Pure-quantum Self-consistent Harmonic Approximation Research Articles

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.

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 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.

Thermodynamics of the two-dimensional easy-axis quantum antiferromagnet

The thermodynamics of the two-dimensional quantum Heisenberg antiferromagnet with easy-axis anisotropy (EA-QHAF) on the square lattice is studied by means of the semiclassical approach of the pure-quantum self-consistent harmonic approximation (PQSCHA). The anisotropic model shows a phase transition at finite temperature with critical exponents of the two-dimensional Ising model for every value of the anisotropy. Our theoretical results are compared with the experimental data on the real compound Rb 2MnF 4 both above (correlation length) and below (staggered magnetization) the transition: a good agreement is found in both the disordered and the ordered phase.

Magnetic correlations in theS=52quadratic lattice Heisenberg antiferromagnetMn(HCOO)2⋅2(ND2)2CO

The magnetic correlations in the quadratic lattice $S=5/2$ Heisenberg antiferromagnet $\mathrm{Mn}(\mathrm{HCOO}{)}_{2}\ensuremath{\cdot}2({\mathrm{ND}}_{2}{)}_{2}\mathrm{CO}$ ${(T}_{\mathrm{N}}=3.77 \mathrm{K})$ have been studied by means of specific heat and neutron-scattering experiments. With a universal temperature scale, the temperature behavior of both the magnetic heat capacity and spin correlations are quantitatively accounted for by the pure quantum self-consistent harmonic approximation by Cuccoli et al. for $S=5/2.$

The two-dimensional quantum Heisenberg antiferromagnet with Ising-like anisotropy

We study the two dimensional quantum Heisenberg antiferromagnet on the square lattice with easy-axis exchange anisotropy by the semiclassical method called pure-quantum self-consistent harmonic approximation. In particular, we focus on the problem of the existence of a nite-temperature transition in such a model, and study the corresponding critical temperature as the spin value and the anisotropy vary. We find that an Ising-like transition characterizes the model even when the anisotropy is of the order of 10-2J (J being the intra-layer exchange integral). The good agreement found between our theoretical results and the experimental data for the compounds Rb2MnF4, K2MnF4, and K2NiF4 shows that the insertion of the easy-axis exchange anisotropy, with quantum effects properly taken into account, provides a quantitative description and explanation of the real system's critical behaviour.

Finite-temperature ordering in two-dimensional magnets

We study the two-dimensional quantum Heisenberg antiferromagnet on the square lattice with easy-axis exchange anisotropy. By the semiclassical method called pure-quantum self-consistent harmonic approximation we analyze several thermodynamic quantities and investigate the existence of a finite temperature transition, possibly describing the low-temperature critical behavior experimentally observed in many layered real compounds. We find that an Ising-like transition characterizes the model even when the anisotropy is of the order of ${10}^{\ensuremath{-}2}J$ $(J$ being the intralayer exchange integral), as in most experimental situations. On the other hand, typical features of the isotropic Heisenberg model are observed for both values of anisotropy considered, one in the quasi-isotropic limit and the other in a more markedly easy-axis region. The good agreement found between our theoretical results and the experimental data relative to the real compound ${\mathrm{Rb}}_{2}{\mathrm{MnF}}_{4}$ shows that the insertion of the easy-axis exchange anisotropy, with quantum effects properly taken into account, provides a quantitative description and explanation of the experimental data, thus allowing us to recognize in such anisotropy the main agent for the observed onset of finite temperature long-range order.

Quantum effects on the BKT phase transition of two-dimensional Josephson arrays

The phase diagram of two-dimensional Josephson arrays is studied by means of the mapping to the quantum $\mathrm{XY}$ model. The quantum effects on the thermodynamics of the system can be evaluated with quantitative accuracy by a semiclassical method, the pure-quantum self-consistent harmonic approximation, and those of dissipation can be included in the same framework by the Caldeira-Leggett model. Within this scheme, the critical temperature of the superconductor-metal transition, which is a Berezinskii-Kosterlitz-Thouless one, can be calculated in an extremely easy way as a function of the quantum coupling and of the dissipation mechanism. Previous quantum Monte Carlo results for the same model appear to be rather inaccurate, while a comparison with experimental data leads us to conclude that the commonly assumed dissipation model is not suitable to describe in detail a real system.

Phase transitions in the quantum easy-plane antiferromagnet on the triangular lattice

The quantum effects on the thermodynamics of the easy-plane triangular antiferromagnet, displaying classically both an Ising and a Berezinskii–Kosterlitz–Thouless phase transition, are evaluated by means of the pure-quantum self-consistent harmonic approximation, which allows one to deal with any spin value through classical Monte Carlo simulations. Data for the specific heat, the static spin correlation functions, and the in-plane correlation length are presented in a broad range of temperatures, for different values of the spin and of the exchange anisotropy. Our results for the quantum transition temperatures are in good agreement with the few available theoretical and numerical estimates.

Spin dynamics and magnetic correlation length in two-dimensional quantum heisenberg antiferromagnets

The correlated spin dynamics and temperature dependence of the correlation length xi(T) in two-dimensional quantum (S = 1/2) Heisenberg antiferromagnets (2DQHAF) on a square lattice are discussed in light of experimental results of proton spin lattice relaxation in copper formiate tetradeuterate. In this compound the exchange constant is much smaller than the one in recently studied 2DQHAF, such as La2CuO4 and Sr2CuO2Cl2. Thus the spin dynamics can be probed in detail over a wider temperature range. The NMR relaxation rates turn out to be in excellent agreement with a theoretical mode-coupling calculation. The deduced temperature behavior of xi(T) is in agreement with high-temperature expansions, quantum Monte Carlo simulations, and the pure quantum self-consistent harmonic approximation. Contrary to the predictions of the theories based on the nonlinear sigma model, no evidence of crossover between different quantum regimes is observed.

