Metallic states beyond Tomonaga-Luttinger liquids in one dimension

Abstract

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. We also propose new chiral metallic states. All those new gapless states are strongly correlated in the sense that they do not belong to the usual Tomonaga-Luttinger phase of fermions, i.e., they cannot be smoothly deformed into the non-interacting fermion systems of the same symmetry. Our non-perturbative results are obtained by noticing that gapless quantum systems have emergent categorical symmetries, i.e., non-invertible gravitational anomalies), which are described by multi-component partition functions that are modular covariant. This allows us to calculate the scaling dimensions and quantum numbers of all the low energy operators for those strongly correlated gapless states. This demonstrates an application of emergent categorical symmetries in determining low energy properties of strongly correlated gapless states, which are hard to obtain otherwise.

arXiv comment32 pages, 4 figures

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• Symmetry as a shadow of topological order and a derivation of topological holographic principle
• Holographic theory for continuous phase transitions -- the emergence and symmetry protection of gaplessness
• Quantum Phases and Transitions in Spin Chains with Non-Invertible Symmetries
• Bosonic Rational Conformal Field Theories in Small Genera, Chiral Fermionization, and Symmetry/Subalgebra Duality
• The boundary phase transitions of the 2+1D ${\mathbb{Z}}_N$ topological order via topological Wick rotation