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.
A bootstrap SDP with a dual 'inequalities of motion' formulation rigorously bounds Euclidean two-point correlators and extracts the low-lying adjoint spectrum of one-matrix quantum mechanics.
A finite-dimensional regularized master field that minimizes residual loop equations reproduces exact Euclidean and perturbative Minkowski results for one- and two-matrix 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.
New positivity constraints from open bubbles and color matrices provide sharp bounds on unitary tensor integrals at finite N and probe deviations from Gaussian universality.
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.
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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Bootstrapping Euclidean Two-point Correlators
A bootstrap SDP with a dual 'inequalities of motion' formulation rigorously bounds Euclidean two-point correlators and extracts the low-lying adjoint spectrum of one-matrix quantum mechanics.
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Regularized Master-Field Approximation for Large-$N$ Reduced Matrix Models
A finite-dimensional regularized master field that minimizes residual loop equations reproduces exact Euclidean and perturbative Minkowski results for one- and two-matrix 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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Additional constraints for the tensor bootstrap
New positivity constraints from open bubbles and color matrices provide sharp bounds on unitary tensor integrals at finite N and probe deviations from Gaussian universality.
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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.