Quantum critical points and phase separation instabilities in Hubbard nanoclusters

TL;DR

This paper investigates quantum critical points and phase separation in Hubbard nanoclusters, revealing mechanisms for unconventional superconductivity, spin liquid behavior, and nanoscale phase coexistence relevant to high-temperature superconductors.

Contribution

It provides an exact theoretical analysis of phase separation, quantum criticality, and pairing mechanisms in 2D Hubbard nanoclusters with next-nearest neighbor interactions, highlighting new routes to superconductivity.

Findings

Identification of phase separation instabilities and quantum critical points.

Proposal of separate charge and spin pairing leading to Bose-Einstein condensation.

Relevance of inhomogeneous nanoscale phases to high-$T_c$ superconductors.

Abstract

Spontaneous phase separation instabilities with the formation of various types of charge and spin pairing (pseudo)gaps in $U>0$ Hubbard model including the {\it next nearest neighbor coupling} are calculated with the emphasis on the two-dimensional (square) lattices generated by 8- and 10-site Betts unit cells. The exact theory yields insights into the nature of quantum critical points, continuous transitions, dramatic phase separation instabilities and electron condensation in spatially inhomogeneous systems. The picture of coupled anti-parallel (singlet) spins and paired charged holes suggests full Bose condensation and coherent pairing in real space at zero temperature of electrons complied with the Bose-Einstein statistics. Separate pairing of charge and spin degrees at distinct condensation temperatures offers a new route to superconductivity different from the BCS scenario. The conditions for spin liquid behavior coexisting with unsaturated and saturated Nagaoka ferromagnetism due to spin-charge separation are established. The phase separation critical points and classical criticality found at zero and finite temperatures resemble a number of inhomogeneous, coherent and incoherent nanoscale phases seen near optimally doped high-$T_c$ cuprates, pnictides and CMR nanomaterials.