From PT-symmetric quantum mechanics to conformal field theory

Abstract

One of the simplest examples of a PT-symmetric quantum system is the scaling Yang-Lee model, a quantum field theory with cubic interaction and purely imaginary coupling. We give a historical review of some facts about this model in d <= 2 dimensions, from its original definition in connection with phase transitions in the Ising model and its relevance to polymer physics, to the role it has played in studies of integrable quantum field theory and of PT-symmetric quantum mechanics. We also discuss some more general results on PT-symmetric quantum mechanics and the ODE/IM correspondence, and mention applications to magnetic systems and cold atom physics.

27 pages, 12 figures, contribution to the Proceedings of PHHQP VIII (Mumbai, January 2009)

References in corpus (7)

• Faster than Hermitian Quantum Mechanics
• PT-symmetric quantum mechanics
• PT Symmetry on the Lattice: The Quantum Group Invariant XXZ Spin-Chain
• Order parameter statistics in the critical quantum Ising chain
• Giving up the ghost
• PT symmetry breaking and exceptional points for a class of inhomogeneous complex potentials
• How to study correlation functions in fluctuating Bose liquids using interference experiments

Cited by in corpus (16)

• The Bethe Ansatz and the Tzitzéica-Bullough-Dodd equation
• PT Symmetry in Classical and Quantum Statistical Mechanics
• Fundamental length in quantum theories with PT-symmetric Hamiltonians II: The case of quantum graphs
• Pseudo-Hermitian random matrix theory
• Conformal generation of an exotic rotationally invariant harmonic oscillator
• Deforming the ODE/IM correspondence with $\mathrm{T}\bar{\mathrm{T}}$
• Anomalous real spectra of non-Hermitian quantum graphs in strong-coupling regime
• Extrapolating the precision of the Hypergeometric Resummation to Strong couplings with application to the $\mathcal{P}\mathcal{T}-$Symmetric $i{\varphi }^3$ Field Theory
• Topology-controlled spectra of imaginary cubic oscillators in the large-L approach
• BRST cohomology of timelike Liouville theory
• Conformal bridge in a cosmic string background
• PT-symmetric eigenvalues for homogeneous potentials
• Intrinsic exceptional point -- a challenge in quantum theory
• Cryptohermitian Hamiltonians on graphs. II. Hermitizations
• Lattice and PT symmetries in tensor-network renormalization group: Case study of a hard-square lattice gas model
• Emergence and localization of exceptional points in an exactly solvable toy model