Quantum phase transition in the spin boson model
arXiv:1106.2654 · doi:10.1007/978-3-642-11470-0_6
Abstract
In this paper we give a general introduction to quantum critical phenomena, which we practically illustrate by a detailed study of the low energy properties of the spin boson model (SBM), describing the dynamics of a spin 1/2 impurity (or more generically a two-level system) coupled to a bath of independent harmonic oscillators. We show that the behavior of the model is very sensitive to the bath spectrum, in particular how the properties of the quantum critical point in the SBM are affected by the functional form of the bath Density of States (DoS). To this effect, we review the renormalization group (RG) treatment of the SBM for various bath DoS, based on an unconventional Majorana representation of the spin 1/2 degree of freedom. We also discuss the derivation of Shiba's relation for the sub-ohmic SBM, and explicitely derive an effective action vindicating the quantum to classical mapping.
Introductory book chapter. 18 pages, 8 figures
References in corpus (5)
- Fermi-liquid instabilities at magnetic quantum phase transitions
- Numerical Renormalization Group for Bosonic Systems and Application to the Subohmic Spin-Boson Model
- Spin-spin correlators in Majorana representation
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Cited by in corpus (7)
- Efficient non-Markovian quantum dynamics using time-evolving matrix product operators
- Numerical Renormalization Group for the sub-ohmic spin-boson model: A conspiracy of errors
- Dissipative spin dynamics near a quantum critical point: Numerical Renormalization Group and Majorana diagrammatics
- Impurity-Induced Environmental Quantum Phase Transitions in the Quadratic-Coupling Spin-Boson Model
- Equilibrium Dynamics of the Sub-Ohmic Spin-boson Model Under Bias
- Single Mode Approximation for sub-Ohmic Spin-Boson Model: Adiabatic Limit and Critical Properties
- No spin-localization phase transition in the spin-boson model without local field