Lang-Firsov approaches to polaron physics: From variational methods to unbiased quantum Monte Carlo simulations

We review variational and quantum Monte Carlo approaches based on (extended) Lang-Firsov transformations of the Hamiltonian. Derivations for one, two and many electrons are given, and results for the Holstein polaron, the Holstein-Hubbard bipolaron, and the spinless Holstein model at finite carrier densities are presented.Comment: 40 pages, 15 figures, to be published in Polarons in Advanced Materials, Ed. A. S. Alexandrov (Canopus/Springer Publishing, Bristol) (2007); V2: typo in authors list correcte

A numerical projection technique for large-scale eigenvalue problems

We present a new numerical technique to solve large-scale eigenvalue problems. It is based on the projection technique, used in strongly correlated quantum many-body systems, where first an effective approximate model of smaller complexity is constructed by projecting out high energy degrees of freedom and in turn solving the resulting model by some standard eigenvalue solver. Here we introduce a generalization of this idea, where both steps are performed numerically and which in contrast to the standard projection technique converges in principle to the exact eigenvalues. This approach is not just applicable to eigenvalue problems encountered in many-body systems but also in other areas of research that result in large scale eigenvalue problems for matrices which have, roughly speaking, mostly a pronounced dominant diagonal part. We will present detailed studies of the approach guided by two many-body models.Comment: 7 pages, 4 figure

Prediction of high-Tc conventional superconductivity in the ternary lithium borohydride system

We investigate the superconducting ternary lithium borohydride phase diagram at pressures of 0 and 200 GPa using methods for evolutionary crystal structure prediction and linear-response calculations for the electron-phonon coupling. Our calculations show that the ground state phase at ambient pressure, LiBH4, stays in the Pnma space group and remains a wide band-gap insulator at all pressures investigated. Other phases along the 1:1:x Li:B:H line are also insulating. However, a full search of the ternary phase diagram at 200 GPa revealed a metallic Li2BH6 phase, which is thermodynamically stable down to 100 GPa. This superhydride phase, crystallizing in a Fm¯3m space group, is characterized by sixfold hydrogen-coordinated boron atoms occupying the fcc sites of the unit cell. Due to strong hydrogen-boron bonding this phase displays a critical temperature of ∼100K between 100 and 200 GPa. Our investigations confirm that ternary compounds used in hydrogen-storage applications should exhibit high-Tc conventional superconductivity in diamond anvil cell experiments, and suggest a viable route to optimize the superconducting behavior of high-pressure hydrides, exploiting metallic covalent bonds