2026/08/03 by Tabin Dharanikota, Lukasz Fidkowski · 1 citation
Physics and Astronomy · #cond-mat.str-el
1 figure
arxiv created 2026/08/03 · arxiv updated 2026/08/05
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.