1+1d Lattice Dirac Fermions from Non-Onsite Vector and Axial Symmetries
Abstract
We construct an exactly solvable Hamiltonian lattice model realizing a 1+1d Dirac fermion, with exact microscopic vector and axial vector U(1) symmetries. The mixed anomaly between these is accommodated by the not-on-site action of the symmetries. Our Hilbert space is a Z2-graded tensor product of local Z2-graded Hilbert spaces which include infinite dimensional rotor degrees of freedom. The Hamiltonian becomes manifestly exactly solvable after a locality-preserving unitary mapping to an equivalent fermionic Villain Hilbert space. Our construction also allows an exactly solvable realization of interacting fermionic Luttinger liquids. At the free Dirac fixed point, our Hamiltonian contains irrelevant interactions, which we compute to leading order.
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BibTeX
@misc{dharanikota2026lattice,
title = {{1+1d Lattice Dirac Fermions from Non-Onsite Vector and Axial Symmetries}},
author = {Tabin Dharanikota and Lukasz Fidkowski},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.02722},
eprint = {2608.02722},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.02722},
}
RIS
TY - UNPB
TI - 1+1d Lattice Dirac Fermions from Non-Onsite Vector and Axial Symmetries
AU - Tabin Dharanikota
AU - Lukasz Fidkowski
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2608.02722
UR - https://arxiv.org/abs/2608.02722
AB - We construct an exactly solvable Hamiltonian lattice model realizing a 1+1d Dirac fermion, with exact microscopic vector and axial vector U(1) symmetries. The mixed anomaly between these is accommodated by the not-on-site action of the symmetries. Our Hilbert space is a Z_2-graded tensor product of local Z_2-graded Hilbert spaces which include infinite dimensional rotor degrees of freedom. The Hamiltonian becomes manifestly exactly solvable after a locality-preserving unitary mapping to an equivalent fermionic Villain Hilbert space. Our construction also allows an exactly solvable realization of interacting fermionic Luttinger liquids. At the free Dirac fixed point, our Hamiltonian contains irrelevant interactions, which we compute to leading order.
ER -