Kirill Shtengel

Microscopic models of two-dimensional magnets with fractionalized excitations

We demonstrate that spin-charge separation can occur in two dimensions and note its confluence with superconductivity, topology, gauge theory, and fault-tolerant quantum computation. We construct a microscopic Ising-like model and, at a special coupling constant value, find its exact ground state as well as neutral spin 1/2 (spinon), spinless charge e (holon), and

Intersecting loop models on : rigorous results

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CRITICAL BEHAVIOR FOR 2D UNIFORM AND DISORDERED FERROMAGNETS AT SELF-DUAL POINTS

vortex (vison) states and energies. The fractionalized excitations reflect the topological order of the ground state which is evinced by its fourfold degeneracy on the torus -- a degeneracy which is unrelated to translational or rotational symmetry -- and is described by a

Lebowitz inequalities for Ashkin–Teller systems☆

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MEAN-FIELD THEORY FOR PERCOLATION MODELS OF THE ISING TYPE

gauge theory. Our model is related to the quantum dimer model and is a member of a family of topologically-ordered models, one of which is integrable and realizes the toric quantum error correction code.

BreakdownofaTopological Phase:QuantumPhaseTransitioninaLoopGasModel withTension

.We consider a general class of intersecting loop models in d dimensions, including those related to high-temperature expansions of well-known spin models. We find that the loop models exhibit some interesting features ‐ often in the ‘‘unphysical’’ region of parameter space where all connection with the original spin Hamiltonian is apparently lost. For a particular ns 2, ds 2 model, we establish the existence of a phase transition, possibly associated with divergent loops. However, for n4 1 and arbitrary d there is no phase transition marked by the appearance of large . loops. Furthermore, at least for ds 2 and n large we find a phase transition characterised by broken translational symmetry. q 2000 Elsevier Science B.V. All rights reserved.

An extended Hubbard model with a possible non-Abelian topological phase.

Abstract:We consider certain two-dimensional systems with self-dual points including uniform and disordered q-state Potts models. For systems with continuous energy density (such as the disordered versions) it is established that the self-dual point exhibits critical behavior: Infinite susceptibility, vanishing magnetization and power law bounds for the decay of correlations.

Ground state correlations and spectral gap in lattice models with topological phases

We consider the Ashkin–Teller model with negative four-spin coupling but still in the region where the ground state is ferromagnetic. We establish the standard Lebowitz inequality as well as the extension that is necessary to prove a divergent susceptibility.

Graphical Representations and Cluster Algorithms for Ice Rule Vertex Models.

The q=2 random cluster model is studied in the context of two mean-field models: the Bethe lattice and the complete graph. For these systems, the critical exponents that are defined in terms of finite clusters have some anomalous values as the critical point is approached from the high-density side, which vindicates the results of earlier studies. In particular, the exponent γ~′ which characterizes the divergence of the average size of finite clusters is 1/2, and ν~′, the exponent associated with the length scale of finite clusters, is 1/4. The full collection of exponents indicates an upper critical dimension of 6. The standard mean field exponents of the Ising system are also present in this model (ν′=1/2, γ′=1), which implies, in particular, the presence of two diverging length-scales. Furthermore, the finite cluster exponents are stable to the addition of disorder, which, near the upper critical dimension, may have interesting implications concerning the generality of the disordered system/correlation length bounds.