Exact quantum critical points and phase separation instabilities in Betts Hubbard nanoclusters

Abstract

a b s t r a c tSpontaneous phase separation instabilities with the formation of various types of charge and spin pairing (pseudo)gaps in U40 Hubbard model including the 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 antiparallel (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 criticalities 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.

Phase separation instabilities and magnetism in two dimensional square and honeycomb Hubbard model

“…This provides a media with effective attraction of holes or parallel spins that give rise to superconductivity and ferromagnetism. The level crossings in charge and spin excitation gaps found in the finite square lattices generated by (finite) 8and 10-site Betts unit cells [9] further points to the existence of the two quantum critical points at moderate and strong interactions responsible for electron and spin density instabilities in large thermodynamic systems. However, cluster calculations always are invariably tied to some uncertainties due to size and boundary effects and obtained results still remain controversial.…”

Local electronic nematicity in the two-dimensional one-band Hubbard model

“…1(a)) to tile the infinite square and t ′ is the hopping parameter in the reference system. Actually, one can also apply the larger-sized Betts clusters to reduce the size and edge effects [19,20]. The clusters use open boundary conditions according to Ref.…”

“…In this paper, we introduce nematicity locally in the smallest cluster cell; 2 × 2 (square symmetry) clusters are used as the reference system (figure 1(a)) to tile the infinite square and t is the hopping parameter in the reference system. Actually, one can also apply the larger-sized Betts clusters to reduce the size and edge effects [16,17]. The clusters use open boundary conditions according to [12] and t is a variational parameter for the VCA calculation.…”

Phase separation instabilities and pairing modulations in $Bi_2Sr_2CaCu_2O_{8+δ}$

“…An essential element for understanding our results on pairing modulation is the formation of coherent pairing state of n electrons with a negative charge gap and positive spin gap obtained earlier in Refs. [23][24][25][26][27][28][29] and references therein. For completeness here we first briefly summarize the key results of exact diagonalization in small clusters at weak and moderate U values.…”

“…For completeness here we first briefly summarize the key results of exact diagonalization in small clusters at weak and moderate U values. The square lattices, generated recently on optimized (finite) Betts unit cells, provide strong evidence for the phase separation instabilities found in generic 2 × 2, 2 × 4 and other clusters [28,29].…”