Time-dependent self-consistent harmonic approximation: Anharmonic nuclear quantum dynamics and time correlation functions

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.

Quantum-phase transition in a XY model

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.

Low-temperature thermodynamic study of the diluted planar rotator model using a self-consistent harmonic approximation

ABSTRACTThermal quantum time-correlation functions are of fundamental importance in quantum dynamics, allowing experimentally measurable properties such as reaction rates, diffusion constants and vibrational spectra to be computed from first principles. Since the exact quantum solution scales exponentially with system size, there has been considerable effort in formulating reliable linear-scaling methods involving exact quantum statistics and approximate quantum dynamics modelled with classical-like trajectories. Here, we review recent progress in the field with the development of methods including centroid molecular dynamics , ring polymer molecular dynamics (RPMD) and thermostatted RPMD (TRPMD). We show how these methods have recently been obtained from ‘Matsubara dynamics’, a form of semiclassical dynamics which conserves the quantum Boltzmann distribution. We also apply the Matsubara formalism to reaction rate theory, rederiving t → 0+ quantum transition-state theory (QTST) and showing that Matsubara-TST, like RPMD-TST, is equivalent to QTST. We end by surveying areas for future progress.

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

The phase diagram of a granular superconductor is constructed in the self-consistent harmonic approximation (SCHA) for the order-parameter-phase fluctuation. At zero temperature, the condition for the existence of coherence (CJ ≥ 0.07) obtained in the SCHA in the ordered-granule-lattice model turns out to be less rigid than the corresponding condition derived without any allowance for the correlation between the phase oscillations of different granules. The long-wave spectrum of the phase oscillations in a granular superconductor is determined.

We present results from an extensive analytic and numerical study of a two-dimensional model of a square array of ultrasmall Josephson junctions. We include the ultrasmall self and mutual capacitances of the junctions, for the same parameter ranges as those produced in the experiments. The model Hamiltonian studied includes the Josephson, $E_J$, as well as the charging, $E_C$, energies between superconducting islands. The corresponding quantum partition function is expressed in different calculationally convenient ways within its path-integral representation. The phase diagram is analytically studied using a WKB renormalization group (WKB-RG) plus a self-consistent harmonic approximation (SCHA) analysis, together with non-perturbative quantum Monte Carlo simulations. Most of the results presented here pertain to the superconductor to normal (S-N) region, although some results for the insulating to normal (I-N) region are also included. We find very good agreement between the WKB-RG and QMC results when compared to the experimental data. To fit the data, we only used the experimentally determined capacitances as fitting parameters. The WKB-RG analysis in the S-N region predicts a low temperature instability i.e. a Quantum Induced Transition (QUIT). We carefully simulations and carry out a finite size analysis of $T_{QUIT}$ as a function of the magnitude of imaginary time axis $L_\tau$. We find that for some relatively large values of $\alpha=E_C/E_J$ ($1\leq \alpha \leq 2.25)$, the $L_\tau\to\infty$ limit does appear to give a {\it non-zero} $T_{QUIT}$, while for $\alpha \ge 2.5$, $T_{QUIT}=0$. We use the SCHA to analytically understand the $L_\tau$ dependence of the QMC results with good agreement between them. Finally, we also carried out a WKB-RG analysis in the I-N region and found no evidence of a low temperature QUIT, up to lowest order in ${\alpha}^{-1}$

The atomic motion controls important properties of materials, such as thermal transport, phase transitions, and vibrational spectra. However, simulating the ionic dynamics is exceptionally challenging when quantum fluctuations are relevant (e.g., at low temperatures or with light atoms) and the energy landscape is anharmonic. In this paper, we present the time-dependent self-consistent harmonic approximation (TDSCHA) [L. Monacelli and F. Mauri, Phys. Rev. B 103, 104305 (2021)] in the Wigner framework, paving the way for the efficient computation of the nuclear motion in systems with sizable quantum and thermal anharmonic fluctuations. Besides the improved numerical efficiency, the Wigner formalism unveils the classical limit of TDSCHA and provides a link with the many-body perturbation theory of Feynman diagrams. We further extend the method to account for the nonlinear couplings between phonons and photons, responsible, e.g., for a nonvanishing Raman signal in high-symmetry Raman inactive crystals, firstly discussed by Rasetti and Fermi. We benchmark the method in phase III of high-pressure hydrogen ab initio. The nonlinear photon-phonon coupling reshapes the IR spectra and explains the high-frequency shoulder of the H2 vibron observed in experiments. The Wigner TDSCHA is computationally cheap and derived from first principles. It is unbiased by assumptions on the phonon-phonon and phonon-photon scattering and does not depend on empirical parameters. Therefore, the method can be adopted in unsupervised high-throughput calculations.

