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arXiv:1701.08529 · Physical review. B./Physical review. B

Effects of random potentials in three-dimensional quantum electrodynamics

Peng-Lu Zhao, An Min Wang, Guo-Zhu Liu

Published Jun 26, 2017• 10 citations
arXivHTMLPDF

Abstract

Three-dimensional quantum electrodynamics exhibits a number of interesting properties, such as dynamical chiral symmetry breaking, weak confinement, and non-Fermi-liquid behavior, and also has wide applications in condensed-matter physics. We study the effects of random potentials, which exist in almost all realistic condensed-matter systems, on the low-energy behaviors of massless Dirac fermions by means of renormalization-group method, and show that the role of random mass is significantly enhanced by the gauge interaction, whereas random scalar and vector potentials are insusceptible to the gauge interaction at the one-loop order. The static random potential breaks the Lorentz invariance, and as such induces unusual renormalization of fermion velocity. We then consider the case in which three types of random potentials coexist in the system. The random scalar potential is found to play a dominant role in the low-energy region, and drives the system to undergo a quantum phase transition.

DOI
10.1103/physrevb.95.235144

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Three-dimensional quantum electrodynamics exhibits a number of interesting properties, such as dynamical chiral symmetry breaking, weak confinement, and non-Fermi-liquid behavior, and also has wide applications in condensed-matter physics. We study the effects of random potentials, which exist in almost all realistic condensed-matter systems, on the low-energy behaviors of massless Dirac fermions by means of renormalization-group method, and show that the role of random mass is significantly enhanced by the gauge interaction, whereas random scalar and vector potentials are insusceptible to the gauge interaction at the one-loop order. The static random potential breaks the Lorentz invariance, and as such induces unusual renormalization of fermion velocity. We then consider the case in which three types of random potentials coexist in the system. The random scalar potential is found to play a dominant role in the low-energy region, and drives the system to undergo a quantum phase transition.
Metallic phases have been observed in several disordered two-dimensional (2D) systems, including thin films near superconductor-insulator transitions and quantum Hall systems near plateau transitions. The existence of 2D metallic phases at zero temperature generally requires an interplay of disorder and interaction effects. Consequently, experimental observations of 2D metallic behavior have largely defied explanation. We formulate a general stability criterion for strongly interacting, massless Dirac fermions against disorder, which describe metallic ground states with vanishing density of states. We show that (2+1)-dimensional quantum electrodynamics (QED3{\mathrm{QED}}_{3}QED3​) with a large, even number of fermion flavors remains metallic in the presence of weak scalar potential disorder due to the dynamic screening of disorder by gauge fluctuations. We also show that QED3{\mathrm{QED}}_{3}QED3​ with weak mass disorder exhibits a stable, dirty metallic phase in which both interactions and disorder play important roles.
This work deals with quantum phase transitions in Dirac systems where the symmetries involved play a key role in the nature of the transition and are enlarged at criticality. By using functional renormalization group (FRG) methods, we show that an emergent relativistic symmetry not present at the bare level is a common feature of several different kinds of phase transitions. In three different projects, the interplay of emergent symmetries and universality in critical phenomena are explored through FRG techniques. In the first project, we studied the relation between discrete symmetry breaking and the emergence of two diverging length scales with their respective critical exponents. A second project explored the relation between multicritical points where two adjacent symmetry-breaking phases are compatible and the possibility of a continuous, order-to-order transition. The third and final project was concerned with the persistence of chiral symmetry in three-dimensional quantum electrodynamics - here seen as an effective description of different condensed matter systems - for the lowest possible number of fermion flavours, as well as with a dual description that has the potential to provide exact results for this strongly correlated theory.
