Bootstrapping Matrix Quantum Mechanics
| Autor: | Jorrit Kruthoff, Sean A. Hartnoll, Xizhi Han |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
High Energy Physics - Theory
Physics Operator (physics) Anharmonicity Spectrum (functional analysis) FOS: Physical sciences General Physics and Astronomy Duality (optimization) Computer Science::Digital Libraries 01 natural sciences Matrix (mathematics) High Energy Physics - Theory (hep-th) Quantum mechanics Bounded function 0103 physical sciences 010306 general physics Ground state Quantum |
| Zdroj: | Physical Review Letters |
| ISSN: | 1079-7114 0031-9007 |
| DOI: | 10.1103/physrevlett.125.041601 |
| Popis: | Large $N$ matrix quantum mechanics is central to holographic duality but not solvable in the most interesting cases. We show that the spectrum and simple expectation values in these theories can be obtained numerically via a `bootstrap' methodology. In this approach, operator expectation values are related by symmetries -- such as time translation and $SU(N)$ gauge invariance -- and then bounded with certain positivity constraints. We first demonstrate how this method efficiently solves the conventional quantum anharmonic oscillator. We then reproduce the known solution of large $N$ single matrix quantum mechanics. Finally, we present new results on the ground state of large $N$ two matrix quantum mechanics. 11 pages. 3 figures. v2: more details of numerical methods and minor additions. code available online: https://github.com/hanxzh94/matrix-bootstrap |
| Databáze: | OpenAIRE |
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