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Critical phenomena in the two-dimensional Ising model with a defect line are studied using boundary conformal field theory on the c = 1 orbifold. Novel features of the boundary states arising from the orbifold structure, including continuously varying boundary critical exponents, are elucidated. New features of the Ising defect problem are obtained… (More)

Boundary critical phenomena are studied in the 3-State Potts model in 2 dimensions using conformal field theory, duality and renormalization group methods. A presumably complete set of boundary conditions is obtained using both fusion and orbifold methods. Besides the previously known free, fixed and mixed boundary conditions a new one is obtained. This… (More)

- Ian Affleck
- 1993

A brief review is given of a new method for studying the critical behavior of quantum impurity problems, based on conformal field theory techniques, which I developed with Andreas Ludwig. Some results on the overscreened Kondo problem are reviewed. It is shown that the simple open and periodic fixed points, which occur in quantum spin chain impurity models,… (More)

- Ian Affleck
- 2008

The boundary conformal field theory approach to quantum impurity problems is used to study the Fermi edge singularity, occuring in the X-ray ad-sorption probablility. The deep-hole creation operator, in the effective low-energy theory, changes the boundary condition on the conduction electrons. By a conformal mapping, the dimension of such an operator is… (More)

Using the density matrix renormalization group and a bosonization approach, we study a spin-1/2 antiferromagnetic Heisenberg chain with near-neighbor coupling J 1 and frustrating second-neighbor coupling J 2 , particularly in the limit J 2 >> J 1. This system exhibits both dimerization and incommensurate spiral spin correlations. We argue that this system… (More)

A systematic field-theory approach to Electron Spin Resonance (ESR) in the S = 1/2 quantum antiferromagnetic chain at low temperature T (compared to the exchange coupling J) is developed. In particular, effects of a transverse staggered field h and an exchange anisotropy (including a dipolar interaction) δ on the ESR lineshape are discussed. In the lowest… (More)

Non-magnetic impurities in an S=1/2 Heisenberg antiferromagnetic chain are studied using boundary conformal field theory techniques and finite-temperature quantum Monte Carlo simulations. We calculate the static structure function, S imp (k), measured in neutron scattering and the local susceptibility , χ i measured in Knight shift experiments. S imp (k)… (More)

- Ian Affleck
- Nature
- 2010

- Tzu-Chieh Wei, Ian Affleck, Robert Raussendorf
- Physical review letters
- 2011

Universal quantum computation can be achieved by simply performing single-qubit measurements on a highly entangled resource state, such as cluster states. The family of Affleck-Kennedy-Lieb-Tasaki states has recently been intensively explored and shown to provide restricted computation. Here, we show that the two-dimensional Affleck-Kennedy-Lieb-Tasaki… (More)

A scaling form for the local susceptibility, derived from renormalization group arguments, is proposed. The scale over which the uniform part of this scaling form varies can be viewed as a definition of the Kondo " screening cloud " ∼ ξ K. The proposed scaling form interpolates between Ruderman-Kittel-Kasuya-Yosida (RKKY) results in the high temperature… (More)