Pristine and Pseudo-gapped Boundaries of the Deconfined Quantum Critical Points

TL;DR

This paper explores the complex boundary phenomena of deconfined quantum critical points (DQCP), revealing various edge states and pseudogap behaviors influenced by bulk fluctuations and boundary conditions, with implications for quantum information and weak measurements.

Contribution

It introduces a detailed analysis of boundary effects in DQCPs, highlighting the emergence of pseudogap behaviors and the impact of boundary conditions on edge states, including quantum information perspectives.

Findings

Rich boundary states including pseudogap behavior.

Bulk fluctuations influence edge state properties.

Weak measurements alter boundary conditions and correlator behavior.

Abstract

Bulk topology and criticality can both lead to nontrivial boundary effects. Topological orders are often characterized by their robust edge states, while bulk critical points can have different boundary scalings governed by boundary conditions. The interplay between these two different boundary effects is an intriguing problem. The boundary of the deconfined quantum critical point (DQCP) is the ideal platform for the interplay of the two boundary effects, as the DQCP is also an intrinsically gapless symmetry protected topological (igSPT) state. In this work we discuss the boundary of several analogues of the DQCP. We demonstrate that the fluctuation of the bulk order parameters and their various boundary conditions lead to a rich possibility of the edge states, including a "pseudogap" (or super power-law decay) behavior. We also discuss the quantum information perspective of our work, i.e. the implication of our results on DQCP under weak-measurement. Weak-measurement followed by post-selection can change the boundary condition at the temporal boundary in the path-integral representation of a density matrix, which will lead to different behaviors of the "strange correlator".