Metallic states beyond Tomonaga-Luttinger liquids in one dimension

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In this paper, we propose some new strongly correlated gapless states (or critical states) of spin-1/2 electrons in 1+1-dimensions, such as doped anti-ferromagnetic spin-1/2 Ising chain.

• We find doped anti-ferromagnetic Ising chain to be a different metallic phase from the doped ferromagnetic Ising chain, despite the two have identical symmetry.
• The doped anti-ferromagnetic Ising chain has a finite energy gap for all charge-1 fermionic excitations even without pairing caused by attractive interactions, resembling the pseudo-gap phase of underdoped high Tc superconductors.
• Applying a transverse field to the ferromagnetic and anti-ferromagnetic metallic phases can restore the $Z_2$ symmetry, which gives rise to two distinct critical points despite that the two transitions have exactly the same symmetry breaking pattern.