Effective Hamiltonian with holomorphic variables

The pure-quantum self-consistent harmonic approximation (PQSCHA) permits to study a quantum system by means of an effective classical Hamiltonian – depending on ℏ and temperature – and classical-like expressions for the averages of observables. In this work the PQSCHA is derived in terms of the holomorphic variables connected to a set of bosonic operators. The holomorphic formulation, based on the path integral for the Weyl symbol of the density matrix, makes it possible to approach directly general Hamiltonians given in terms of bosonic creation and annihilation operators.

Thermodynamics of the quantum easy-plane antiferromagnet on the triangular lattice

The classical $\mathrm{XXZ}$ triangular-lattice antiferromagnet shows both an Ising and a Berezinskii-Kosterlitz-Thouless transition, related to the chirality and the in-plane spin components, respectively. In this paper the quantum effects on the thermodynamic quantities are evaluated by means of the pure-quantum self-consistent harmonic approximation, which allows one to deal with any spin value through classical Monte Carlo simulations. We present data for the internal energy, the specific heat, the static spin correlation functions, and the in-plane correlation length for different values of the spin and of the exchange anisotropy. The quantum transition temperatures turn out to be smaller the smaller the spin, and agree with the few available theoretical and numerical estimates.

The Schrödinger formulation of the Feynman path centroid density

We present an analysis of the Feynman path centroid density that provides new insight into the correspondence between the path integral and the Schrödinger formulations of statistical mechanics. The path centroid density is a central concept for several approximations (centroid molecular dynamics, quantum transition-state theory, and pure quantum self-consistent harmonic approximation) that are used in path integral studies of thermodynamic and dynamical properties of quantum particles. The centroid density is related to the quasistatic response of the equilibrium system to an external force. The path centroid dispersion is the canonical correlation of the position operator, which measures the linear change in the mean position of a quantum particle upon the application of a constant external force. At low temperatures, this quantity provides an approximation to the excitation energy of the quantum system. In the zero temperature limit, the particle’s probability density obtained by fixed centroid path integrals corresponds to the probability density of minimum energy wave packets, whose average energy defines the Feynman effective classical potential.

Thermodynamics of quantum dissipative many-body systems.

We consider quantum nonlinear many-body systems with dissipation described within the Caldeira-Leggett model, i.e., by a nonlocal action in the path integral for the density matrix. Approximate classical-like formulas for thermodynamic quantities are derived for the case of many degrees of freedom, with general kinetic and dissipative quadratic forms. The underlying scheme is the pure-quantum self-consistent harmonic approximation (PQSCHA), equivalent to the variational approach by the Feynman-Jensen inequality with a suitable quadratic nonlocal trial action. A low-coupling approximation permits us to get manageable PQSCHA expressions for quantum thermal averages with a classical Boltzmann factor involving an effective potential and an inner Gaussian average that describes the fluctuations originating from the interplay of quanticity and dissipation. The application of the PQSCHA to a quantum phi(4) chain with Drude-like dissipation shows nontrivial effects of dissipation, depending upon its strength and bandwidth.

The quantum Heisenberg antiferromagnet on the square lattice

The thermodynamic behavior of the quantum Heisenberg antiferromagnet on the square lattice (QHAF) is tackled by the pure-quantum self-consistent harmonic approximation, a semiclassical method based on the path-integral formulation of quantum statistical mechanics. Results for various properties are obtained for different values of the spin and the effects of the dipolar anisotropy are considered. Furthermore, the validity of the quantum nonlinear σ model approach is discussed and shown to be inadequate to describe the behavior of the QHAF with spin value S⩾1 in the experimentally accessible temperature region.

Heisenberg antiferromagnet on the square lattice forS>~1

Theoretical predictions of a semiclassical method---the pure-quantum self-consistent harmonic approximation---for the correlation length and staggered susceptibility of the two-dimensional quantum Heisenberg antiferromagnet (2DQHAF) on the square lattice agree very well with recent quantum Monte Carlo data for $S=1,$ as well as with experimental data for the $S=5/2$ compounds ${\mathrm{Rb}}_{2}{\mathrm{MnF}}_{4}$ and ${\mathrm{KFeF}}_{4}.$ The theory is parameter free and can be used to estimate the exchange coupling: for ${\mathrm{KFeF}}_{4}$ we find $J=2.33\ifmmode\pm\else\textpm\fi{}0.33$ meV, consistent with previously determined values. On this basis, the adequacy of the quantum nonlinear $\ensuremath{\sigma}$ model approach in describing the 2DQHAF when $S>~1$ is discussed.

Two-dimensional quantum Heisenberg antiferromagnet: Effective-Hamiltonian approach to the thermodynamics

In this paper we present an extensive study of the thermodynamic properties of the two-dimensional quantum Heisenberg antiferromagnet on the square lattice; the problem is tackled by the pure-quantum self-consistent harmonic approximation, previously applied to quantum spin systems with easy-plane anisotropies, modeled to fit the peculiar features of an isotropic system. Internal energy, specific heat, correlation functions, staggered susceptibility, and correlation length are shown for different values of the spin, and compared with the available high-temperature expansion and quantum Monte Carlo results, as well as with the available experimental data.