We describe a method for performing nuclear quantum dynamics calculations using standard, grid-based algorithms, including the multiconfiguration time-dependent Hartree (MCTDH) method, where the potential energy surface (PES) is calculated "on-the-fly". The method of Gaussian process regression (GPR) is used to construct a global representation of the PES using values of the energy at points distributed in molecular configuration space during the course of the wavepacket propagation. We demonstrate this direct dynamics approach for both an analytical PES function describing 3-dimensional proton transfer dynamics in malonaldehyde and for 2- and 6-dimensional quantum dynamics simulations of proton transfer in salicylaldimine. In the case of salicylaldimine we also perform calculations in which the PES is constructed using Hartree-Fock calculations through an interface to an ab initio electronic structure code. In all cases, the results of the quantum dynamics simulations are in excellent agreement with previous simulations of both systems yet do not require prior fitting of a PES at any stage. Our approach (implemented in a development version of the Quantics package) opens a route to performing accurate quantum dynamics simulations via wave function propagation of many-dimensional molecular systems in a direct and efficient manner.

By computer simulation, using both quantum and classical dynamics, we determined the rate constant and the kinetic isotope effect of the rate-determining step in the neutral hydrolysis of p-methoxyphenyl dichloroacetate in aqueous solution. This step involves a proton transfer concerted with the formation of a CO bond. A method of biased sampling was used; the Gibbs free energy of the biased configuration from which proton transfer is likely to occur was determined by a combination of semiempirical quantum calculations and thermodynamic integration. The proton dynamics was modeled with the quantum-dynamical density matrix evolution method that includes nonadiabatic pathways. The proton dynamics is driven by a fluctuating proton potential that was derived from a classical molecular dynamics simulation of the system including solvent. The calculated rate constant of 3×10-2 s-1 agrees within the error of the calculation with the experimentally observed value of 2.78×10-3 . The calculated pseudo-first-order kinetic isotope effect of 3.9 is in good agreement with the experimentally observed value of 3.2. The results show the feasibility of computational approaches to slow reactions in complex environments, where proton transfer with an essential quantum-dynamical nature is the rate-limiting step. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 886-895, 1999.

The spin-1 anisotropic Heisenberg antiferromagnet on a square lattice at low temperatures

We use the self-consistent harmonic approximation (SCHA) to study static properties of the two-dimensional quantum Heisenberg model with easy-axis anisotropy. We calculate the critical temperature as a function of the spin value, and compare with classical results. Specifically, we compare how the ratio of critical temperatures varies as a function of the spin S in the quantum and classical cases, for afixed anisotropy parameter. We see that, for values of spin near 5/2, the classical result approximates to the quantum results and the classical calculation is justified. We have also studied the behavior of the magnetization for very small anisotropies. We have shown that our magnetization curves do not present a plateau in the limit of very small anisotropies, as predicted by the real-space renormalization-group calculations.

It is shown that bulk superconductivity of a three-dimensional granular metal can become unstable with respect to the diverging zero-point phase fluctuations which result from grain charging. A model of Josephson-coupled superconducting grains is used to calculate the effect of charging energy on the average order parameter at $T=0$. In the mean-field approximation this system exhibits a second-order transition to normal state at a certain critical value of the ratio of the Josephson-coupling constant to the charging energy. The self-consistent harmonic approximation is shown to yield a spurious first-order transition.

Views Icon Views Article contents Figures & tables Video Audio Supplementary Data Peer Review Share Icon Share Twitter Facebook Reddit LinkedIn Tools Icon Tools Reprints and Permissions Cite Icon Cite Search Site Citation Jorge V. José; Phase transitions in arrays of ultrasmall two-dimensional Josephson junction arrays. AIP Conf. Proc. 15 May 1998; 427 (1): 295–312. https://doi.org/10.1063/1.55289 Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentAIP Publishing PortfolioAIP Conference Proceedings Search Advanced Search |Citation Search