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Science News

Quantum collapse of an atomic cluster

I. Peterson

Published Apr 26, 1997• 0 citations
Publisher
DOI
10.2307/4018492

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Quantum Monte Carlo impurity solver for cluster dynamical mean-field theory and electronic structure calculations with adjustable cluster base

Kristjan Haule

We generalized the recently introduced impurity solver [P. Werner et al., Phys. Rev. Lett. 97, 076405 (2006)] based on the diagrammatic expansion around the atomic limit and quantum Monte Carlo summation of the diagrams. We present generalization to the cluster of impurities, which is at the heart of the cluster dynamical mean-field methods, and to realistic multiplet structure of a correlated atom, which will allow a high-precision study of actinide and lanthanide based compounds with the combination of the dynamical mean-field theory and band-structure methods. The approach is applied to both the two-dimensional Hubbard and $t\text{\ensuremath{-}}J$ models within cellular dynamical mean-field method. The efficient implementation of the algorithm, which we describe in detail, allows us to study coherence of the system at low temperature from the underdoped to overdoped regime. We show that the point of maximal superconducting transition temperature coincides with the point of maximum scattering rate, although this optimal doped point appears at different electron densities in the two models. The power of the method is further demonstrated in the example of the Kondo volume collapse transition in cerium. The valence histogram of the dynamical mean-field theory solution is presented, showing the importance of the multiplet splitting of the atomic states.

arXiv:cond-mat/0612172•Physical Review B•Apr 23, 2007•613 citations
Doping helium nanodroplets with more than a single Mg atom leads to a shift of the atomic absorption from 279nmto282nm279\phantom{\rule{0.3em}{0ex}}\mathrm{nm}\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}282\phantom{\rule{0.3em}{0ex}}\mathrm{nm}279nmto282nm. This behavior is stable against a change of the chosen droplet size. There is evidence that the interplay of the weak long-range potential between individual Mg atoms and the interaction with the surrounding quantum fluid leads to the formation of metastable very weakly bound complexes high above the global energy minimum. They resemble a bubble foam, where the individual Mg atoms are separated by a helium layer. The formation of compact Mg clusters is hindered by density variations within the superfluid solvent. The distance between the Mg atoms is substantially larger compared to the ground state. We estimate a value of roughly 10A˚10\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}10A˚ and the barrier, preventing the formation of compact Mg clusters to only a few kelvin. Upon laser excitation the metastable complexes collapse on a time scale of 20ps20\phantom{\rule{0.3em}{0ex}}\mathrm{ps}20ps as measured with a femtosecond pump-probe experiment.
We examine the physics of two, three, and four heavy fermions interacting with a single light fermion via short-range interactions. Four-particle bosonic Efimov states have proven important experimentally and also been the subject of significant theoretical effort. Similar fermionic systems are just now being investigated. We find that with some simple interactions the four- and five-particle states collapse to the interaction range at smaller mass ratios than the three-body state, and also before larger clusters can collapse. These states and their excitations can be studied in cold atom experiments, providing unique insights into the role of few-body systems in many-body physics.
We generalized the recently introduced impurity solver [P. Werner et al., Phys. Rev. Lett. 97, 076405 (2006)] based on the diagrammatic expansion around the atomic limit and quantum Monte Carlo summation of the diagrams. We present generalization to the cluster of impurities, which is at the heart of the cluster dynamical mean-field methods, and to realistic multiplet structure of a correlated atom, which will allow a high-precision study of actinide and lanthanide based compounds with the combination of the dynamical mean-field theory and band-structure methods. The approach is applied to both the two-dimensional Hubbard and $t\text{\ensuremath{-}}J$ models within cellular dynamical mean-field method. The efficient implementation of the algorithm, which we describe in detail, allows us to study coherence of the system at low temperature from the underdoped to overdoped regime. We show that the point of maximal superconducting transition temperature coincides with the point of maximum scattering rate, although this optimal doped point appears at different electron densities in the two models. The power of the method is further demonstrated in the example of the Kondo volume collapse transition in cerium. The valence histogram of the dynamical mean-field theory solution is presented, showing the importance of the multiplet splitting of the atomic states.