Journal•ISSN: 0003-4916

# Annals of Physics

About: Annals of Physics is an academic journal. The journal publishes majorly in the area(s): Hamiltonian (quantum mechanics) & Quantum field theory. It has an ISSN identifier of 0003-4916. Over the lifetime, 8261 publication(s) have been published receiving 354644 citation(s).

Topics: Hamiltonian (quantum mechanics), Quantum field theory, Gauge theory, Scattering, Renormalization

##### Papers

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Abstract: A two-dimensional quantum system with anyonic excitations can be considered as a quantum computer Unitary transformations can be performed by moving the excitations around each other Measurements can be performed by joining excitations in pairs and observing the result of fusion Such computation is fault-tolerant by its physical nature

4,365 citations

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Abstract: * in terms of a few constants, which may be identified with the coupling constants of a unique effective low energy Lagrangian. The low energy representation of several Green’s functions and form factors and of the na scattering amplitude are then calculated. The values of the low energy coupling constants are extracted from available experimental data. The corrections of order Mj, to the xz scattering lengths and effective ranges turn out to be substantial and the improved low energy theorems agree very well with the measured phase shifts. The observed differences between the data and the uncorrected soft pion theorems may even be used to measure the scalar radius of the pion, which plays a central role in the low energy expansion. 0 1984 Academic Press, Inc.

3,062 citations

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Abstract: A spin-1/2 system on a honeycomb lattice is studied. The interactions between nearest neighbors are of XX, YY or ZZ type, depending on the direction of the link; different types of interactions may differ in strength. The model is solved exactly by a reduction to free fermions in a static Z2 source gauge field. A phase diagram in the parameter space is obtained. One of the phases has an energy gap and carries excitations that are Abelian anyons. The other phase is gapless, but acquires a gap in the presence of magnetic field. In the latter case excitations are non-Abelian anyons whose braiding rules coincide with those of conformal blocks for the Ising model. We also consider a general theory of free fermions with a gapped spectrum, which is characterized by a spectral Chern number ν. The Abelian and non-Abelian phases of the original model correspond to ν = 0 and ν = ±1, respectively. The anyonic properties of excitation depend on ν mod 16, whereas ν itself governs edge thermal transport. The paper also provides mathematical background on anyons as well as an elementary theory of Chern number for quasidiagonal matrices.

3,055 citations

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IBM

^{1}Abstract: Two genuinely quantum mechanical models for an antiferromagnetic linear chain with nearest neighbor interactions are constructed and solved exactly, in the sense that the ground state, all the elementary excitations and the free energy are found. A general formalism for calculating the instantaneous correlation between any two spins is developed and applied to the investigation of short- and long-range order. Both models show nonvanishing long-range order in the ground state for a range of values of a certain parameter X which is analogous to an anisotropy parameter in the Heisenberg model. A detailed comparison with the Heisenberg model suggests that the latter has no long-range order in the isotropic case but finite long-range order for any finite amount of anisotropy. The unreliability of variational methods for determining long-range order is emphasized. It is also shown that for spin ½ systems having rather general isotropic Heisenberg interactions favoring an antiferromagnetic ordering, the ground state is nondegenerate and there is no energy gap above the ground state in the energy spectrum of the total system.

2,999 citations

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2,449 citations