Ground-state Average Research Articles

Polaritonic excitations and Bose-Einstein condensation in the Rabi lattice model

The unitary transformation method is used to study the properties of the polaritonic states and Bose-Einstein condensation in the Rabi lattice model, where the on-site two-level systems (TLSs) are coupled with the intersite hopping photons. It is shown that the counter-rotating coupling (CRC) between TLS and photon, which breaks down the conservation of the excitation numbers, may induce a long-range Ising-like interaction among intersite TLSs. We have shown that the coupled TLSs and photons are hybridized to form the polaritonic states, and the corresponding ground state and polaritonic excitation spectra are calculated by diagonalizing our transformed Hamiltonian. When the photon hopping $J$ is weak, the excitation spectrum is gapped. But the gap decreases with increasing $J$, and at critical value $J={J}_{c}$ the gap becomes zero at the $\mathrm{\ensuremath{\Gamma}}$ point and the ground state becomes instable. Thus, ${J}_{c}$ is the phase transition point where the polaritons are condensed at the $\mathrm{\ensuremath{\Gamma}}$ point to form the delocalized superradiant phase. The results show that the larger detuning between TLS and photon favors the disorder insulator phase, which requires the stronger ${J}_{c}$ to get the long-range order phase. The phase diagram of the delocalized superradiant phase transition has been obtained where there are no Mott lobes since the CRC breaks down the number conservation. The ground state and the excitation spectra of the delocalized superradiant phase are also calculated. It is shown that in the delocalized superradiant state the order parameter is the nonzero ground-state average of the photon annihilation operator. The polaritonic excitation has a finite excitation gap because the CRC breaks down the number conservation but leaves only a discrete symmetry, the parity conservation.

Polarization amplitude near quantum critical points

We discuss the polarization amplitude of quantum spin systems in one dimension. In particular, we closely investigate it in gapless phases of those systems based on the two-dimensional conformal field theory. The polarization amplitude is defined as the ground-state average of a twist operator which induces a large gauge transformation attaching the unit amount of the U(1) flux to the system. We show that the polarization amplitude under the periodic boundary condition is sensitive to perturbations around the fixed point of the renormalization-group flow rather than the fixed point itself even when the perturbation is irrelevant. This dependence is encoded into the scaling law with respect to the system size. In this paper, we show how and why the scaling law of the polarization amplitude encodes the information of the renormalization-group flow. In addition, we show that the polarization amplitude under the antiperiodic boundary condition is determined fully by the fixed point in contrast to that under the periodic one and that it visualizes clearly the nontriviality of spin systems in the sense of the Lieb-Schultz-Mattis theorem.

Entanglement evolution and quantum phase transition of biaseds=1/2spin-boson model

The ground state and the spectral structure of lower-lying excited states of a dissipative two-level system coupled to a sub-Ohmic bath (s = 1/2) with nonzero bias have been studied using the unitary transformation method. By calculating the ground-state entanglement entropy, the ground-state average of σ(z)(G), and the static susceptibility of the two-level system, we explore the nature of the transition (crossover) between the delocalized and localized state of the two-level system. Furthermore, we calculate the time-dependent expectation (σ(z)(t)) and the time evolution of the entanglement entropy to show that, when the system undergoes a transition (crossover) from the delocalized to the localized state, the time evolution of the two-level system changes from coherent to decoherent dynamics.

Reptation Quantum Monte Carlo: A Method for Unbiased Ground-State Averages and Imaginary-Time Correlations

We introduce a new stochastic method for calculating ground-state properties of quantum systems. Segments of a Langevin random walk guided by a trial wave function are subject to a Metropolis rejection test performed on the time integral of the local energy. The algorithm---which is as simple as variational Monte Carlo---for bosons provides exact expectation values of local observables, as well as their static and dynamic (in imaginary time) response functions, without mixed-estimate nor population-control biases. Our method is demonstrated with a few case applications to ${}^{4}\mathrm{He}$.

A comparison of ground-state averages in electron propagator theory

In the Dyson equation, the self-energy describes all relaxation and correlation corrections to Koopmans's theorem. Energy-independent contributions to the self-energy depend on the one-electron reduced density matrix of the reference state. Three formalisms for calculating these terms are considered: perturbation theory, coupled-cluster theory, and contour integral theory. In one method, combinations of coupled-cluster singles and doubles amplitudes are substituted for first-order double excitation coefficients and for second-order single excitation coefficients. Another approach generates a description of reference state correlation through the evaluation of approximate contour integral expressions. Calculations on electron binding energies of closed-shell molecules and anions reveal that the coupled-cluster results for the energy-independent self-energy terms are closer to the perturbative results than to the contour integral values. © 1993 John Wiley & Sons, Inc.

