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Ian Affleck

Publications and source records attributed to Ian Affleck.

7 recordsLinked to original sources
PubMed2006

Boundary effects in the critical scaling of entanglement entropy in 1D systems.

We present exact diagonalization and density matrix renormalization group results for the entanglement entropy of critical spin-1/2 XXZ chains. We find that open boundary conditions induce an alternating term in both the energy density and the entanglement entropy which are approximately proportional, decaying away from the boundary with a power law. The power varies with anisotropy along the critical line and is corrected by a logarithmic factor, which we calculate analytically, at the isotropic point. A heuristic resonating valence bond explanation is suggested.

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PubMed2005

Kondo screening in a magnetically frustrated nanostructure: exact results on a stable non-fermi-liquid phase.

Triangular symmetry stabilizes a novel non-Fermi-liquid phase in the three-impurity Kondo model with frustrating antiferromagnetic interactions between half-integer impurity spins. The phase arises without fine-tuning of couplings, and is stable against magnetic fields and particle-hole symmetry breaking. We find a conformal field theory describing this phase, verify it using the numerical renormalization group, and extract various exact, universal low-energy properties. Signatures predicted in electrical transport may be testable in scanning tunneling microscopy or quantum-dot experiments.

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PubMed2005

Kondo screening cloud around a quantum dot: large-scale numerical results.

Measurements of the persistent current in a ring containing a quantum dot would afford a unique opportunity to finally detect the elusive Kondo screening cloud. We present the first large-scale numerical results on this controversial subject using exact diagonalization and density matrix renormalization group (RG). These extremely challenging numerical calculations confirm RG arguments for weak to strong coupling crossover with varying ring length and give results on the universal scaling functions. We also study, analytically and numerically, the important and surprising effects of particle-hole symmetry breaking.

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PubMed2003

Junctions of three quantum wires and the dissipative Hofstadter model.

We study a junction of three quantum wires enclosing a magnetic flux. This is the simplest problem of a quantum junction between Tomonaga-Luttinger liquids in which Fermi statistics enter in a nontrivial way. We present a direct connection between this problem and the dissipative Hofstadter problem, or quantum Brownian motion in two dimensions in a periodic potential and an external magnetic field, which in turn is connected to open string theory in a background electromagnetic field. We find nontrivial fixed points corresponding to a chiral conductance tensor leading to an asymmetric flow of the current.

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PubMed2002

Finite-size effects in conductance measurements on quantum dots.

The observation of the Kondo effect in quantum dots has provided new opportunities to finally observe the controversial Kondo screening cloud. Here we study the conductance of a quantum dot embedded in a finite length quantum wire, predicting a change in behavior when the length of the wire is comparable to the size of the screening cloud.

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PubMed2002

Néel order in doped quasi-one-dimensional antiferromagnets.

We study the Néel temperature of quasi-one-dimensional S = 1/2 antiferromagnets containing nonmagnetic impurities. We first consider the temperature dependence of the staggered susceptibility of finite chains with open boundary conditions, which shows an interesting difference for even and odd length chains. We then use a mean field theory treatment to incorporate the three-dimensional interchain couplings. The resulting Néel temperature shows a pronounced drop as a function of doping by up to a factor of 5.

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