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14
Anyons in an exactly solved model and beyond
, 2005
"... 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 gauge f ..."
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Cited by 29 (2 self)
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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 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 nonAbelian 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 nonAbelian 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.
Nonabelian anyons and topological quantum computation
 Reviews of Modern Physics
"... Contents Topological quantum computation has recently emerged as one of the most exciting approaches to constructing a faulttolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are partic ..."
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Cited by 12 (0 self)
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Contents Topological quantum computation has recently emerged as one of the most exciting approaches to constructing a faulttolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles known as NonAbelian anyons, meaning that they obey nonAbelian braiding statistics. Quantum information is stored in states with multiple quasiparticles,
NonAbelian Anyons and Topological Quantum Computation
, 2007
"... Topological quantum computation has recently emerged as one of the most exciting approaches to constructing a faulttolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles know ..."
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Cited by 6 (1 self)
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Topological quantum computation has recently emerged as one of the most exciting approaches to constructing a faulttolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles known as NonAbelian anyons, meaning that they obey nonAbelian braiding statistics. Quantum information is stored in states with multiple quasiparticles, which
Relating Field Theories via Stochastic Quantization
, 903
"... This note aims to subsume several apparently unrelated models under a common framework. Several examples of well–known quantum field theories are listed which are connected via stochastic quantization. We highlight the fact that the quantization method used to obtain the quantum crystal is a discret ..."
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Cited by 3 (2 self)
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This note aims to subsume several apparently unrelated models under a common framework. Several examples of well–known quantum field theories are listed which are connected via stochastic quantization. We highlight the fact that the quantization method used to obtain the quantum crystal is a discrete analog of stochastic quantization. This model is of interest for string theory, since the (classical) melting crystal corner is related to the topological A–model. We outline several ideas for interpreting the quantum crystal on the string theory side of the correspondence, exploring interpretations in the Wheeler–De Witt framework and in terms of a non–Lorentz invariant limit of topological M–theory. Contents
Quantum crystals and spin chains
 Nuclear Physics B
"... In this note, we discuss the quantum version of the melting crystal corner in one, two, and three dimensions, generalizing the treatment for the quantum dimer model. Using a mapping to spin chains we find that the two–dimensional case (growth of random partitions) is integrable and leads directly to ..."
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Cited by 1 (0 self)
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In this note, we discuss the quantum version of the melting crystal corner in one, two, and three dimensions, generalizing the treatment for the quantum dimer model. Using a mapping to spin chains we find that the two–dimensional case (growth of random partitions) is integrable and leads directly to the Hamiltonian of the Heisenberg XXZ ferromagnet. The three–dimensional case of the melting crystal corner is described in terms of a system of coupled XXZ spin chains. We give a conjecture for its mass gap and analyze the system numerically. Contents
Keywords: Field Theories in Lower Dimensions, Gaugegravity correspondence,
, 908
"... Abstract: Black holes in asymptotically Lifshitz spacetime provide a window onto finite temperature effects in strongly coupled Lifshitz models. We add a Maxwell gauge field and charged matter to a recently proposed gravity dual of 2+1 dimensional Lifshitz theory. This gives rise to charged black ho ..."
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Abstract: Black holes in asymptotically Lifshitz spacetime provide a window onto finite temperature effects in strongly coupled Lifshitz models. We add a Maxwell gauge field and charged matter to a recently proposed gravity dual of 2+1 dimensional Lifshitz theory. This gives rise to charged black holes with scalar hair, which correspond to the superconducting phase of holographic superconductors with z> 1 Lifshitz scaling. Along the way we analyze the global geometry of static, asymptotically Lifshitz black holes at arbitrary critical exponent z> 1. In all known exact solutions there is a null curvature singularity in the black hole region, and, by a general argument, the same applies to generic Lifshitz black holes.
Concepts in High Temperature
, 2002
"... It is the purpose of this paper to explore the theory of high temperature superconductivity. Much of the motivation for this comes from the study of cuprate high temperature superconductors. However, we do not focus in great detail on the remarkable and exciting physics that has been discovered in t ..."
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It is the purpose of this paper to explore the theory of high temperature superconductivity. Much of the motivation for this comes from the study of cuprate high temperature superconductors. However, we do not focus in great detail on the remarkable and exciting physics that has been discovered in these materials. Rather, we focus on the core theoretical issues associated with the mechanism of high temperature superconductivity. Although our discussions of theoretical issues in a strongly correlated superconductor are intended to be self contained and pedagogically complete, our discussions of experiments in the cuprates are, unfortunately, considerably more truncated and impressionistic. Our primary focus is on physics at intermediate temperature scales of order Tc (as well as the somewhat larger “pseudogap ” temperature) and energies of order the gap maximum, ∆0. Consequently (and reluctantly) we have omitted any detailed discussion of a number of fascinating topics in cuprate superconductivity, including the low energy physics associated with nodal quasiparticles, the properties of the vortex matter which results from the application of a magnetic field, the effects of disorder, and a host of material specific issues. This paper is long enough as it is! 2 E. W. Carlson, V. J. Emery, S. A. Kivelson, and D. Orgad Contents
Yejin Huh Quantum Phase Transitions in dwave Superconductors
, 2011
"... Strongly correlated systems are of interest due to their exotic collective behavior. In this thesis we study low energy effective theory and quantum phase transitions of dwave superconductors and spin liquids. First we examine the quantum theory of the spontaneous breaking of lattice rotation symme ..."
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Strongly correlated systems are of interest due to their exotic collective behavior. In this thesis we study low energy effective theory and quantum phase transitions of dwave superconductors and spin liquids. First we examine the quantum theory of the spontaneous breaking of lattice rotation symmetry in dwave superconductors on the square lattice. This is described by a field theory of an Ising nematic order parameter coupled to the gapless fermionic quasiparticles. We determine the structure of the renormalization group to all orders in a 1/Nf expansion, where Nf is the number of fermion spin components. Asymptotically exact results are obtained for the quantum critical theory in which, as in the large Nf theory, the nematic order has a large anomalous dimension, and the fermion spectral functions are highly anisotropic. Next we study quantum phase transitions in antiferromagnetic kagome lattices. Due to the high geometric frustration, this system poses as a good candidate for a spin liquid with exotic excitations. Here we look at physics of the spinon and vison