Boundary Criticality in the 2d Random Quantum Ising Model

TL;DR

This paper uses a numerical real-space renormalization group to analyze boundary criticality in a 2D disordered quantum Ising model, revealing three distinct boundary phases and universal scaling behaviors.

Contribution

It introduces a scalable RSRG method for studying boundary criticality in large 2D disordered quantum systems, identifying multiple boundary universality classes.

Findings

Identified three classes of boundary criticality.

Extracted universal scaling exponents for correlations.

Demonstrated the method's applicability to large disordered systems.

Abstract

The edge of a quantum critical system can exhibit multiple distinct types of boundary criticality. We use a numerical real-space renormalization group (RSRG) to study the boundary criticality of a 2d quantum Ising model with random exchange couplings and transverse fields, whose bulk exhibits an infinite randomness critical point. This approach enables an asymptotically numerically exact extraction of universal scaling data from very large systems with many thousands of spins that cannot be efficiently simulated directly. We identify three distinct classes of boundary criticality, and extract key scaling exponents governing boundary-boundary and boundary-bulk correlations and dynamics. We anticipate that this approach can be generalized to studying a broad class of (disordered) boundary criticality, including symmetry-enriched criticality and edge modes of gapless symmetry-protected topological states, in contexts were other numerical methods are restricted to one-dimensional chains.