This Thesis explores the formation of novel phases in Dirac systems that are driven by strong many-body interactions and collective quantum fluctuations. The central focus is the half-filled honeycomb lattice, which is the prototypical Dirac semimetal with low-energy excitations described by Dirac fermions. Of particular interest are exotic phases of matter that are not favoured at mean-field but are stabilised by fluctuations. Self-consistent path integral techniques are used to demonstrate that extended repulsive interactions favour charge order that breaks translational and other lattice symmetries. This charge order outcompetes interaction induced topological insulating phases, which are dominant at the mean-field level. The interacting quantum critical point was found to be near the critical point of a topological Lifshitz transition. Interacting Dirac fermions exhibit perhaps the simplest example of fermionic quantum criticality. Gross-Neveu-Yukawa field theories describe the universality class of semimetal-insulator transitions, which are driven by on-site and nearest neighbour repulsive interactions on the honeycomb lattice. The Dirac fermions couple to the dynamical order parameter fields and play a crucial role in determining the universal behaviour. Naturally, this variety of criticality is outside of the Ginzburg-Landau-Wilson paradigm. This idea is extended to include the translational symmetry breaking charge order. Here it is found that the breaking of crystal symmetries corresponds to Lorentz violating effective field theories. The criticality is analysed with the renormalisation group. The low energy excitations at the topological transition are gapless semi-Dirac fermionic quasiparticles that disperse linearly in one direction and quadratically in the other. The instabilities induced by generic short-range repulsions are investigated. The criticality of this anisotropic system is analysed with the renormalisation group in two spatial dimensions, and it is found to exhibit anisotropic order parameter correlations.
We study the quantum electrodynamics of Luttinger fermions with quadratic band-crossing dispersion in three dimensions. The model can be viewed as the low-energy effective theory of a putative U(1) quantum spin liquid with fermionic Luttinger spinons, or as an extension of the Luttinger-Abrikosov-Beneslavskii (LAB) model that accounts for transverse gauge fluctuations with finite photon velocity. Aided by a renormalization group analysis below four dimensions, we elucidate the presence and stability of quantum critical phenomena in this model. We find that the non-Fermi liquid LAB phase is stable against gauge fluctuations and can thus also be viewed as a U(1) spin liquid with gapless Luttinger spinons. We discover a multicritical point with Lifshitz scaling that corresponds to a time-reversal symmetry-breaking quantum phase transition from the LAB state to a chiral spin liquid with spinon Landau levels and birefringent emergent photons. This multicritical point is characterized by a finite fermion-photon coupling in the infrared and can be viewed as a fermionic analog of the Rokhsar-Kivelson point in three-dimensional quantum dimer models.
We study the effects of generic short-ranged interactions on a system of two-dimensional (2D) Dirac fermions subject to a special kind of static disorder, often referred to as ``chiral.'' The noninteracting system is a member of the disorder class BDIBD\mathrm{I}BDI [M. R. Zirnbauer, J. Math. Phys. 37, 4986 (1996)]. It emerges, for example, as a low-energy description of a time-reversal invariant tight-binding model of spinless fermions on a honeycomb lattice, subject to random hopping, and possessing particle-hole symmetry. It is known that, in the absence of interactions, this disordered system is special in that it does not localize in 2D, but possesses extended states and a finite conductivity at zero energy, as well as a strongly divergent low-energy density of states. In the context of the hopping model, the short-range interactions that we consider are particle-hole symmetric density-density interactions. Using a perturbative one-loop renormalization group analysis, we show that the same mechanism responsible for the divergence of the density of states in the noninteracting system leads to an instability, in which the interactions are driven strongly relevant by the disorder. This result should be contrasted with the limit of clean Dirac fermions in 2D, which is stable against the inclusion of weak short-ranged interactions. Our work suggests a mechanism wherein a clean system, initially insensitive to interaction effects, can be made unstable to interactions upon the inclusion of weak static disorder. We dub this mechanism a ``disorder-driven Mott transition.'' Our result for 2D fermions also contrasts sharply with known results in one dimension, where a similar delocalized phase has been shown to be robust against the inclusion of weak interaction effects.
I describe a condensed matter system in terms of interacting quantum fields. In this electronic system, gauge interactions of non electromagnetic origin are generated effectively with a topological term in the effective action and play a leading role in describing the physics. Using the renormalization group and large-N expansion technique, I analyze the low energy sector of a U (1) × U (1) model in three dimensional space-time with a potential of sixth order in the scalar fields coupled to mixed Chern-Simons gauge fields. From the quantum effective potential, I derive various renormalization group functions and the fixed points associated with a quantum phase transition.