Self-consistent Harmonic Approximation Research Articles

The phase diagram and critical properties of the two-dimensional anisotropicXY model

In this paper we present a study of the phase diagram and critical properties of the square-lattice quantumXY model, with a single-ion anisotropy and spinS = 1, as a function of theanisotropy parameter D. For D less thana critical value DC, which is the critical point for a quantum phase transition atT = 0, the model presents a Berezinskii–Kosterlitz–Thouless (BKT) transition. This region isadequately described by the self-consistent harmonic approximation. We show that, if wewant to use a Schwinger boson theory in this region, we should include fluctuationsaround the mean-field approximation (which leads to a gauge field) to describecorrectly the BKT transition. However both methods are inadequate to describe thelarge-D phase, and we show that this phase can be studied using the bond operator formalismwhich gives the correct behaviour for the correlation length as a function of thetemperature in the critical point and above. Our results agree with scaling arguments.

Kosterlitz-Thouless phase transition in microcavity polariton system

The Kosterlitz-Thouless phase transition in a system of exciton-polaritons in a microcavity is studied. The transition temperature to superfluid state was found as a function of exciton-photon detuning. A nonquadratic dispersion law was taken into account in the framework of the self-consistent harmonic approximation (SCHA).

Quantum-phase transition in a XY model

In this paper we study quantum-phase transition in the one-dimensional XY model with an XY easy-plane single ion anisotropy. We use the path-integral formalism, but consider the effect of quantum fluctuations, which renormalize the parameters of the system, using the self-consistent harmonic approximation. We show that the quantum fluctuations increase the effective coupling constant of the model.

Phase diagram of the two-dimensional quantum antiferromagnet in a magnetic field

The two-dimensional Heisenberg antiferromagnet experiences an effective easy-plane anisotropy when a magnetic field is applied, giving rise to Berezinskii-Kosterlitz-Thouless (BKT) critical behavior. Remarkably, the strength of the effective anisotropy, and consequently the critical BKT temperature, can be tuned by varying the field. By means of the pure-quantum self-consistent harmonic approximation, that reduces the quantum model to an effective classical system, the phase diagram is constructed from its known classical counterpart. By classical Monte Carlo simulations of the effective system the thermodynamic quantities can be calculated. Comparison is made with the behavior observed experimentally in the S=5∕2 compound Mn(HCOO)22H2O.

Comparative study between a two-dimensional anisotropic Heisenberg antiferromagnet with easy-axis single-ion anisotropy and one with easy-axis exchange anisotropy

Generally, in literature, easy-axis single ion anisotropy and easy-axis exchange anisotropy was treated in indistinct way. In this work we propose to perform a comparative study of the effects of these two easy-axis anisotropies on the behavior of the magnetization and the critical temperature ( T c ) in the 2D classical Heisenberg antiferromagnetic model. In order to study the low-temperature thermodynamics of this model, we should consider the contribution of anisotropic spin waves, using a self-consistent harmonic approximation (SCHA) theory. We compare the predictions of SCHA with numerical simulations on L × L square lattices using Monte Carlo (MC) simulations, which include effects due to all thermodynamically allowed excitations. Our SCHA results are in good agreement with our MC simulations results and have shown that the strong K limit gives two different Ising-like behavior. In the exchange anisotropic case, the dependence of T c on anisotropic parameter K becomes linear and in the single-ion anisotropic case, T c becomes independent of K . Also, using MC simulations and finite size scaling, we show that the critical exponents in the two anisotropic case are compatible with the 2D Ising values α = 0.125 and γ = 1.75 .

Adiabatic-antiadiabatic crossover in a spin-Peierls chain

We consider an XXZ spin-1/2 chain coupled to optical phonons with non-zero frequency $\omega_0$. In the adiabatic limit (small $\omega_0$), the chain is expected to spontaneously dimerize and open a spin gap, while the phonons become static. In the antiadiabatic limit (large $\omega_0$), phonons are expected to give rise to frustration, so that dimerization and formation of spin-gap are obtained only when the spin-phonon interaction is large enough. We study this crossover using bosonization technique. The effective action is solved both by the Self Consistent Harmonic Approximation (SCHA)and by Renormalization Group (RG) approach starting from a bosonized description. The SCHA allows to analyze the lowfrequency regime and determine the coupling constant associated with the spin-Peierls transition. However, it fails to describe the SU(2) invariant limit. This limit is tackled by the RG. Three regimes are found. For $\omega_0\ll\Delta_s$, where $\Delta_s$ is the gap in the static limit $\omega_0\to 0$, the system is in the adiabatic regime, and the gap remains of order $\Delta_s$. For $\omega_0>\Delta_s$, the system enters the antiadiabatic regime, and the gap decreases rapidly as $\omega_0$ increases. Finally, for $\omega_0>\omega_{BKT}$, where $\omega_{BKT}$ is an increasing function of the spin phonon coupling, the spin gap vanishes via a Berezinskii-Kosterlitz-Thouless transition. Our results are discussed in relation with numerical and experimental studies of spin-Peierls systems.

