Brillouin-Wigner Theory Research Articles

Topological magnon insulator with Dzyaloshinskii–Moriya interaction under the irradiation of light**Project supported by the National Natural Science Foundation of China (Grant No. 61604106) and Shandong Provincial Natural Science Foundation, China (Grant No. ZR2014FL025).

The topological magnon insulator on a honeycomb lattice with Dzyaloshinskii–Moriya interaction (DMI) is studied under the application of a circularly polarized light. At the high-frequency regime, the effective tight-binding model is obtained based on Brillouin–Wigner theory. Then, we study the corresponding Berry curvature and Chern number. In the Dirac model, the interplay between a light-induced handedness-dependent effective DMI and intrinsic DMI is discussed.

Improving mean-field theory for bosons in optical lattices via degenerate perturbation theory

The objective of this paper is the theoretical description of the Mott-insulator to superfluid quantum phase transition of a Bose gas in an optical lattice. In former works the Rayleigh-Schr\"odinger perturbation theory was used within a mean-field approach, which yields partially non-physical results since the degeneracy between two adjacent Mott lobes is not taken into account. In order to correct such non-physical results we apply the Brillouin-Wigner perturbation theory to the mean-field approximation of the Bose-Hubbard model. Detailed explanations of how to use the Brillouin-Wigner theory are presented, including a graphical approach that allows to efficiently keep track of the respective analytic terms. To prove the validity of this computation, the results are compared with other works. Besides the analytic calculation of the phase boundary from Mott-insulator to superfluid phase, the condensate density is also determined by simultaneously solving two algebraic equations. The analytical and numerical results turn out to be physically meaningful and can cover a region of system parameters inaccessible until now. Our results are of particular interest provided an harmonic trap is added to the former calculations in an homogeneous system, in view of describing an experiment within the local density approximation. Thus, the paper represents an essential preparatory work for determining the experimentally observed wedding-cake structure of particle-density profile at both finite temperature and hopping.

Erratum: Brillouin-Wigner theory for high-frequency expansion in periodically driven systems: Application to Floquet topological insulators [Phys. Rev. B 93 , 144307 (2016)

Received 4 January 2019DOI:https://doi.org/10.1103/PhysRevB.99.019902©2019 American Physical SocietyPhysics Subject Headings (PhySH)Physical SystemsFloquet systemsTopological insulatorsTechniquesPerturbation theoryCondensed Matter, Materials & Applied Physics

Brillouin-Wigner theory for high-frequency expansion in periodically driven systems: Application to Floquet topological insulators

We construct a systematic high-frequency expansion for periodically driven quantum systems based on the Brillouin-Wigner (BW) perturbation theory, which generates an effective Hamiltonian on the projected zero-photon subspace in the Floquet theory, reproducing the quasienergies and eigenstates of the original Floquet Hamiltonian up to desired order in $1/\omega$, with $\omega$ being the frequency of the drive. The advantage of the BW method is that it is not only efficient in deriving higher-order terms, but even enables us to write down the whole infinite series expansion, as compared to the van Vleck degenerate perturbation theory. The expansion is also free from a spurious dependence on the driving phase, which has been an obstacle in the Floquet-Magnus expansion. We apply the BW expansion to various models of noninteracting electrons driven by circularly polarized light. As the amplitude of the light is increased, the system undergoes a series of Floquet topological-to-topological phase transitions, whose phase boundary in the high-frequency regime is well explained by the BW expansion. As the frequency is lowered, the high-frequency expansion breaks down at some point due to band touching with nonzero-photon sectors, where we find numerically even more intricate and richer Floquet topological phases spring out. We have then analyzed, with the Floquet dynamical mean-field theory, the effects of electron-electron interaction and energy dissipation. We have specifically revealed that phase transitions from Floquet-topological to Mott insulators emerge, where the phase boundaries can again be captured with the high-frequency expansion.

Effects of a single fermion in a Bose Josephson junction

We consider the tunneling properties of a single fermionic impurity immersed in a Bose-Einstein condensate in a double-well potential. For strong boson-fermion interaction, we show the existence of a tunnel resonance where a large number of bosons and the fermion tunnel simultaneously. We give analytical expressions for the line shape of the resonance using degenerate Brillouin-Wigner theory. We finally compute the time-dependent dynamics of the mixture. Using the fermionic tunnel resonances as a beam splitter for wave functions, we construct a Mach-Zehnder interferometer that allows complete population transfer from one well to the other by tilting the double-well potential and only taking into account the fermion's tunnel properties.

