Ground States in the Spin Boson Model

Abstract

We prove that the Hamiltonian of the model describing a spin which is linearly coupled to a field of relativistic and massless bosons, also known as the spin-boson model, admits a ground state for small values of the coupling constant lambda. We show that the ground state energy is an analytic function of lambda and that the corresponding ground state can also be chosen to be an analytic function of lambda. No infrared regularization is imposed. Our proof is based on a modified version of the BFS operator theoretic renormalization analysis. Moreover, using a positivity argument we prove that the ground state of the spin-boson model is unique. We show that the expansion coefficients of the ground state and the ground state energy can be calculated using regular analytic perturbation theory.

References in corpus (2)

• Absence of Ground States for a Class of Translation Invariant Models of Non-relativistic QED
• Quantitative estimates on the Hydrogen ground state energy in non-relativistic QED

Cited by in corpus (26)

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• Relation between the Resonance and the Scattering Matrix in the massless Spin-Boson Model
• Spin-Boson type models analysed using symmetries
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• Existence of Resonances for the Spin-Boson-Model with Critical Coupling Function
• Ground States for translationally invariant Pauli-Fierz Models at zero Momentum
• Spectral analysis of the spin-boson Hamiltonian with two photons for arbitrary coupling
• FKN Formula and Ground State Energy for the Spin Boson Model with External Magnetic Field
• A vanishing theorem for operators in Fock space
• Renormalization Analysis for Degenerate Ground States
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• Smoothness and analyticity of perturbation expansions in QED
• Degenerate perturbation theory for models of quantum field theory with symmetries
• Symmetries in non-relativistic quantum electrodynamics
• Spin-Boson Model through a Poisson-Driven Stochastic Process
• The first order expansion of a ground state energy of the ${\varphi }^4$ model with cutoffs
• Spectral analysis of the spin-boson Hamiltonian with two bosons for arbitrary coupling and bounded dispersion relation
• Absence of submultiplicative norms for Wick-ordered Operator Products
• Ground States of Quantum Electrodynamics with Cutoffs
• Differential Equations of Quantum Mechanics
• Discrete eigenvalues of the spin-boson Hamiltonian with two photons: on a problem of Minlos and Spohn