Computing quantum phase transitions

Abstract

This article first gives a concise introduction to quantum phase transitions, emphasizing similarities with and differences to classical thermal transitions. After pointing out the computational challenges posed by quantum phase transitions, a number of successful computational approaches is discussed. The focus is on classical and quantum Monte Carlo methods, with the former being based on the quantum-to classical mapping while the latter directly attack the quantum problem. These methods are illustrated by several examples of quantum phase transitions in clean and disordered systems.

99 pages, 15 figures, submitted to Reviews in Computational Chemistry

References in corpus (8)

• The numerical renormalization group method for quantum impurity systems
• "Deconfined" quantum critical points
• Weak magnetism and non-Fermi liquids near heavy-fermion critical points
• Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions
• Fractionalized Fermi liquids
• Phase diagram and critical exponents of a dissipative Ising spin chain in a transverse magnetic field
• Universal conductance of nanowires near the superconductor-metal quantum transition
• Quantum Monte Carlo Study of Disordered Fermions