Coupling term derivation and general implementation of state-specific multireference coupled cluster theories

Simple closed-form expressions are derived for the "same vacuum" renormalization terms that arise in state-specific multireference coupled cluster (MRCC) theories. Explicit equations are provided for these coupling terms through the triple excitation level of MRCC theory, and a general expression is included for arbitrary-order excitations. The first production-level code (PSIMRCC) for state-specific and rigorously size-extensive Mukherjee multireference coupled cluster singles and doubles (MkCCSD) computations has been written. This code is also capable of evaluating analogous Brillouin-Wigner multireference energies (BWCCSD), including a posteriori size-extensivity corrections. Using correlation-consistent basis sets (cc-pVXZ, X=D,T,Q), MkCCSD and BWCCSD were tested and compared on two classic multireference problems: (1) the dissociation potential curve of molecular fluorine (F(2)) and (2) the structure and vibrational frequencies of ozone. Comparison with experimental data shows that the Mukherjee method is generally superior to the Brillouin-Wigner theory in predicting energies, structures, and vibrational frequencies. Particularly accurate results for F(2) are obtained by applying the MkCCSD method with localized molecular orbitals. Although the MkCCSD theory greatly improves upon single-reference CCSD for the geometric parameters and a(1) vibrational frequencies of ozone, the antisymmetric stretching frequency omega(3)(b(2)) remains pathological and cannot be properly treated without the inclusion of connected triple excitations. Finally, preliminary multireference MkCCSD results are reported for the singlet-triplet splittings in ortho-, meta-, and para-benzyne, coming within 1.5 kcal mol(-1) of experiment in all cases.

Projection operator approach to time-independent perturbation theory in quantum mechanics

The time-independent perturbation theory in quantum mechanics is formulated using projection operator techniques. The determination of the perturbed eigenvalue can be decoupled from that of the perturbed eigenstate. Both the Brillouin–Wigner theory and the Rayleigh–Schrödinger theory come out straightforwardly. Both degenerate and nondegenerate cases can be treated in a unified way for arbitrarily high order perturbations.

Mixed valency of Pr in a Y1-xPrxBa2Cu3O7 bilayer.

A bilayer model of ${\mathrm{Y}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Pr}}_{\mathit{x}}$${\mathrm{Ba}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ is presented, and the Brillouin-Wigner theory in the large-N limit is adopted to study the mixed-valence behavior of praseodymium. The chemical valence ${\mathit{N}}_{\mathit{f}}$ (or ${\mathit{N}}_{\mathit{f}0}$) of the Pr dopant as functions of the energy-level difference ${\mathit{E}}_{\mathit{f}}$ between 4f configurations, the mixing interaction strength ${\mathit{v}}_{\mathit{k}}$ between 4f electrons and conduction holes, and the hole content P are investigated and discussed.

Brillouin-Wigner theory of mixed-valence impurities in BCS superconductor: T c/T c0 and ΔC/ΔC 0

The (lowest order) Brillouin-Wigner perturbational expansion theory is adopted to describe the mixed-valence impurities in the BCS superconductor. Two substantial quantities characterizing the superconducting state, i.e. the reduced transition temperature T c / T c0 and the reduced specific heat jump Δ C/Δ C 0 are calculated numerically as a function of the impurity concentration x and the energy level difference E f between two 4 f configurations. A comparison with the experimental data of the Th 1− x Ce x and Th 1− x U x alloys is also included with a more reasonable fitting than Kaiser's theory.

A revised diagrammatic technique for the degenerate Anderson model

The Goldstone diagrammatic technique developed by Keiter and Kimball for single impurity Anderson model is reformulated. Instead of having the self-energy functions defined on the real axis as the Brillouin–Wigner theory, we have defined the functions on the complex plane. This avoids the complicated and cumbersome regularization procedure required in the Keiter and Kimball formulation. Most important of all it makes the numerical calculations possible. The exact partition function may be written down in terms of irreducible self-energy diagrams. The Green function and spectral function are derived.

Use of Projection Operators in Perturbation Theory

By the use of projection operators a series of approximations to the perturbed problem is generated, the first of which turns out to be the second-order Brillouin-Wigner theory. This connection is used to show that the latter is in certain cases either an upper or a lower bound to the correct energy.