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Register a new userGaussian time-dependent variational principle for the finite-temperature anharmonic lattice dynamics
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The anharmonic lattice is a representative example of an interacting bosonic many-body system. The self-consistent harmonic approximation has proven versatile for the study of the equilibrium properties of anharmonic lattices. However, the study of dynamical properties therewithin resorts to an ansatz, whose validity has not yet been theoretically proven. Here, we apply the time-dependent variational principle, a recently emerging useful tool for studying the dynamic properties of interacting many-body systems, to the anharmonic lattice Hamiltonian at finite temperature using the Gaussian states as the variational manifold. We derive an analytic formula for the position-position correlation function and the phonon self-energy, proving the dynamical ansatz of the self-consistent harmonic approximation. We establish a fruitful connection between time-dependent variational principle and the anharmonic lattice Hamiltonian, providing insights in both fields. Our work expands the range of applicability of time-dependent variational principle to first-principles lattice Hamiltonians and lays the groundwork for the study of dynamical properties of the anharmonic lattice using a fully variational framework.
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Two-dimensional (2D) ZrS2 monolayer (ML) has emerged as a promising candidate for thermoelectric (TE) device applications due to its high TE figure of merit, which is mainly contributed by its inherently low lattice thermal conductivity. This work investigates the effect of the lattice anharmonicity driven by temperature-dependent phonon dispersions on thermal transport of ZrS2 ML. The calculations are based on the self-consistent phonon (SCP) theory to calculate the thermodynamic parameters along with the lattice thermal conductivity. The higher- order (quartic) force constants were extracted by using an efficient compressive sensing lattice dynamics technique, which estimates the necessary data based on the emerging machine learning program as an alternative of computationally expensive density functional theory calculations. Resolve of the degeneracy and hardening of the vibrational frequencies of low-energy optical modes were predicted upon including the quartic anharmonicity. As compared to the conventional Boltzmann transport equation (BTE) approach, the lattice thermal conductivity of the optimized ZrS2 ML unit cell within SCP + BTE approach is found to be significantly enhanced (e.g., by 21% at 300 K). This enhancement is due to the relatively lower value of phonon linewidth contributed by the anharmonic frequency renormalization included in the SCP theory. Mainly, the conventional BTE approach neglects the temperature dependence of the phonon frequencies due to the consideration of harmonic lattice dynamics and treats the normal process of three-phonon scattering incorrectly due to the use of quasi-particle lifetimes. These limitations are addressed in this work within the SCP + BTE approach, which signifies the validity and accuracy of this approach.
We present a generalization of the Time Dependent Variational Principle (TDVP) to any finite sized loop-free tensor network. The major advantage of TDVP is that it can be employed as long as a representation of the Hamiltonian in the same tensor network structure that encodes the state is available. Often, such a representation can be found also for long-range terms in the Hamiltonian. As an application we use TDVP for the Fork Tensor Product States tensor network for multi-orbital Anderson impurity models. We demonstrate that TDVP allows to account for off-diagonal hybridizations in the bath which are relevant when spin-orbit coupling effects are important, or when distortions of the crystal lattice are present.
An accurate and easily extendable method to deal with lattice dynamics of solids is offered. It is based on first-principles molecular dynamics simulations and provides a consistent way to extract the best possible harmonic - or higher order - potential energy surface at finite temperatures. It is designed to work even for strongly anharmonic systems where the traditional quasiharmonic approximation fails. The accuracy and convergence of the method are controlled in a straightforward way. Excellent agreement of the calculated phonon dispersion relations at finite temperature with experimental results for bcc Li and bcc Zr is demonstrated.
We present a general variational principle for the dynamics of impurity particles immersed in a quantum-mechanical medium. By working within the Heisenberg picture and constructing approximate time-dependent impurity operators, we can take the medium to be in any mixed state, such as a thermal state. Our variational method is consistent with all conservation laws and, in certain cases, it is equivalent to a finite-temperature Greens function approach. As a demonstration of our method, we consider the dynamics of heavy impurities that have suddenly been introduced into a Fermi gas at finite temperature. Using approximate time-dependent impurity operators involving only one particle-hole excitation of the Fermi sea, we find that we can successfully model the results of recent Ramsey interference experiments on $^{40}$K atoms in a $^6$Li Fermi gas [M.~Cetina et al., Science textbf{354}, 96 (2016)]. We also show that our approximation agrees well with the exact solution for the Ramsey response of a fixed impurity at finite temperature. Our approach paves the way for the investigation of impurities with dynamical degrees of freedom in arbitrary quantum-mechanical mediums.
We present a vibrational dynamical mean-field theory (VDMFT) of the dynamics of atoms in solids with anharmonic interactions. Like other flavors of DMFT, VDMFT maps the dynamics of a periodic anharmonic lattice of atoms onto those of a self-consistently defined impurity problem with local anharmonicity and coupling to a bath of harmonic oscillators. VDMFT is exact in the harmonic and molecular limits, nonperturbative, systematically improvable through its clusters extensions, and usable with classical or quantum impurity solvers, depending on the importance of nuclear quantum effects. When tested on models of anharmonic optical and acoustic phonons, we find that classical VDMFT gives good agreement with classical molecular dynamics, including the temperature dependence of phonon frequencies and lifetimes. Using a quantum impurity solver, signatures of nuclear quantum effects are observed at low temperatures.
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