The causal bootstrap computes rigorous bounds on smeared spectral functions from non-perturbative Euclidean data by optimizing over the convex set of compatible positive spectral densities and reducing dual problems to semidefinite programs for certain kernels.
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Fractional operator powers generate non-positivity constraints that determine the SYK bilinear spectrum and converge to exact eigenvalues under truncation.
A bootstrap method using density-matrix positivity and steady-state conditions produces bounds on steady-state expectation values, the critical coupling, and the Liouvillian gap for the quantum contact process.
Finite-N bootstrap yields N-independent bounds for matrix models but N-dependent novel bounds on the two-point function versus quartic coupling for tensor models.
Derives explicit recursion relations for Puiseux expansion coefficients in non-Hermitian perturbation theory at exceptional points of order N, with two equivalent forms for the first two eigenvalue corrections.
SDP yields exact ground-state energies and fermion correlators for free-fermion spin chains but only qualitative agreement for general Ising/Potts models and requires input that scales poorly with volume.
Bootstrap method in quantum mechanics has an ambiguity problem for mixed potential and operator types, with three proposed resolutions.
A regularized finite-dimensional master field numerically solves large-N reduced matrix models, reproducing exact Euclidean solutions and perturbative Minkowski results for one- and two-matrix cases.
citing papers explorer
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The Causal Bootstrap: Bounding Smeared Spectral Functions from Non-Perturbative Euclidean Data
The causal bootstrap computes rigorous bounds on smeared spectral functions from non-perturbative Euclidean data by optimizing over the convex set of compatible positive spectral densities and reducing dual problems to semidefinite programs for certain kernels.
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Quantum mechanical bootstrap without inequalities: SYK bilinear spectrum
Fractional operator powers generate non-positivity constraints that determine the SYK bilinear spectrum and converge to exact eigenvalues under truncation.
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Bootstrapping Open Quantum Many-body Systems with Absorbing Phase Transitions
A bootstrap method using density-matrix positivity and steady-state conditions produces bounds on steady-state expectation values, the critical coupling, and the Liouvillian gap for the quantum contact process.
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Finite-$N$ Bootstrap Constraints in Matrix and Tensor Models
Finite-N bootstrap yields N-independent bounds for matrix models but N-dependent novel bounds on the two-point function versus quartic coupling for tensor models.
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Non-Hermitian Rayleigh-Schr\"{o}dinger-like Perturbation Theory at Exceptional Point
Derives explicit recursion relations for Puiseux expansion coefficients in non-Hermitian perturbation theory at exceptional points of order N, with two equivalent forms for the first two eigenvalue corrections.
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Successes and challenges of using Semidefinite Programming for the study of Spin Chain Hamiltonians
SDP yields exact ground-state energies and fermion correlators for free-fermion spin chains but only qualitative agreement for general Ising/Potts models and requires input that scales poorly with volume.
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Ambiguity problem of the Bootstrap Method in Quantum Mechanics
Bootstrap method in quantum mechanics has an ambiguity problem for mixed potential and operator types, with three proposed resolutions.
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Regularized Master-Field Approximation for Large-$N$ Reduced Matrix Models
A regularized finite-dimensional master field numerically solves large-N reduced matrix models, reproducing exact Euclidean solutions and perturbative Minkowski results for one- and two-matrix cases.