Chiral Anomaly and Spin Gap in One-Dimensional Interacting Fermions

Symmetric mass generation is the interaction-induced opening of a fermion gap without spontaneous symmetry breaking. The anomaly-free 3-4-5-0 model of Wang and Wen provides a minimal one-dimensional setting for this phenomenon, but a direct lattice realization faces two obstacles: fermion doubling for local chiral discretizations and perturbative irrelevance of the six-fermion gapping interaction. We address both obstacles. First, we formulate the model on a strictly one-dimensional tangent-fermion lattice, where a nonlocal hopping produces a single chiral branch without a mirror partner while retaining an efficient tensor-network representation. Second, we add a Hubbard-type density-density interaction (Luttinger parameter $K$ ) that reduces the scaling dimension of the 3-4-5-0 interaction from $5$ to $5K$ , making it relevant for $K<2/5$ . Density-matrix renormalization group calculations show the opening of an excitation gap in this regime without the appearance of a degenerate ground state, the hallmark of symmetric mass generation.Symmetric mass generation is the interaction-induced opening of a fermion gap without spontaneous symmetry breaking. The anomaly-free 3-4-5-0 model of Wang and Wen provides a minimal one-dimensional setting for this phenomenon, but a direct lattice realization faces two obstacles: fermion doubling for local chiral discretizations and perturbative irrelevance of the six-fermion gapping interaction. We address both obstacles. First, we formulate the model on a strictly one-dimensional tangent-fermion lattice, where a nonlocal hopping produces a single chiral branch without a mirror partner while retaining an efficient tensor-network representation. Second, we add a Hubbard-type density-density interaction (Luttinger parameter $K$) that reduces the scaling dimension of the 3-4-5-0 interaction from $5$ to $5K$, making it relevant for $K<2/5$. Density-matrix renormalization group calculations show the opening of an excitation gap in this regime without the appearance of a degenerate ground state, the hallmark of symmetric mass generation.

hep-thCross-listedarXiv:2606.24713Physical Review ResearchJun 24, 20260 citations

Naoto Nagaosa, Masaki Oshikawa

Semiclassical approach has been developed for the one-dimensional interacting fermion systems. Starting from the incommensurate spin density wave (SDW) mean field state for the repulsive Hubbard model in 1D, the non-Abelian bosonized Lagrangian describing the spin-charge separation is obtained. The Berry phase term is derived from the chiral anomaly, and we obtain the massless Tomonaga-Luttinger liquid in the single chain case while the spin gap opens in the double-chain system. This approach offers a new method to identify the strong-coupling fixed point, and its relation to the Abelian bosonization formalism is discussed on the spin gap state. The generalization to higher dimensions is also discussed.Semiclassical approach has been developed for the one-dimensional interacting fermion systems. Starting from the incommensurate spin density wave (SDW) mean field state for the repulsive Hubbard model in 1D, the non-Abelian bosonized Lagrangian describing the spin-charge separation is obtained. The Berry phase term is derived from the chiral anomaly, and we obtain the massless Tomonaga-Luttinger liquid in the single chain case while the spin gap opens in the double-chain system. This approach offers a new method to identify the strong-coupling fixed point, and its relation to the Abelian bosonization formalism is discussed on the spin gap state. The generalization to higher dimensions is also discussed.

arXiv:cond-mat/9412003Journal of the Physical Society of JapanJul 15, 199636 citations

Spin chains and chiral lattice fermions

H.B. Thacker

arXiv:hep-lat/9412019Nuclear Physics B - Proceedings SupplementsApr 1, 19954 citations

Nonabelian Chiral Anomaly and the Spin Gap in One-Dimensional Interacting Electron Systems

Akihiro Tanaka, Masahiko Machida

We critically examine the issue raised by Nagaosa and Oshikawa [J. Phys. Soc. Jpn. 65 (1996) 2241] on how Fujikawa's Jacobian arising from chiral anomaly contributes a topological term to the derivative expansion of the 1d Hubbard model at half filling, thus governing the behaviour of the spin gap. We find that when the nonabelian nature of the system is properly accounted for, the scheme requires modification. The modified result is shown to agree with nonabelian bosonization. Extensions to spin-Peierls systems are outlined.We critically examine the issue raised by Nagaosa and Oshikawa [J. Phys. Soc. Jpn. 65 (1996) 2241] on how Fujikawa's Jacobian arising from chiral anomaly contributes a topological term to the derivative expansion of the 1d Hubbard model at half filling, thus governing the behaviour of the spin gap. We find that when the nonabelian nature of the system is properly accounted for, the scheme requires modification. The modified result is shown to agree with nonabelian bosonization. Extensions to spin-Peierls systems are outlined.

Journal of the Physical Society of JapanMar 15, 19985 citations

K

) that reduces the scaling dimension of the 3-4-5-0 interaction from

5

5K

, making it relevant for

K<2/5

. Density-matrix renormalization group calculations show the opening of an excitation gap in this regime without the appearance of a degenerate ground state, the hallmark of symmetric mass generation.