2019/01/23 by Paul Fendley · 1 citation
Physics and Astronomy · Mathematics · #cond-mat.stat-mech #hep-th #math-ph #math.MP
paper · pdf · doi:10.1088/1751-8121/ab305d
published as J. Phys. A: Math. Theor. 52 (2019) 335002 · 31 pages
arxiv created 2019/01/23 · arxiv updated 2019/11/06
I solve a quantum chain whose Hamiltonian is comprised solely of local four-fermi operators by constructing free-fermion raising and lowering operators. The free-fermion operators are both non-local and highly non-linear in the local fermions. This construction yields the complete spectrum of the Hamiltonian and an associated classical transfer matrix. The spatially uniform system is gapless with dynamical critical exponent z=3/2, while staggering the couplings gives a more conventional free-fermion model with an Ising transition. The Hamiltonian is equivalent to that of a spin-1/2 chain with next-nearest-neighbour interactions, and has a supersymmetry generated by a sum of fermion trilinears. The supercharges are part of a large non-abelian symmetry algebra that results in exponentially large degeneracies. The model is integrable for either open or periodic boundary conditions but the free-fermion construction only works for the former, while for the latter the extended symmetry is broken and the degeneracies split.