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The non-Abelian analog of the classical Coulomb gas is discussed. The statistical mechanics of arrays of classical particles which transform under various representations of a non-Abelian gauge group and which interact through non-Abelian…
We develop methods to probe the excitation spectrum of topological phases of matter in two spatial dimensions. Applying these to the Fibonacci string nets perturbed away from exact solvability, we analyze a topological phase transition…
Exactly solvable models of topologically ordered phases with non-abelian anyons typically require complicated many-body interactions which do not naturally appear in nature. This motivates the "inverse problem" of quantum many-body physics:…
We study the properties of classical vortex solutions in a non-Abelian gauge theory. A system of two adjoint Higgs fields breaks the SU(2) gauge symmetry to $Z_2$, producing 't Hooft-Polyakov monopoles trapped on cosmic strings, termed…
The recent success of the NIST group in generating abelian gauge field in cold atoms has created opportunities to simulate electronic transports in solids using atomic gases. Very recently, the NIST group has also announced in a DARPA…
Within the (dual) Abelian Higgs model, confining strings do not disappear at small distances but rather become short strings. In compact 3D electrodynamics, as we argue here, the confining strings are also manifested at small distances in…
Boundary conformal field theory is brought to bear on the study of topological insulating phases of non-abelian anyonic chains. These topologically non-trivial phases display protected anyonic end modes. We consider antiferromagnetically…
The standard notion of the non-Abelian duality in string theory is generalized to the class of $\si$-models admitting `non-commutative conserved charges'. Such $\si$-models can be associated with every Lie bialgebra $(\cg ,\cgt)$ and they…
Anyons are exotic quasi-particles with fractional charge that can emerge as fundamental excitations of strongly interacting topological quantum phases of matter. Unlike ordinary fermions and bosons, they may obey non-abelian statistics--a…
An exotic feature of the fractional quantum Hall effect is the emergence of anyons, which are quasiparticle excitations with fractional statistics. In the presence of a symmetry, such as $U(1)$ charge conservation, it is well known that…
Trapped-ion arrays offer interesting possibilities for quantum simulation. We show that a proper arrangement of elliptical micro-traps combined with the external driving of the micro-trap frequencies allows, without the need of any precise…
A non-abelian anyon can only occur in the presence of ground state degeneracy in the plane. It is conceivable that for some strange anyon with quantum dimension $>1$ that the resulting representations of all $n$-strand braid groups $B_n$…
We study quantum charge transport in two-dimensional networks in the presence of a magnetic field and spin-orbit interaction. The interplay of the corresponding Abelian and non-Abelian gauge fields leads to an intricate behavior of the…
We study oscillating string solutions in the Klebanov-Witten and its non-Abelian T-dual background dualised along an SU(2) isometry. We find the string energy as the function of oscillation number and angular momentum. We show that for a…
The talk is about the power corrections in QCD. Renormalons, both infrared and ultraviolet, provide with a kind of a kinematical framework to fix exponents of the leading power corrections to various observables. Any viable dynamical…
String representation of the Wilson loop in 3D Abelian-projected SU(3)-gluodynamics is constructed in the approximation that Abelian-projected monopoles form a gas. Such an assumption is much weaker than the standard one, demanding the…
It is well-known that many topological phase transitions of intrinsic Abelian topological phases are accompanied by condensation and confinement of anyons. However, for non-Abelian topological phases, more intricate phenomena can occur at…
The possibility of realizing non-Abelian statistics and utilizing it for topological quantum computation (TQC) has generated widespread interest. However, the non-Abelian statistics that can be realized in most accessible proposals is not…
Superconducting LaOFeAs family of even electron metallic systems have striking resemblance to odd electron cuprates. We suggest that this resemblance is caused by presence of two coupled 2D resonating valence bond systems in LaOFeAs . Bond…
QCD as a gauge non-Abelian theory imposes severe constraints on the structure of the baryon wave function. We point out that, contrary to a widely accepted belief, the traces of baryon number in a high-energy process can reside in a…