This work shows that a strongly correlated phase which is gapped to collective spin excitations but gapless to charge fluctuations emerges as a universal feature in one-dimensional fermionic systems obeying certain discrete symmetries whenever one pair of spin-degenerate subbands is occupied and an arbitrarily weak spin-orbit interaction is present. This general result is independent of the details of the one-dimensional confinement, the fermionic spin, or nature of the spin-orbit interaction. In narrow-gap semiconductors, this gap may be of order 10 \textmu{}eV. This strongly correlated phase may be identified both via an anomalous
h/2e flux periodicity in Aharonov-Bohm oscillations and
2e periodic Coulomb blockade, features which reflect the existence of fermionic pairing despite the absence of superconductivity and the repulsive nature of the interaction.
We discuss the possible existence of a ``spin-gap'' phase in the low-doping regime of strongly correlated two-dimensional (2D) electrons within the gauge field description of the t-J model. The spin-gap phase was recently shown by \"Ubbens and Lee to be destroyed by gauge field quantum fluctuations for a single-layer 2D system in the absence of disorder and for a full gap. We show that the same conclusion applies both in the dirty limit and for the case of a gapless spinon condensate. \textcopyright{} 1996 The American Physical Society.
Exotic strongly correlated quantum spin liquid (SCQSL) is formed in an insulator Herbertsmithite ZnCu3(OH)6Cl2 with such hypothetic particles as fermionic spinons carrying spin 1=2 and no charge. Here we calculate its thermodynamic and relaxation properties. Our calculations unveil the fundamental properties of SCQSL, forming strongly correlated Fermi system located at a fermion condensation quantum phase transition. These are in good agreement with experimental data and allow us to detect the behavior of SCQSL as that observed in heavy fermion metals and 2D 3He. We predict that the thermal resistivity of SCQSL under the application of magnetic fields at fixed temperature demonstrates a very specific behavior. The key features of our findings are the presence of spin-charge separation and QSL formed with itinerant heavy spinons in herbertsmithite.