Boundary Criticality of Topological Quantum Phase Transitions in $2d$ systems

Abstract

We discuss the boundary critical behaviors of two dimensional quantum phase transitions with fractionalized degrees of freedom in the bulk, motivated by the fact that usually it is the $1d$ boundary that is exposed and can be conveniently probed in many experimental platforms. In particular, we mainly discuss boundary criticality of two examples: i. the quantum phase transition between a $2d$ $Z_2$ topological order and an ordered phase with spontaneous symmetry breaking; ii. the continuous quantum phase transition between metal and a particular type of Mott insulator (U(1) spin liquid). This theoretical study could be relevant to many purely $2d$ systems, where recent experiments have found correlated insulator, superconductor, and metal in the same phase diagram.

arXiv comment6 pages, 2 figures

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• Gapless topological phases and symmetry-enriched quantum criticality
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• Gauge Enhanced Quantum Criticality Between Grand Unifications: Categorical Higher Symmetry Retraction
• Quantum phase transition between topologically distinct quantum critical points
• Boundary operator expansion and extraordinary phase transition in the tricritical O(N) model
• Boundary and defect criticality in topological insulators and superconductors
• Boundary criticality in two-dimensional interacting topological insulators