ChemInform Abstract: THE GROUND‐STATE AVERAGE STRUCTURE OF METHYL ISOCYANIDE

Chemischer InformationsdienstVolume 14, Issue 7 Physical Organic Chemistry ChemInform Abstract: THE GROUND-STATE AVERAGE STRUCTURE OF METHYL ISOCYANIDE M. W. MACKENZIE, M. W. MACKENZIESearch for more papers by this authorJ. L. DUNCAN, J. L. DUNCANSearch for more papers by this author M. W. MACKENZIE, M. W. MACKENZIESearch for more papers by this authorJ. L. DUNCAN, J. L. DUNCANSearch for more papers by this author First published: February 15, 1983 https://doi.org/10.1002/chin.198307072AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article. Volume14, Issue7February 15, 1983 RelatedInformation

The ground-state average structure of methyl isocyanide

The use of recently determined highly precise inertial data for various isotopic modifications of methyl isocyanide has enabled the ground-state average, or rz, structure to be determined to within very narrow limits. Harmonic corrections to ground-state rotational constants have been calculated using a high-quality, experimentally determined harmonic force field. The derived zero-point inertial constants are sufficiently accurate to enable changes in the CH bond length and NCH bond angle on deuteration to be determined. The present rz structure determination is believed to be a physically realistic estimate of the ground-state average geometry of methyl isocyanide.

The microwave spectrum, harmonic force field, and structure of formyl chloride

Extensive measurements were made of the microwave spectra of nine isotopic species of formyl chloride, HCOCl. Analysis of these spectra gave accurate rotational constants, chlorine nuclear quadrupole coupling constants, and centrifugal distortion constants. The distortion constants, together with the vibrational wavenumbers, were used to evaluate a valence harmonic force field. Effective, substitution, ground-state average, and estimated equilibrium structures are presented.

The harmonic force field and ground-state average structure of allene

Existing spectroscopic data for allene-H 4, -D 4, and -1,1-D 2 are improved and augmented by gas-phase Raman and solid-phase infrared studies. A number of 13C vibration frequencies are identified in natural abundance by each technique. A total of 58 input data enable 22 of the 23 force field parameters to be determined, the 13C frequency shift data removing the ambiguity of choice between two sets of A 1 and B 2 species force constants. The remaining interaction force constant is constrained to the predicted ab initio value of Botschwina and Pulay. The force field is used to determine the ground-state average ( r z ) structure of allene. Observed trends in the H-D isotopic effects on the r z structures of ethylene, allene, and ketene are in accordance with those expected.

Calculation of Coefficients in the Power Series Expansion of the Long-Range Dispersion Force between Atoms

By applying an Unsöld approximation to the expression for the second-order perturbation energy between two atoms and assuming no overlap of charge distributions, we have derived an expression for C2n, the coefficient of the R−2n term in the attractive potential, in terms of C6 and ground-state averages of even powers of the electron—nucleus distance in the isolated atom. Values of C8 and C10 are calculated for H, He, Ne, Ar, and Kr, and estimates are made as to the accuracy of the calculations. Several comments are made on the convergence of the power series expression for the second-order energy.

Molecular Magnetic Susceptibility Tensor in Sulfur Dioxide

The diagonal elements in the magnetic susceptibility tensor in the principal molecule-fixed inertial axis system in SO2 have been determined by observing the molecular rotational Zeeman effect with a high-resolution microwave spectrometer. The signs of gaa, gbb, gcc have been found to be negative from theroetical considerations. The principal values of the magnetic susceptibility tensor, paramagnetic susceptibility tensor, and diamagnetic susceptibility tensor are, respectively: χaa = − 14.4 ± 1.2, χbb = − 19.6 ± 0.5, χcc = − 20.6 ± 0.6; χaap = 38.9 ± 0.3, χbbp = 129.3 ± 1.4, χccp = 139.5 ± 1.2; χaad = − 53.3 ± 1.2, χbbd = − 148.9 ± 1.5, χccd = − 160.1 ± 1.3 (all in units of 10−6 erg/G2·mole). The ground-state averages of the sum of the squares of the electronic coordinates, and approximate values of the diagonal components of the quadrupole moment tensor have also been determined.

New Theory of Lattice Dynamics at 0°K

It has previously been shown that the optimum choice of harmonic Hamiltonian with which to approximate a crystal Hamiltonian is one is which the force constants are equal to the ground-state expectation value of the second derivative of the crystal potential, the expectation value being computed self-consistently with the ground-state eigenfunction of the harmonic Hamiltonian. It is shown here that the appearance of ground-state averages of various derivatives of the potential is due to an explicit or implicit expansion of the potential in a Hermite polynomial series, and that such an expansion is superior to the conventional Taylor-series expansion for anharmonic systems. In addition, it is shown that one can systematically treat very anharmonic systems by expanding the Hamiltonian in a set of polynomials orthogonalized with respect to weight function chosen to cut off the potential at short range, and that explicit incorporation of an easily optimized Gaussian factor in this weight function provides a computationally convenient way of introducing certain desirable features into the general expansion.

A new identity in the Green's function approach to the many-body problem

The basic equation of the coupled heirarchy for the energy-dependent thermodynamic Green's function of two operators is shown to be equivalent to an obvious identity. This clear notion of the meaning of the equation permits a discussion of the connection between poles and excitation energies. It is shown that difficulties which arise from the use of the grand-canonical distribution may be avoided by using a simple ground-state average.