Abstract
We study the quantum mechanics of three-index Majorana fermions governed by a quartic Hamiltonian with symmetry. Similarly to the Sachdev-Ye-Kitaev model, this tensor model has a solvable large- limit dominated by the melonic diagrams. For the total number of states is , but they naturally break up into distinct sectors according to the charges under the Cartan subgroup of one of the O(4) groups. The biggest sector has vanishing charges and contains over 165 million states. Using a Lanczos algorithm, we determine the spectrum of the low-lying states in this and other sectors. We find that the absolute ground state is nondegenerate. If the symmetry is gauged, it is known from earlier work that the model has 36 states and a residual discrete symmetry. We study the discrete symmetry group in detail; it gives rise to degeneracies of some of the gauge singlet energies. We find all the gauge singlet energies numerically and use the results to propose exact analytic expressions for them.
- Received 13 September 2018
DOI:https://doi.org/10.1103/PhysRevLett.122.011601
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.
Published by the American Physical Society