Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Part I Near-equilibrium critical dynamics
- 1 Equilibrium critical phenomena
- 2 Stochastic dynamics
- 3 Dynamic scaling
- 4 Dynamic perturbation theory
- 5 Dynamic renormalization group
- 6 Hydrodynamic modes and reversible mode couplings
- 7 Phase transitions in quantum systems
- Part II Scale invariance in non-equilibrium systems
- Index
- References
7 - Phase transitions in quantum systems
from Part I - Near-equilibrium critical dynamics
Published online by Cambridge University Press: 05 June 2014
- Frontmatter
- Dedication
- Contents
- Preface
- Part I Near-equilibrium critical dynamics
- 1 Equilibrium critical phenomena
- 2 Stochastic dynamics
- 3 Dynamic scaling
- 4 Dynamic perturbation theory
- 5 Dynamic renormalization group
- 6 Hydrodynamic modes and reversible mode couplings
- 7 Phase transitions in quantum systems
- Part II Scale invariance in non-equilibrium systems
- Index
- References
Summary
This chapter addresses phase transitions and dynamic scaling occurring in systems comprised of interacting indistinguishable quantum particles, for which entanglement correlations are crucial. It first describes how the dynamics (in real time) and thermodynamics (in imaginary time) of quantum many-particle Hamiltonians can be mapped onto field theories based on coherent-state path integrals. While bosons are described by complex-valued fields, fermions are represented by anticommuting Grassmann variables. Since quantum-mechanical systems are of inherently dynamical nature, the corresponding field theory action entails d + 1 dimensions, with time playing a special role. For Hamiltonians that incorporate only two-particle interactions, we can make contact with the previously studied Langevin equations, yet with effectively multiplicative rather than additive noise. As an illustration, this formalism is applied to deduce fundamental properties of weakly interacting boson superfluids. Whereas Landau–Ginzburg theory already provides a basic hydrodynamic description, the Gaussian approximation allows the computation of density correlations, the Bose condensate fraction, and the normal- and superfluid densities from the particle current correlations. We next establish that quantum fluctuations are typically irrelevant for thermodynamic critical phenomena, provided that Tc > 0, and readily extend finite-size scaling theory to the imaginary time axis to arrive at general scaling forms for the free energy. Intriguing novel phenomena emerge in the realm of genuine quantum phase transitions at zero temperature, governed by other control parameters such as particle density, interaction or disorder strengths.
- Type
- Chapter
- Information
- Critical DynamicsA Field Theory Approach to Equilibrium and Non-Equilibrium Scaling Behavior, pp. 251 - 304Publisher: Cambridge University PressPrint publication year: 2014