Pith. sign in

REVIEW 7 cited by

Bootstrapping Matrix Quantum Mechanics

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2004.10212 v2 pith:DDQ3X74Y submitted 2020-04-21 hep-th

Xizhi Han , Sean A. Hartnoll , Jorrit Kruthoff This is my paper · ORCID
classification hep-th
keywords quantummatrixmechanicslargeexpectationthenvaluesanharmonic
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

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.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 7 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. On the strong coupling limit of Yang-Mills matrix models

    hep-th 2026-07 conditional novelty 7.0 of 10

    In mass-deformed Yang–Mills matrix models, strong-coupling commutativity sets in at or above the critical fermion count N_c = 2(D−2), with the supersymmetric models sitting at the critical boundary where huge-operator...

  2. An exact algorithm for U(N) matrix models in the gauge-invariant singlet sector

    hep-th 2026-07 conditional novelty 7.0 of 10

    A group-theoretic algorithm computes U(N)-singlet Hamiltonian matrix elements as closed-form polynomials in N, validated for one matrix against the exact fermion mapping.

  3. Bootstrapping Euclidean Two-point Correlators

    hep-th 2025-11 unverdicted novelty 7.0 of 10

    A semidefinite programming bootstrap is formulated for Euclidean two-point correlators in quantum mechanics, yielding rigorous bounds and low-lying spectrum extraction in the ungauged one-matrix model.

  4. Bootstrapping Yang-Mills matrix integrals

    hep-th 2025-10 conditional novelty 7.0 of 10

    Bootstrap bounds on ⟨tr XX⟩ and ⟨tr XXXX⟩ in D-matrix Yang-Mills integrals shrink to islands matching Monte Carlo, with large-D trajectories guiding a positivity-free ansatz.

  5. Bootstrapping periodic quantum systems

    hep-th 2025-07 conditional novelty 7.0 of 10

    A bootstrap method that includes the translation operator and uses reality conditions computes accurate Bloch-band dispersion relations for the cosine potential without positivity constraints.

  6. High-Precision Bootstrap of Multimatrix Quantum Mechanics

    hep-th 2025-07 conditional novelty 6.0 of 10

    Semidefinite bootstrap bounds fix the large-N ground-state energy and ⟨trX²⟩ of bosonic matrix quantum mechanics to up to eight significant digits.

  7. Real-time dynamics from convex geometry

    hep-lat 2025-02 conditional novelty 3.0 of 10

    The paper derives model-independent, tight bounds on smeared real-time correlators from Euclidean lattice data by solving a finite-dimensional convex program.

Pith tools