Ground state(s) of the spin-boson Hamiltonian
type: Item
instance of: scholarly article
title: Ground state(s) of the spin-boson Hamiltonian
zbMATH Open document ID: 0667.60108
DOI: 10.1007/BF01238859
author: Herbert Spohn
published in: Communications in Mathematical Physics
publication date: 1989-01-01T00:00:00Z
review text: We establish that the finite temperature KMS states of the spin-boson hamiltonian have a limit as the temperature drops to zero. Using recent advances on the one-dimensional Ising model with long range, \(1/r^ 2\) interactions, we prove qualitative properties of the ground state(s) in the ohmic case. We show (i) the asymptotics of the critical coupling as the bare energy gap goes to zero and to infinity, (ii) a jump in the order parameter, and (iii) that the number of bosons is finite below and infinite at and above the critical coupling strength.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 82B05
Mathematics Subject Classification ID: 81P20
zbMATH DE Number: 4092542
zbMATH Keywords: spin-boson hamiltonian
zbMATH Keywords: Ising model
zbMATH Keywords: interactions
zbMATH Keywords: critical coupling strength
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01238859
OpenAlex ID: W1978089399
description: scientific article; zbMATH DE number 4092542