TY - JOUR

T1 - Spectrum of Majorana Quantum Mechanics with O (4)3 Symmetry

AU - Pakrouski, Kiryl

AU - Klebanov, Igor R.

AU - Popov, Fedor

AU - Tarnopolsky, Grigory

N1 - Funding Information:
The simulations presented in this Letter were performed on computational resources managed and supported by Princeton’s Institute for Computational Science & Engineering and OIT Research Computing. We are grateful to Yakov Kononov and Douglas Stanford for useful discussions. K. P. was supported by the Swiss National Science Foundation through the Early Postdoc.Mobility Grant No. P2EZP2_172168. The work of I. R. K. and F. P. was supported in part by the US NSF under Grant No. PHY-1620059. The work of G. T. was supported in part by the MURI Grant No. W911NF-14-1-0003 from ARO and by DOE Grant No. de-sc0007870.
Publisher Copyright:
© 2019 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the »https://creativecommons.org/licenses/by/4.0/» 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 SCOAP .

PY - 2019/1/10

Y1 - 2019/1/10

N2 - We study the quantum mechanics of three-index Majorana fermions ψabc 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 232, 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.

AB - We study the quantum mechanics of three-index Majorana fermions ψabc 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 232, 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.

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U2 - 10.1103/PhysRevLett.122.011601

DO - 10.1103/PhysRevLett.122.011601

M3 - Article

C2 - 31012729

AN - SCOPUS:85059817699

SN - 0031-9007

VL - 122

JO - Physical review letters

JF - Physical review letters

IS - 1

M1 - 011601

ER -