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.
Bootstrapping the gap in quantum spin systems,
6 Pith papers cite this work. Polarity classification is still indexing.
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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 hierarchy of SDPs yields lower bounds on spectral gaps of frustration-free Hamiltonians that encompass and improve upon Knabe's bound on 1D spin chains.
Derives lower bound on collective mean free path ℓ = √(τ D) in Drude-Kadanoff-Martin model from Green's function bounds, implying Mott-Ioffe-Regel limit for lattice models.
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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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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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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A Hierarchy of Spectral Gap Certificates for Frustration-Free Spin Systems
A hierarchy of SDPs yields lower bounds on spectral gaps of frustration-free Hamiltonians that encompass and improve upon Knabe's bound on 1D spin chains.
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Bootstrapping transport in the Drude-Kadanoff-Martin model
Derives lower bound on collective mean free path ℓ = √(τ D) in Drude-Kadanoff-Martin model from Green's function bounds, implying Mott-Ioffe-Regel limit for lattice models.
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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.