2020/04/30 by Xizhi Han, Sean A. Hartnoll, Jorrit Kruthoff · 2 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Matrix (chemical analysis) #Noncommutative and Quantum Gravity Theories #Physics #Quantum #Quantum Electrodynamics and Casimir Effect #Quantum dynamics #Quantum mechanics #Quantum process #Quantum statistical mechanics #hep-th
paper · pdf · doi:10.1103/physrevlett.125.041601
published as Phys. Rev. Lett. 125, 041601 (2020) · 11 pages. 3 figures. v2: more details of numerical methods and minor additions. code available online: https://github.com/hanxzh94/matrix-bootstrap
openalex publication_date 2020/07/22 · arxiv created 2020/07/24 · arxiv updated 2020/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.