Quantum criticality and quantum phase transitions


Quantum physics governs the dynamics of particles at microscopic distances and very low temperatures.  If the coherence between the particles extends to macroscopic distances, the laws of quantum mechanics affect the global behavior of solids and may manifest itself in macroscopic effects such as phase transitions.

Quantum critical behavior is realized and observed in systems with a strong interaction between the valence electrons of solids. Itinerant magnetism and superconductivity are the paradigm quantum macroscopic phenomena in strongly correlated electron systems.

However, despite of its imporatnce for potential applications, a comprehensive theory of quantum critical behavior comparable with that of classical criticality is still missing. Therefore, we use the technique of Green functions and Feynman diagrams to assess analytically the effects of strong electron interaction with the aim to describe quantum critical behavior in nanoscale as well as bulk materials.

Our approach is based on renormalization of the electron interaction balancing multiple scatterings of electrons with other electrons and holes. The ultimate objective is to develop a semi-analytic thermodynamically consistent theory of mean-field type of quantum critical behavior and quantum phase transitions, which would qualitatively correctly  take into account both the local quantum dynamical and spatial fluctuations in thermodynamic as well as spectral functions of strongly correlated solids.

Spectral function of strongly correlated electron systems
Typical temperature behavior of the spectral function of strongly correlated electron systems with no long-range order. The combined effect of strong electron repulsion and thermal fluctuations expel electrons from the Fermi energy to satellite Hubbard bands. Lowering the temperature enhances the quantum coherence and a narrow central quasiparticle peak starts to develop reflecting formation of local magnetic moments in metals while the Hubbard bands remains present. The energy unit is the effective bandwidth of the metal.
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