Spectrum of Majorana Quantum Mechanics with O(4)3 Symmetry
| Autor: | Igor R. Klebanov, Grigory Tarnopolsky, Fedor K. Popov, Kiryl Pakrouski |
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| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Physical Review Letters. 122 |
| ISSN: | 1079-7114 0031-9007 |
| Popis: | We study the quantum mechanics of three-index Majorana fermions ψ^{abc} governed by a quartic Hamiltonian with O(N)^{3} symmetry. Similarly to the Sachdev-Ye-Kitaev model, this tensor model has a solvable large-N limit dominated by the melonic diagrams. For N=4 the total number of states is 2^{32}, but they naturally break up into distinct sectors according to the charges under the U(1)×U(1) 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 SO(4)^{3} 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. |
| Databáze: | OpenAIRE |
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