Average Ground State Energy Research Articles

Consequences of the inherent density dependence in one dimensional Dirac materials

Dirac materials are systems in which the dispersion is linear in the vicinity of the Dirac points. As a consequence of this linear dispersion, the Fermi velocity is independent of density and these systems exhibit unusual behavior and possess unique physical properties that are of considerable interest. In this work we study the ground state behavior of 1D Dirac materials in two ways. First, using the Virial theorem, we find agreement with a previous result in regards to the total average ground state energy. Namely, that the total average ground state energy, regardless of dimensionality, is found to be where rs is a dimensionless constant that’s a measure of density and is a constant independent of rs. As a consequence, thermodynamic results as well as the characteristic exponents of 1D Fermi systems are density independent. Second, using conventional techniques, i.e. Tomanaga–Luttinger theory, we find several unique properties that are a direct consequence of the dispersion. Specifically, the collective modes of the system exhibit electron density independence predicted from the Virial theorem. Finally, possible experimental realization of our predictions of density independent exponents are briefly discussed.

Unzipping of two random heteropolymers: Ground-state energy and finite-size effects

We consider a pair of random heteropolymer chains with quenched primary sequences. For this system we have analyzed the dependence of average ground state energy per monomer E on chain length n in the ensemble of chains with uniform distribution of primary sequences of monomers. Every monomer of the first (second) chain is randomly and independently chosen with the uniform probability distribution p=1/c from a set of c different types A , B , C , D ,... (A', B', C', D',...) . Monomers of the first chain could form saturating reversible bonds with monomers of the second chain. The bonds between similar monomer types (such as A-A', B-B', C-C', etc.) have the attraction energy u , while the bonds between different monomer types (such as A-B', A-D', B-D', etc.) have the attraction energy v . The main attention is paid to the computation of the normalized free energy E(n) for intermediate chain lengths n and different ratios a=v/u at sufficiently low temperatures, when the entropic contribution of the loop formation is negligible compared to direct energetic interactions between chain monomers, and when the partition function of the chains is dominated by the ground state. The performed analysis allows one to derive the force f(x) which is necessary to apply for unzipping of two random heteropolymers of equal lengths whose ends are separated by the distance x , averaged over all equally distributed primary structures at low temperatures for fixed values a and c .

Exchangeable qubit states

We present a characterisation of the two-site marginals of exchangeable and Bose-exchangeable states and provide an elementary proof for the qubit case. A link between the ground state problem for ferromagnetic mean-field models and the additivity of the maximal two-norm for quantum channels is established. We then analyse the corrections on N-particle symmetric states with respect to the exchangeable ones. The finite-size effects on the average ground state energy of the BCS model are explicitly computed.

Extremal optimization for Sherrington-Kirkpatrick spin glasses

Extremal Optimization (EO), a new local search heuristic, is used to approximate ground states of the mean-field spin glass model introduced by Sherrington and Kirkpatrick. The implementation extends the applicability of EO to systems with highly connected variables. Approximate ground states of sufficient accuracy and with statistical significance are obtained for systems with more than N=1000 variables using ±J bonds. The data reproduces the well-known Parisi solution for the average ground state energy of the model to about 0.01%, providing a high degree of confidence in the heuristic. The results support to less than 1% accuracy rational values of ω=2/3 for the finite-size correction exponent, and of ρ=3/4 for the fluctuation exponent of the ground state energies, neither one of which has been obtained analytically yet. The probability density function for ground state energies is highly skewed and identical within numerical error to the one found for Gaussian bonds. But comparison with infinite-range models of finite connectivity shows that the skewness is connectivity-dependent.

Numerical results for ground states of spin glasses on Bethe lattices

The average ground state energy and entropy for +/- J spin glasses on Bethe lattices of connectivities k+1=3...,26 at T=0 are approximated numerically. To obtain sufficient accuracy for large system sizes (up to n=2048), the Extremal Optimization heuristic is employed which provides high-quality results not only for the ground state energies per spin e_{k+1} but also for their entropies s_{k+1}. The results show considerable quantitative differences between lattices of even and odd connectivities. The results for the ground state energies compare very well with recent one-step replica symmetry breaking calculations. These energies can be scaled for all even connectivities k+1 to within a fraction of a percent onto a simple functional form, e_{k+1} = E_{SK} sqrt(k+1) - {2E_{SK}+sqrt(2)} / sqrt(k+1), where E_{SK} = -0.7633 is the ground state energy for the broken replica symmetry in the Sherrington-Kirkpatrick model. But this form is in conflict with perturbative calculations at large k+1, which do not distinguish between even and odd connectivities. We find non-zero entropies s_{k+1} at small connectivities. While s_{k+1} seems to vanish asymptotically with 1/(k+1) for even connectivities, it is indistinguishable from zero already for odd k+1 >= 9.

Photoluminescence of terbium glass investigated by temperature and pressure dependence

The photoluminescence (PL) intensity from terbium glass either decreases or increases with temperature, depending on the wavelength of the excitation argon ion laser. The red shift of photoluminescence excitation (PLE) spectrum with increasing temperature is responsible for this behavior. The absorption spectra also indicates that the excitation resonance is shifting toward lower energy with increasing temperature. At 300 K, the PLE spectrum under 3.6 GPa broadens relative to the one under ambient pressure but with peak position nearly unchanged, indicating that the temperature dependent shift of the excitation resonance is not caused by thermal contraction of the terbium glass but by the fact that electrons have lower average ground state energy at lower temperature.

Ground State of Quantum Spin Glass with Infinite Range Interactions

We have investigated the spin-1/2 random Heisenberg model with infinite range interactions by a numerical method. Extrapolation of finite size ( N ≦16) properties to the infinite system has yielded the following results. The average ground state energy is lower than that of the SK model (Ising spin) by about 25%. In the ground state, a critical point between the spin glass and ferromagnetic (mixed) phases exists just around the critical point (\(\tilde{J}_{0}/\tilde{J}{=}1\)) of the corresponding classical random Heisenberg model. Quantum fluctuations are concluded not to change the ground state properties qualitatively.

Nonlinear response in the ground states of spin-glasses

A spin-glass is sensitive to an external magnetic field. An applied magnetic field dissolves degeneracy in the ground states of a spin-glass. The number of degeneracy is obtained as a function of the strength $H$ of an external magnetic field for the Edwards-Anderson model of a spinglass. Linear and nonlinear susceptibilities are studied at zero temperature. The nonlinear susceptibility ${\ensuremath{\chi}}_{2}$ defined by an expansion $m=\ensuremath{\chi}H+{\ensuremath{\chi}}_{2}{H}^{3}+\ensuremath{\cdots}$ for the magnetization $m$ is closely related to behavior of the local-field distribution around zero value. It is found, for the infinite-range limit of this model, that ${\ensuremath{\chi}}_{2}$ is a small positive quantity (0.04384) in contrast to the Sherrington-Kirkpatrick solution ($\ensuremath{-}\frac{1}{3\sqrt{2\ensuremath{\pi}}}=\ensuremath{-}0.13298$). The average ground-state energy is obtained for each applied magnetic field. Comparison with computer simulations is made for the infinite-range limit.