The theory of avoided criticality in quantum motion in a random potential in high dimensions

Abstract

The density of states of a three dimensional Dirac equation with a random potential as well as in other problems of quantum motion in a random potential placed in sufficiently high spatial dimensionality appears to be singular at a certain critical disorder strength. This was seen numerically in a variety of studies as well as supported by detailed renormalization group calculations. At the same time it was suggested by a number of arguments accompanied by detailed numerical simulations that this singularity is rounded off by the rare region fluctuations of random potential, and that tuning the disorder past its critical value is not a genuine phase transition but rather a crossover. Here we develop an analytic theory which explains how rare region effects indeed lead to rounding off of the singularity and to the crossover replacing the transition. In particular, this theory relates the maximum correlation length at the crossover to the disorder induced density of states.

arXiv commentAn expanded version with typos fixed

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• Weyl semimetal to metal phase transitions driven by quasiperiodic potentials
• Do the surface Fermi arcs in Weyl semimetals survive disorder?
• Rare regions and avoided quantum criticality in disordered Weyl semimetals and superconductors
• Interplay between short-range correlated disorder and Coulomb interaction in nodal-line semimetals
• Nodal points of Weyl semimetals survive the presence of moderate disorder
• From weak to strong disorder in Weyl semimetals: Self-consistent Born approximation
• Electronic properties of disordered Weyl semimetals at charge neutrality
• Avoided quantum criticality in exact numerical simulations of a single disordered Weyl cone
• Anomalous Transport Signatures in Weyl Semimetals with Point Defects
• Condition for the emergence of a bulk Fermi arc in disordered Dirac-fermion systems
• Multifractality at the Weyl semimetal-diffusive metal transition for generic disorder
• Fermi arcs and surface criticality in dirty Dirac materials
• Topological diffusive metal in amorphous transition metal monosilicides
• Nodal vacancy bound states and resonances in three-dimensional Weyl semimetals
• Non-Anderson critical scaling of the Thouless conductance in 1D
• Duality between disordered nodal semimetals and systems with power-law hopping
• Surface quantum critical phenomena in disordered Dirac semimetals
• Chiral anomaly without Landau levels: From the quantum to the classical regime
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