Fracton Critical Point in Higher-Order Topological Phase Transition
Abstract
The theory of quantum phase transitions separating different phases with distinct symmetry patterns at zero temperature is one of the foundations of modern quantum many-body physics. In this paper we demonstrate that the existence of a 2D topological phase transition between a higher-order topological insulator (HOTI) and a trivial Mott insulator with the same symmetry eludes this paradigm. We present a theory of this quantum critical point (QCP) driven by the fluctuations and percolation of the domain walls between a HOTI and a trivial Mott insulator region. Due to the spinon zero modes that decorate the rough corners of the domain walls, the fluctuations of the phase boundaries trigger a spinon-dipole hopping term with fracton dynamics. Hence we find the QCP is characterized by a critical dipole liquid theory with subsystem symmetry and the breakdown of the area law entanglement entropy which exhibits a logarithmic enhancement: . Using the density matrix renormalization group (DMRG) method, we analyze the dipole stiffness together with structure factor at the QCP which provide strong evidence of a critical dipole liquid with a Bose surface. These numerical signatures further support the fracton dynamics of the QCP, and suggest a new paradigm for 2D quantum criticality proximate to a topological phase.
Cite
@article{arxiv.2008.01746,
title = {Fracton Critical Point in Higher-Order Topological Phase Transition},
author = {Yizhi You and Julian Bibo and Frank Pollmann and Taylor L. Hughes},
journal= {arXiv preprint arXiv:2008.01746},
year = {2020}
}