Quantum fluctuations in low-dimensional easy-plane spin models

A self-consistent harmonic approximation is used to treat the low temperature limit of the one and two dimensional S=1 easy plane magnets. For the one dimensional (1D) model, we calculate the gap caused by the presence of an external magnetic field applied in the easy-plane. The quantum phase transition of the one-dimensional model at T=0 is also studied. For the two-dimensional case, the Kosterlitz-Thouless (KT) transition temperature as a function of a single-ion anisotropy term is calculated. The line ends at a quantum critical point, where the KT temperature goes to zero.

Impurity Pinning of Spin Density Wave

The collective excitations from the spin density wave pinned by some impurities are investigated with the self-consistent harmonic approximation applied for the phase Hamiltonian. It is found that the pinning-depinning transition due to the quantum fluctuation in the ground state cannot occur in two-dimensional nor three-dimensional isotropic system. In contrast, it. has already been revealed that the quantum depinning (melting) can occur in one dimension. It suggests that the critical dimension of the quantum localization-delocalization phase transition is one, within the present approximation. The present result is also available for the charge density wave pinned by some impurities.

Quantum Effect on the Mott Glass State in One-Dimension

We study one-dimensional density wave, which is pinned by impurity potential and commensurate potential at half-filling. The former pinning leads to Anderson glass (AG) state while the latter pinning results in Mott insulator (MI) state. The Mott glass (MG) state, which has been found in the classical case, is located between AG state and MI state, and exhibits a gap for a single particle excitation but no gap for the collective excitation. We examine the effect of quantum fluctuation on such a MG state by calculating a soliton-formation energy and an optical conductivity at low frequencies. The self-consistent harmonic approximation is applied to calculate the spring constant for the potential, which determines the magnitude of pinning frequency. It is found that the MG state still exists for small quantum fluctuation and that further increase of the fluctuation leads to the disappearance of the MG state due to the large reduction of the soliton-formation energy. The results are discussed in terms of the local distribution of pinning frequency.

Finite-size bosonization and self-consistent harmonic approximation

The self-consistent harmonic approximation is extended in order to account for theexistence of Klein factors in bosonized Hamiltonians. This is important for the study offinite systems where Klein factors cannot be ignored a priori. As a test we apply themethod to interacting spinless fermions with modulated hopping. We calculatethe finite-size corrections to the energy gap and the Drude weight and compareour results with the exact solution for special values of the model parameters.

Reconciling field-theoretical and semiclassical approaches to quantum 2D antiferromagnets

We show that, starting from the field-theoretical expression for the correlation length ξ of the 2D quantum Heisenberg antiferromagnet corrected for cut-off effects and our knowledge of the classical thermodynamics of the model, the observed temperature dependence of ξ can be reproduced. We find also that the cut-off effects contains the same pure-quantum renormalizations of the pure-quantum self-consistent harmonic approximation semiclassical framework: the gap between quantum field theoretical and semiclassical results is thus bridged.

Ising transition in the two-dimensional quantum J1-J2 Heisenberg model.

We study the thermodynamics of the spin-S two-dimensional quantum Heisenberg antiferromagnet on the square lattice with nearest (J1) and next-nearest (J2) neighbor couplings in its collinear phase (J(2)/J(1)>0.5), using the pure-quantum self-consistent harmonic approximation. Our results show the persistence of a finite-temperature Ising phase transition for every value of the spin, provided that the ratio J(2)/J(1) is greater than a critical value corresponding to the onset of collinear long-range order at zero temperature. We also calculate the spin and temperature dependence of the collinear susceptibility and correlation length, and we discuss our results in light of the experiments on Li2VOSiO4 and related compounds.

Reconciling field-theoretical and semiclassical approaches to quantum 2D antiferromagnets

We show that, starting from the field-theoretical expression for the correlation length ξ of the 2D quantum Heisenberg antiferromagnet corrected for cut-off effects and our knowledge of the classical thermodynamics of the model, the observed temperature dependence of ξ can be reproduced. We find also that the cut-off effects contains the same pure-quantum renormalizations of the pure-quantum self-consistent harmonic approximation semiclassical framework: the gap between quantum field theoretical and semiclassical results is thus bridged.

