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The interface between a topological insulator and a ferromagnetic insulator exhibits an interesting interplay of topological Dirac electrons and magnetism. As has been shown recently, the breaking of time-reversal invariance by magnetic order generates a Chern-Simons term in the action, that in turn leads to a Berry phase and a magnetoelectric effect of topological origin. Here, we consider the system in the presence of long-range Coulomb interaction between the Dirac electrons, and find that the magnetoelectric effect of the fluctuating electric field becomes non-local. We derive a Landau-Lifshitz equation for the fluctuation-induced magnetization dynamics and the Euler-Lagrange equation of the Coulomb field by explicit one-loop calculations. Via the Coulomb interaction, divergences in the in-plane magnetization affect the magnetization dynamics over large distances in a topologically protected way., Comment: 6 pages, 25 References, 1 figure. To appear in Phys. Rev. B

Motivated by recent experiments on EuS/Bi$_2$Se$_3$ heterostructures, we study the temperature dependent screening effects on the surface of a three-dimensional topological insulator proximate to a ferromagnetically ordered system. In general, we find that besides the chemical potential and temperature, the screening energy scale also depends on the proximity-induced electronic gap in an essential way. In particular, at zero temperature the screening energy vanishes if the chemical potential is smaller than the proximity-induced electronic gap. We show that at finite temperature, $T$, and/or chemical potential, $\mu$, the Chern-Simons (topological) mass, which is generated by quantum fluctuations arising from the proximity-effect, can be calculated analytically in the insulating regime. In this case the topological mass yields the Hall conductivity associated to edge states. We show that when the chemical potential is inside the gap the topological mass remains nearly quantized at finite temperature., Comment: 5 pages, 1 figure; v3: extended version; improved discussion of the Hall conductivity at finite temperature

We consider a Ginzburg-Landau model for superconductivity with a Chern-Simons term added. The flow diagram contains two charged fixed points corresponding to the tricritical and infrared stable fixed points. The topological coupling controls the fixed point structure and eventually the region of first order transitions disappears. We compute the critical exponents as a function of the topological coupling. We obtain that the value of the $\nu$ exponent does not vary very much from the XY value, $\nu_{XY}=0.67$. This shows that the Chern-Simons term does not affect considerably the XY scaling of superconductors. We discuss briefly the possible phenomenological applications of this model., Comment: RevTex, 7 pages, 8 figures

We demonstrate that the low-energy effective theory for a deconfined quantum critical point in $d=2+1$ dimensions contains a leading order contribution given by the Faddeev-Skyrme model. The Faddeev-Skyrme term is shown to give rise to the crucial Maxwell term in the CP$^1$ field theory governing the deconfined quantum critical point. We derive the leading contribution to the spin stiffness near the quantum critical point and show that it exhibits a logarithmic correction to scaling of the same type as recently observed numerically in low dimensional models of quantum spin systems featuring a quantum critical point separating an antiferromagnetically ordered state from a valence bond solid state. These corrections, appearing away from upper or lower critical dimensions, reflect an emergent gauge symmetry of low-dimensional antiferromagnetic quantum spin systems., 5 pages, 1 figure; v2: Text improved. The final third of the preprint has been thoroughly revised

The gauge dependence of the renormalization group functions of the Ginzburg-Landau model is investigated. The analysis is done by means of the Ward-Takahashi identities. After defining the local superconducting order parameter, it is shown that its exponent $\beta$ is in fact gauge independent. This happens because in $d=3$ the Landau gauge is the only gauge having a physical meaning, a property not shared by the four-dimensional model where any gauge choice is possible. The analysis is done in both the context of the $\epsilon$-expansion and in the fixed dimension approach. It is pointed out the differences that arise in both of these approaches concerning the gauge dependence., Comment: RevTex, 3 pages, no figures; accepted for publication in PRB; this paper is a short version of cond-mat/9905276

Quantum electrodynamics in 2+1 dimensions is an effective gauge theory for the so called algebraic quantum liquids. A new type of such a liquid, the algebraic charge liquid, has been proposed recently in the context of deconfined quantum critical points [R. K. Kaul {\it et al.}, Nature Physics {\bf 4}, 28 (2008)]. In this context, we show by using the renormalization group in $d=4-\epsilon$ spacetime dimensions, that a deconfined quantum critical point occurs in a SU(2) system provided the number of Dirac fermion species $N_f\geq 4$. The calculations are done in a representation where the Dirac fermions are given by four-component spinors. The critical exponents are calculated for several values of $N_f$. In particular, for $N_f=4$ and $\epsilon=1$ ($d=2+1$) the anomalous dimension of the N\'eel field is given by $\eta_N=1/3$, with a correlation length exponent $\nu=1/2$. These values change considerably for $N_f>4$. For instance, for $N_f=6$ we find $\eta_N\approx 0.75191$ and $\nu\approx 0.66009$. We also investigate the effect of chiral symmetry breaking and analyze the scaling behavior of the chiral holon susceptibility, $G_\chi(x)\equiv$., Comment: 13 pages, 3 figures; published version

We discuss compact $2+1$ dimensional Maxwell electrodynamics coupled to fermionic matter with $N$ replica. For large enough $N$, the latter corresponds to an effective theory for the nearest neighbor $\mathrm{SU}(N)$ Heisenberg antiferromagnet, in which the fermions represent solitonic excitations known as spinons. Here, we show that the spinons are deconfined for $Ng{N}_{c}=36$, thus leading to an insulating state known as spin liquid. A previous analysis considerably underestimated the value of ${N}_{c}$. We show further that for $20lN\ensuremath{\leqslant}36$, there can be either a confined or a deconfined phase, depending on the instanton density. For $N\ensuremath{\leqslant}20$, only the confined phase exists. For the physically relevant value $N=2$, we argue that no paramagnetic phase can emerge since chiral symmetry breaking would disrupt it. In such a case, a spin liquid or any other nontrivial paramagnetic state (for instance, a valence-bond solid) is only possible if doping or frustrating interactions are included.