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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 85 (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 49 (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,
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 9 (3 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
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 8 (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
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 3 (2 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
Engineered open systems and quantum simulations with atoms and ions
 Advances In Atomic, Molecular, and Optical Physics
, 2012
"... The enormous experimental progress in atomic, molecular and optical (AMO) physics during the last decades allows us nowadays to isolate single, a few or even manybody ensembles of microscopic particles, and to manipulate their quantum properties at a level of precision, which still seemed unthin ..."
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The enormous experimental progress in atomic, molecular and optical (AMO) physics during the last decades allows us nowadays to isolate single, a few or even manybody ensembles of microscopic particles, and to manipulate their quantum properties at a level of precision, which still seemed unthinkable some years ago. This versatile set of tools has enabled the development of the wellestablished concept of engineering of manybody Hamiltonians in various physical platforms. These available tools, however, can also be harnessed to extend the scenario of Hamiltonian engineering to a more general Liouvillian setting, which in addition to coherent dynamics also includes controlled dissipation in manybody quantum systems. Here, we review recent theoretical and experimental progress in different directions along these lines, with a particular focus on physical realizations with systems
Deformations of Lifshitz holography
"... The simplest gravity duals for quantum critical theories with z = 2 ‘Lifshitz ’ scale invariance admit a marginally relevant deformation. Generic black holes in the bulk describe the field theory with a dynamically generated momentum scale Λ as well as finite temperature T. We describe the thermodyn ..."
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The simplest gravity duals for quantum critical theories with z = 2 ‘Lifshitz ’ scale invariance admit a marginally relevant deformation. Generic black holes in the bulk describe the field theory with a dynamically generated momentum scale Λ as well as finite temperature T. We describe the thermodynamics of these black holes in the quantum critical regime where T Λ2. The deformation changes the asymptotics of the spacetime mildly and leads to intricate UV sensitivities of the theory which we control perturbatively in Λ2/T. ar
From AdS to Schrödinger/Lifshitz dual spacetimes without or with hyperscaling violation
 JHEP 1311, 113 (2013) [arXiv:1306.1071 [hepth
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