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 (46)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• The density-matrix renormalization group
• An efficient, multiple range random walk algorithm to calculate the density of states
• Electronic Structure Calculations with Dynamical Mean-Field Theory: A Spectral Density Functional Approach
• Fermi-liquid instabilities at magnetic quantum phase transitions
• Multicanonical Ensemble: A New Approach to Simulate First-order Phase Transitions
• The numerical renormalization group method for quantum impurity systems
• "Deconfined" quantum critical points
• Continuous Quantum Phase Transitions
• Quantum Monte Carlo with Directed Loops
• Stochastic series expansion method with operator-loop update
• Quantum phase transitions
• Weak magnetism and non-Fermi liquids near heavy-fermion critical points
• Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions
• Critical exponents and equation of state of the three-dimensional Heisenberg universality class
• Fractionalized Fermi liquids
• Critical behavior of the three-dimensional XY universality class
• Cluster Algorithm for Vertex Models
• Infinite-randomness quantum Ising critical fixed points
• Variational study of hard-core bosons in a 2-D optical lattice using Projected Entangled Pair States (PEPS)
• The superconductor-insulator transition in 2D dirty boson systems
• Critical Exponents of the Classical 3D Heisenberg Model: A Single-Cluster Monte Carlo Study
• Meron-Cluster Solution of Fermion Sign Problems
• A Numerical Study of the Random Transverse-Field Ising Spin Chain
• Order-Disorder Transition in a Two-Layer Quantum Antiferromagnet
• Zero--Temperature Quantum Phase Transition of a Two--Dimensional Ising Spin--Glass
• Revealing Superfluid--Mott-Insulator Transition in an Optical Lattice
• Disorder-induced rounding of certain quantum phase transitions
• Critical Behavior and Griffiths-McCoy Singularities in the Two-Dimensional Random Quantum Ising Ferromagnet
• Griffiths Singularities in the Disordered Phase of a Quantum Ising Spin Glass
• Phase diagram and critical exponents of a dissipative Ising spin chain in a transverse magnetic field
• Critical temperature for the two-dimensional attractive Hubbard Model
• Universal conductance of nanowires near the superconductor-metal quantum transition
• Cluster Monte Carlo Algorithm for the Quantum Rotor Model
• On the accuracy of the density matrix renormalization group method
• Non-Fermi liquid behavior from two-dimensional antiferromagnetic fluctuations: a renormalization-group and large-N analysis
• Finite Temperature and Dynamical Properties of the Random Transverse-Field Ising Spin Chain
• Multi-critical point in a diluted bilayer Heisenberg quantum antiferromagnet
• Exotic vs. conventional scaling and universality in a disordered bilayer quantum Heisenberg antiferromagnet
• Quantum vs. Geometric Disorder in a Two-Dimensional Heisenberg Antiferromagnet
• Quantum percolation in two-dimensional antiferromagnets
• Directed geometrical worm algorithm applied to the quantum rotor model
• Quantum Monte Carlo study of the 3D attractive Hubbard model
• Strong Randomness Fixed Point in the Dissipative Random Transverse Field Ising Model
• Quantum phase transitions of the diluted O(3) rotor model
• Quantum Monte Carlo Study of Disordered Fermions