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Fractonic critical point proximate to a higher-order topological insulator: How UV blend with IR?

Yizhi You, Julian Bibo, Taylor L. Hughes, Frank Pollmann

Published Jan 1, 2021• 6 citations
Publisher

Abstract

We propose an unconventional topological quantum phase transition connecting a higher-order topological insulator (HOTI) and a featureless Mott insulator sharing the same symmetry patterns. We delineate the effective theory description of the quantum critical point (QCP) by combining the bosonization approach and the coupled-stripe construction of 1D critical spin ladders. The phase transition theory is characterized by a critical dipole liquid theory with subsystem $U(1)$ symmetry whose low energy modes contain a Bose surface along the $k_x,k_y$ axis. Such a quantum critical point manifests fracton dynamics and the breakdown of the area law entanglement entropy due to the existence of a Bose surface. We numerically confirm this finding by measuring the entanglement entropy, topological Berry phase, and the static structure factor throughout the topological transition and compare it with our previous approach obtained from the percolation picture. A significant new element of our phase transition theory is that the infrared (IR) effective theory is controlled by short wave-length fluctuation with peculiar UV-IR mixing.

DOI
10.13140/rg.2.2.35681.74084

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We propose an unconventional topological quantum phase transition connecting a higher-order topological insulator (HOTI) and a featureless Mott insulator sharing the same symmetry patterns. We delineate the effective theory description of the quantum critical point (QCP) by combining the bosonization approach and the coupled-stripe construction of 1D critical spin ladders. The phase transition theory is characterized by a critical dipole liquid theory with subsystem U(1)U(1)U(1) symmetry whose low energy modes contain a Bose surface along the kx,kyk_x,k_ykx​,ky​ axis. Such a quantum critical point manifests fracton dynamics and the breakdown of the area law entanglement entropy due to the existence of a Bose surface. We numerically confirm this finding by measuring the entanglement entropy, topological Berry phase, and the static structure factor throughout the topological transition and compare it with our previous approach obtained from the percolation picture. A significant new element of our phase transition theory is that the infrared (IR) effective theory is controlled by short wave-length fluctuation with peculiar UV-IR mixing.
We propose an unconventional topological quantum phase transition connecting a higher-order topological insulator (HOTI) and a featureless Mott insulator sharing the same symmetry patterns. We construct an effective theory description of the quantum critical point (QCP) by combining a bosonization approach and the coupled-stripe construction of 1D critical spin ladders. The phase transition theory is characterized by a critical dipole liquid theory with subsystem U(1)U(1)U(1) symmetry whose low energy modes contain a Bose surface along the kx,kyk_x,k_ykx​,ky​ axis. Such a quantum critical point manifests fracton dynamics and the breakdown of the area law entanglement entropy due to the existence of a Bose surface. We numerically confirm our findings by measuring the entanglement entropy, topological rank-2 Berry phase, and the static structure factor throughout the topological transition and compare it with our previous approach obtained from the percolation picture. A significant new element of our phase transition theory is that the infrared~(IR) effective theory is controlled by short wave-length fluctuations with peculiar UV-IR mixing.
We propose an unconventional topological quantum phase transition between a higher-order topological insulator (HOTI) and a featureless Mott insulator, both sharing the same symmetry patterns. Our approach constructs an effective theory for the quantum critical point (QCP) by combining a bosonization technique with the coupled-stripe construction of 1D critical spin ladders. This phase transition is characterized by a critical dipole liquid theory with subsystem (1) symmetry, where the low-energy modes contain a Bose surface along the axis. This quantum critical point exhibits fracton dynamics and a breakdown of the area law for entanglement entropy, attributed to the presence of the Bose surface. We numerically validate our findings by measuring the entanglement entropy, topological rank-2 Berry phase, and static structure factor throughout the topological transition, comparing these results with our previous approach derived from the percolation picture. A significant new aspect of our phase transition theory is that the infrared (IR) effective theory is governed by short-wavelength fluctuations, demonstrating a unique UV-IR mixing.
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. Here we demonstrate that the existence of a two-dimensional 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 that the QCP is characterized by a critical dipole liquid theory with subsystem U(1) symmetry and the breakdown of the area law entanglement entropy which exhibits a logarithmic enhancement: Lln(L)Lln(L)Lln(L). Using the density matrix renormalization group method, we analyze the dipole stiffness together with the structure factor at the QCP, which provides strong evidence of a critical dipole liquid with a Bose surface, UV-IR mixing, and a dispersion relation $\ensuremath{\omega}={k}_{x}{k}_{y}.$
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 U(1)U(1)U(1) symmetry and the breakdown of the area law entanglement entropy which exhibits a logarithmic enhancement: Lln⁡(L)L \ln(L)Lln(L). 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.
We consider close-packed tiling models of geometric objects---a mixture of hardcore dimers and plaquettes---as a generalization of the familiar dimer models. Specifically, on an anisotropic cubic lattice, we demand that each site be covered by either a dimer on a zzz link or a plaquette in the $x\text{\ensuremath{-}}y$ plane. The space of such fully packed tilings has an extensive degeneracy. This maps onto a fracton-type ``higher-rank electrostatics,'' which can exhibit a plaquette-dimer liquid and an ordered phase. We analyze this theory in detail, using height representations and T-duality to demonstrate that the concomitant phase transition occurs due to the proliferation of dipoles formed by defect pairs. The resultant critical theory can be considered as a fracton version of the Kosterlitz-Thouless transition. A significant new element is its UV-IR mixing, where the low-energy behavior of the liquid phase and the transition out of it is dominated by local (short-wavelength) fluctuations, rendering the critical phenomenon beyond the renormalization group paradigm.
The deconfined quantum critical point, a prototype Landau-forbidden transition, could exist, in principle, in the phase transitions involving a symmetry-protected topological phase; however, examples of such kinds of transitions in physical systems are rare beyond one-dimensional systems. Here, using a density-matrix renormalization-group calculation, we unveil a bosonic integer quantum Hall phase in a two-dimensional correlated honeycomb lattice, by full identification of its internal structure from the topological K\mathbf{K}K matrix. Moreover, we demonstrate that imbalanced periodic chemical potentials can destroy the bosonic integer quantum Hall state and drive it into a featureless trivial (Mott) insulator, where all physical observables evolve smoothly across the critical point. At the critical point, the entanglement entropy reveals a characteristic scaling behavior, which is consistent with the critical field theory as an emergent QED3{\mathrm{QED}}_{3}QED3​ with two flavors of Dirac fermions.