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arXiv:1702.04723 · Physical review. B./Physical review. B

Quantum electrodynamics in 2+1 dimensions with quenched disorder: Quantum critical states with interactions and disorder

Alex Thomson, Subir Sachdev A

Published Jun 26, 2017• 30 citations
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Abstract

Quantum electrodynamics in 2+1 dimensions (${\mathrm{QED}}_{3}$) is a strongly coupled conformal field theory (CFT) of a U(1) gauge field coupled to $2N$ two-component massless fermions. The $N=2$ CFT has been proposed as a ground state of the spin-1/2 kagome Heisenberg antiferromagnet. We study ${\mathrm{QED}}_{3}$ in the presence of weak quenched disorder in its two spatial directions. When the disorder explicitly breaks the fermion flavor symmetry from $\mathrm{SU}(2N)$ $\ensuremath{\rightarrow}$ U(1) $\ifmmode\times\else\texttimes\fi{}$ $\mathrm{SU}(N)$ but preserves time-reversal symmetry, we find that the theory flows to a nontrivial fixed line at nonzero disorder with a continuously varying dynamical critical exponent $z>1$. We determine the zero-temperature flavor (spin) conductivity along the critical line. Our calculations are performed in the large-$N$ limit, and the disorder is handled using the replica method.

DOI
10.1103/physrevb.95.235146

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An important yet largely unsolved problem in the statistical mechanics of disordered quantum systems is to understand how quenched disorder affects quantum phase transitions in systems of itinerant fermions. In the clean limit, continuous quantum phase transitions of the symmetry-breaking type in Dirac materials such as graphene and the surfaces of topological insulators are described by relativistic (2+1)-dimensional quantum field theories of the Gross-Neveu-Yukawa (GNY) type. We study the universal critical properties of the chiral Ising, XY, and Heisenberg GNY models perturbed by quenched random-mass disorder, both uncorrelated or with long-range power-law correlations. Using the replica method combined with a controlled triple epsilon expansion below four dimensions, we find a variety of new finite-randomness critical and multicritical points with nonzero Yukawa coupling between low-energy Dirac fields and bosonic order parameter fluctuations, and compute their universal critical exponents. Analyzing bifurcations of the renormalization-group flow, we find instances of the fixed-point annihilation scenario—continuously tuned by the power-law exponent of long-range disorder correlations and associated with an exponentially large crossover length—as well as the transcritical bifurcation and the supercritical Hopf bifurcation. The latter is accompanied by the birth of a stable limit cycle on the critical hypersurface, which represents the first instance of fermionic quantum criticality with emergent discrete scale invariance.