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Existence of Ground States in the Massless Spin Boson Model

Benjamin Hinrichs (Jena University)
Mathematics Seminar
Wednesday, 29 June, 2022 | 15:15–16:00 | Aud. G1 (1532-116)

The spin boson model describes a two-level quantum mechanical system, called spin or qubit, linearly coupled to a field of bosons. If one assumes the bosons to be massive, the system has a spectral gap and hence a ground state exists. However, in the case of massless bosons, the spectral gap closes and the existence of ground states becomes nontrivial. In other models of quantum field theory, it has been observed that massless bosons can lead to the infrared-catastrophe, i.e., the absence of ground states. However, due to the so-called spin flip symmetry, the spin boson model does exhibit a ground state in the infrared-critical case provided the absolute value of the coupling constant is sufficiently small. In this talk, we discuss a recent non-perturbative proof for the existence of ground states in this situation, which allows us to give a simple bound on the absolute value of the coupling constant. We further argue towards the conjecture that there exists no ground state for coupling constants with absolute value larger than a critical value. This talk is based on joint work with David Hasler and Oliver Siebert.