Two-dimensional Disordered Projected Branes: Stability and Quantum Criticality via Dimensional Reduction

TL;DR

This paper demonstrates that 2D disordered projected branes can replicate the phase diagram of 3D disordered systems, supporting stable metallic and semimetallic phases and exhibiting critical behavior similar to their 3D counterparts.

Contribution

It introduces 2D disordered projected branes as quantum holographic images of 3D systems, revealing stable phases and critical exponents comparable to 3D systems, which are inaccessible in conventional 2D lattices.

Findings

2D projected branes reproduce 3D phase diagrams

Stable metallic and semimetallic phases are observed in 2D branes

Critical exponents are close to those of 3D systems

Abstract

The interplay of disorder and dimensionality governs the emergence and stability of electronic phases in quantum materials and quantum phase transitions among them. While three-dimensional (3D) dirty Fermi liquids and Weyl semimetals support robust metallic states, undergoing disorder-driven Anderson localization transitions at strong disorder and the later ones exhibiting additional semimetal-to-metal transition at moderate disorder, conventional two-dimensional (2D) non-interacting systems localize for arbitrarily weak disorder. Here, we show that 2D disordered projected branes, constructed by systematically integrating out degrees of freedom from a 3D cubic lattice via the Schur decomposition, faithfully reproduce the full quantum phase diagram of their 3D parent systems. Using large-scale exact diagonalization and kernel polynomial method, we numerically demonstrate that 2D projected branes host stable metallic and semimetallic phases. Remarkably, the critical exponents governing the semimetal-to-metal and metal-insulator transitions on such 2D projected branes are sufficiently close to those of their 3D counterparts. Our findings thus establish 2D projected branes as genuine quantum holographic images of their higher-dimensional disordered parent crystals, supporting stable semimetallic and metallic phases that are otherwise inaccessible in conventional 2D lattices. Finally, we point to experimentally accessible metamaterial platforms, most notably the photonic lattices with tunable refractive-index disorder, as promising systems to realize and probe these phenomena.