Quantum phase transitions in dissipative tunnel junctions

The Ueda-Guinea model of a dissipative tunnel junction is investigated. This model accounts for final-state effects associated with single-electron tunneling. A quantum phase transition emerges, marking a boundary between insulating (Coulomb blockade) and conducting phases. The system is analyzed by large-$N$ techniques, self-consistent harmonic approximation, and Monte Carlo methods.

Quantum two-dimensional Heisenberg antiferromagnet: Bridging the gap between field-theoretical and semiclassical approaches

The field-theoretical result for the low-$T$ behavior of the correlation length of the quantum Heisenberg antiferromagnet on the square lattice was recently improved by Hasenfratz [Eur. Phys. J. B 13, 11 (2000)], who corrected for cutoff effects. We show that starting from his expression, and exploiting our knowledge of the classical thermodynamics of the model, it is possible to take into account non-linear effects which are responsible for the main features of the correlation length at intermediate temperature. Moreover, we find that cutoff effects lead to the appearance of an effective exchange integral depending on the very same renormalization coefficients derived in the framework of the semiclassical pure-quantum self-consistent harmonic approximation: The gap between quantum field-theoretical and semiclassical results here is eventually bridged.

Anisotropy and Ising-type transition of the S=5/2 two-dimensional Heisenberg antiferromagnet Mn-formate di-Urea

Recently reported measurements of specific heat on the compound Mn-formate di-Urea by Takeda et al. [Phys. Rev. B 63, 024425 (2001)] are considered. As a model to describe the overall thermodynamic behavior of such a compound, the easy-axis two-dimensional Heisenberg antiferromagnet is proposed and studied by means of the pure quantum self-consistent harmonic approximation. In particular, it is shown that when the temperature decreases, the compound exhibits a crossover from two-dimensional (2D) Heisenberg to 2D-Ising behavior, followed by a 2D-Ising-type phase transition, whose location allows one to get a reliable estimate of the easy-axis anisotropy driving the transition itself. Below the critical temperature TN=3.77 K, the specific heat is well described by the two-dimensional easy-axis model down to a temperature T*=1.57 K, where a T3 law sets in, possibly marking a low-temperature crossover of magnetic fluctuations from two to three dimensions.

Solitons in the spin-Peierls compound CuGeO 3

We calculate the excitation gap, the soliton energy, and the soliton density at finite temperature, of the spin-1/2 one dimensional antiferromagnet coupled to phonons, using a self-consistent harmonic approximation, and the thermal-Green function technique. The spin degrees of freedom are represented by the phase Hamiltonian with the help of the boson representation of the spinless fermions. We estimate the critical field Hc above which begins the incommensurate phase. We also present a theoretical calculation for the specific heat in this phase. We use CuGeO3 as an example of a compound where our theory could be applied.

Phase diagrams of a two-dimensional Heisenberg antiferromagnet with single-ion anisotropy

A two-dimensional Heisenberg antiferromagnet with a single-ion anisotropy is studied in the presence of a uniform magnetic field along the easy axis. The concept of effective field-dependent anisotropy is applied to the theoretical description of the phase diagrams. We perform calculations using the self-consistent harmonic approximation to treat the XY phase and the Green function technique for the Ising phase. Monte Carlo simulations on L× L square lattices, with L=8,16,32 and 64, and with periodic boundary conditions were performed for the classical model. In order to test the validity of the effective anisotropy concept we compare our theoretical calculation with simulation data. We also calculate theoretically the phase diagram of the compound Rb 2MnF 4, a quasi-two-dimensional spin 5/2 antiferromagnet, finding good agreement with experimental data. Our estimates for the transition temperature of the compounds K 2MnF 4 and Mn(HCOO) 2·2H 2O, in zero magnetic field, are also in agreement with the experimental values.

2D ferromagnetic models with symmetry-breaking interactions: self-consistent harmonic approximation

The 2D classical planar rotator, XY and Heisenberg ferromagnetic models with uniaxial in-plane anisotropy are investigated using self-consistent harmonic approximation. We found that for sufficiently large anisotropy there is implemented the phase transition from ferromagnetic phase into paramagnetic one. We also determine the range of anisotropy values for which the XY and planar rotator models undergo phase transition in temperature from the state with long-range magnetic order into Berezinskii–Kosterlitz–Thouless phase with topological order. The same calculations are carried out for the models with magnetoelastic coupling.

Phase diagram for the two-dimensional quantum anisotropic XY model

A self-consistent harmonic approximation is used to study the Kosterlitz–Thouless phase transition and the quantum phase transition at T=0 K in the two-dimensional anisotropic quantum XY model.