2009
The physics of the spin glass (SG) state, with magnetic moments (spins) frozen in random orientations, is one of the most intriguing problems in condensed matter physics. While most theoretical studies have focused on the Edwards-Anderson model of Ising spins with only discrete 'up/down' directions, such Ising systems are experimentally rare. LiHoxY1−xF4, where the Ho 3+ moments are well described by Ising spins, is an almost ideal Ising SG material. In LiHoxY1−xF4, the Ho 3+ moments interact predominantly via the inherently frustrated magnetostatic dipole-dipole interactions. The random frustration causing the SG behavior originates from the random substitution of dipolecoupled Ho 3+ by non-magnetic Y 3+. In this paper, we provide compelling evidence from extensive computer simulations that a SG transition at nonzero temperature occurs in a realistic microscopic model of LiHoxY1−xF4, hence resolving the long-standing, and still ongoing, controversy about the existence of a SG transition in disordered dipolar Ising systems.