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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 ..."
Abstract

Cited by 25 (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.
Translation Techniques Between Quantum Circuit Architectures
"... Abstract. We consider techniques for translating quantum circuits between various architectures. Specifically, we are interested in generic techniques for translating a parallelized quantum circuit between two given architectures which give tight asymptotic bounds on the increase in circuit depth. W ..."
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Cited by 3 (0 self)
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Abstract. We consider techniques for translating quantum circuits between various architectures. Specifically, we are interested in generic techniques for translating a parallelized quantum circuit between two given architectures which give tight asymptotic bounds on the increase in circuit depth. We approach the problem using a graphtheoretic model for physical circuit architectures. The architectures considered include the complete graph Kn, the twodimensional and threedimensional square lattices, the cycle, and the graph of a line, which gives rise to the wellstudied Linear Nearest Neighbour (LNN) circuit architecture model. We present results for translating circuits between these architectures, including a generic technique for translating circuits from arbitrary architectures to the LNN architecture. 1
unknown title
, 2008
"... We revisit the exact solution of the two spacetime dimensional quantum field theory of a free massless boson with a periodic boundary interaction and selfdual period. We analyze the model by using a mapping to free fermions with a boundary mass term originally suggested in ref. [24]. We find that ..."
Abstract
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We revisit the exact solution of the two spacetime dimensional quantum field theory of a free massless boson with a periodic boundary interaction and selfdual period. We analyze the model by using a mapping to free fermions with a boundary mass term originally suggested in ref. [24]. We find that the entire SL(2,C) family of boundary states of a single boson are boundary sineGordon states and we derive a simple explicit expression for the boundary state in fermion variables and as a function of sineGordon coupling constants. We use this expression to compute the partition function. We observe that the solution of the model has a strongweak coupling generalization of Tduality. We then examine a class of recently discovered conformal boundary states for compact bosons with radii which are rational numbers times the selfdual radius. These have simple expression in fermion variables. We postulate sineGordonlike field theories with discrete gauge symmetries for which they are the appropriate boundary states. 1 1
unknown title
, 2008
"... We revisit the exact solution of the two spacetime dimensional quantum field theory of a free massless boson with a periodic boundary interaction and selfdual period. We analyze the model by using a mapping to free fermions with a boundary mass term originally suggested in ref. [22]. We find that ..."
Abstract
 Add to MetaCart
We revisit the exact solution of the two spacetime dimensional quantum field theory of a free massless boson with a periodic boundary interaction and selfdual period. We analyze the model by using a mapping to free fermions with a boundary mass term originally suggested in ref. [22]. We find that the entire SL(2,C) family of boundary states of a single boson are boundary sineGordon states and we derive a simple explicit expression for the boundary state in fermion variables and as a function of sineGordon coupling constants. We use this expression to compute the partition function. We observe that the solution of the model has a strongweak coupling generalization of Tduality. We then examine a class of recently discovered conformal boundary states for compact bosons with radii which are rational numbers times the selfdual radius. These have simple expression in fermion variables. We postulate sineGordonlike field theories with discrete gauge symmmetries for which they are the appropriate boundary states. 1 1