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Register a new userTwo dimensional metallic phases from disordered QED$_3$
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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 (QED$_3$) 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 QED$_3$ with weak mass disorder exhibits a stable, dirty metallic phase in which both interactions and disorder play important roles.
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We investigate the effects of quenched randomness on topological quantum phase transitions in strongly interacting two-dimensional systems. We focus first on transitions driven by the condensation of a subset of fractionalized quasiparticles (`anyons) identified with `electric charge excitations of a phase with intrinsic topological order. All other anyons have nontrivial mutual statistics with the condensed subset and hence become confined at the anyon condensation transition. Using a combination of microscopically exact duality transformations and asymptotically exact real-space renormalization group techniques applied to these two-dimensional disordered gauge theories, we argue that the resulting critical scaling behavior is `superuniversal across a wide range of such condensation transitions, and is controlled by the same infinite-randomness fixed point as that of the 2D random transverse-field Ising model. We validate this claim using large-scale quantum Monte Carlo simulations that allow us to extract zero-temperature critical exponents and correlation functions in (2+1)D disordered interacting systems. We discuss generalizations of these results to a large class of ground-state and excited-state topological transitions in systems with intrinsic topological order as well as those where topological order is either protected or enriched by global symmetries. When the underlying topological order and the symmetry group are Abelian, our results provide prototypes for topological phase transitions between distinct many-body localized phases.
We report the observation of a metal-insulator transition in a two-dimensional electron gas in silicon. By applying substrate bias, we have varied the mobility of our samples, and observed the creation of the metallic phase when the mobility was high enough ($mu ~> 1 m^2/Vs$), consistent with the assertion that this transition is driven by electron-electron interactions. In a perpendicular magnetic field, the magnetoconductance is positive in the vicinity of the transition, but negative elsewhere. Our experiment suggests that such behavior results from a decrease of the spin-dependent part of the interaction in the vicinity of the transition.
When translational symmetry is broken by bulk disorder, the topological nature of states in topological crystalline systems may change depending on the type of disorder that is applied. In this work, we characterize the phases of a one-dimensional (1D) chain with inversion and chiral symmetries, where every disorder configuration is inversion-symmetric. By using a basis-independent formulation for the inversion topological invariant, chiral winding number, and bulk polarization, we are able to construct phase diagrams for these quantities when disorder is present. We show that unlike the chiral winding number and bulk polarization, the inversion topological invariant can fluctuate when the bulk spectral gap closes at strong disorder. Using the position-space renormalization group, we are able to compare how the inversion topological invariant, chiral winding number and bulk polarization behave at low energies in the strong disorder limit. We show that with inversion symmetry-preserving disorder, the value of the inversion topological invariant is determined by the inversion eigenvalues of the states at the inversion centers, while quantities such as the chiral winding number and the bulk polarization still have contributions from every state throughout the chain. We also show that it is possible to alter the value of the inversion topological invariant in a clean system by occupying additional states at the inversion centers while keeping the bulk polarization fixed. We discuss the implications of our results for topological crystalline phases in higher-dimensional electronic systems, and in ultra-cold atomic systems.
We consider the two dimensional disordered Bose gas which present a metallic state at low temperatures. A simple model of an interacting Bose system in a random field is propose to consider the interaction effect on the transition in the metallic state.
The QED$_3$-Gross-Neveu model is a (2+1)-dimensional U(1) gauge theory involving Dirac fermions and a critical real scalar field. This theory has recently been argued to represent a dual description of the deconfined quantum critical point between Neel and valence bond solid orders in frustrated quantum magnets. We study the critical behavior of the QED$_3$-Gross-Neveu model by means of an epsilon expansion around the upper critical space-time dimension of $D_c^+=4$ up to the three-loop order. Estimates for critical exponents in 2+1 dimensions are obtained by evaluating the different Pade approximants of their series expansion in epsilon. We find that these estimates, within the spread of the Pade approximants, satisfy a nontrivial scaling relation which follows from the emergent SO(5) symmetry implied by the duality conjecture. We also construct explicit evidence for the equivalence between the QED$_3$-Gross-Neveu model and a corresponding critical four-fermion gauge theory that was previously studied within the 1/N expansion in space-time dimensions 2<D<4.
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