 Award ID(s):
 1846109
 NSFPAR ID:
 10400891
 Date Published:
 Journal Name:
 npj Quantum Materials
 Volume:
 7
 Issue:
 1
 ISSN:
 23974648
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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Abstract The experimental discovery of the fractional Hall conductivity in twodimensional electron gases revealed new types of quantum particles, called anyons, which are beyond bosons and fermions as they possess fractionalized exchange statistics. These anyons are usually studied deep inside an insulating topological phase. It is natural to ask whether such fractionalization can be detected more broadly, say near a phase transition from a conventional to a topological phase. To answer this question, we study a strongly correlated quantum phase transition between a topological state, called a $${{\mathbb{Z}}}_{2}$$ Z 2 quantum spin liquid, and a conventional superfluid using largescale quantum Monte Carlo simulations. Our results show that the universal conductivity at the quantum critical point becomes a simple fraction of its value at the conventional insulatortosuperfluid transition. Moreover, a dynamically selfdual optical conductivity emerges at low temperatures above the transition point, indicating the presence of the elusive vison particles. Our study opens the door for the experimental detection of anyons in a broader regime, and has ramifications in the study of quantum materials, programmable quantum simulators, and ultracold atomic gases. In the latter case, we discuss the feasibility of measurements in optical lattices using current techniques.more » « less

Abstract We determine the phase diagram of a bilayer, YaoLee spinorbital model with interlayer interactions (
J ), for several stackings and moiré superlattices. For AA stacking, a gapped quantum spin liquid phase emerges at a finite$${{\mathbb{Z}}}_{2}$$ ${Z}_{2}$J _{c}. We show that this phase survives in the wellcontrolled largeJ limit, where an isotropic honeycomb toric code emerges. For moiré superlattices, a finiteq interlayer hybridization is stabilized. This connects inequivalent Dirac points, effectively ‘untwisting’ the system. Our study thus provides insight into the spinliquid phases of bilayer spinorbital Kitaev materials. 
null (Ed.)Strong interactions between electrons occupying bands of opposite (orlike) topological quantum numbers (Chern =\pm1 = ± 1 ),and with flat dispersion, are studied by using lowest Landau level (LLL)wavefunctions. More precisely, we determine the ground states for twoscenarios at halffilling: (i) LLL’s with opposite sign of magneticfield, and therefore opposite Chern number; and (ii) LLL’s with the samemagnetic field. In the first scenario – which we argue to be a toy modelinspired by the chirally symmetric continuum model for twisted bilayergraphene – the opposite Chern LLL’s are Kramer pairs, and thus thereexists timereversal symmetry ( \mathbb{Z}_2 ℤ 2 ).Turning on repulsive interactions drives the system to spontaneouslybreak timereversal symmetry – a quantum anomalous Hall state describedby one particle per LLL orbital, either all positive Chern {++\cdots+}\rangle  + + ⋯ + ⟩ or all negative {\cdots}\rangle  − − ⋯ − ⟩ .If instead, interactions are taken between electrons of likeChernnumber, the ground state is an SU(2) S U ( 2 ) ferromagnet, with total spin pointing along an arbitrary direction, aswith the \nu=1 ν = 1 spin \frac{1}{2} 1 2 quantum Hall ferromagnet. The ground states and some of theirexcitations for both of these scenarios are argued analytically, andfurther complimented by density matrix renormalization group (DMRG) andexact diagonalization.more » « less

Certain patterns of symmetry fractionalization in topologicallyordered phases of matter are anomalous, in the sense that they can onlyoccur at the surface of a higher dimensional symmetryprotectedtopological (SPT) state. An important question is to determine how tocompute this anomaly, which means determining which SPT hosts a givensymmetryenriched topological order at its surface. While special casesare known, a general method to compute the anomaly has so far beenlacking. In this paper we propose a general method to compute relativeanomalies between different symmetry fractionalization classes of agiven (2+1)D topological order. This method applies to all types ofsymmetry actions, including anyonpermuting symmetries and generalspacetime reflection symmetries. We demonstrate compatibility of therelative anomaly formula with previous results for diagnosing anomaliesfor \mathbb{Z}_2^{T} ℤ 2 T spacetime reflection symmetry (e.g. where timereversal squares to theidentity) and mixed anomalies for U(1) \times \mathbb{Z}_2^{T} U ( 1 ) × ℤ 2 T and U(1) \rtimes \mathbb{Z}_2^{T} U ( 1 ) ⋊ ℤ 2 T symmetries. We also study a number of additional examples, includingcases where spacetime reflection symmetries are intertwined innontrivial ways with unitary symmetries, such as \mathbb{Z}_4^{T} ℤ 4 T and mixed anomalies for \mathbb{Z}_2 \times \mathbb{Z}_2^{T} ℤ 2 × ℤ 2 T symmetry, and unitary \mathbb{Z}_2 \times \mathbb{Z}_2 ℤ 2 × ℤ 2 symmetry with nontrivial anyon permutations.more » « less

Abstract Robustness to disorder is the defining property of any topological state. The ultimate disorder limits to topological protection are still unknown, although a number of theories predict that even in the amorphous state a quantized conductance might yet reemerge. Here we report that in strongly disordered thin films of the topological material Sb_{2}Te_{3}
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