Bulletin of the American Physical Society
APS March Meeting 2019
Volume 64, Number 2
Monday–Friday, March 4–8, 2019; Boston, Massachusetts
Session L07: Theory of Topological Phases |
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Sponsoring Units: DCMP Chair: Itamar Kimchi, University of Colorado at Boulder Room: BCEC 109B |
Wednesday, March 6, 2019 11:15AM - 11:27AM |
L07.00001: Anomaly manifestations in topological insulator surfaces with strong correlations and disorder Itamar Kimchi, Yang-Zhi Chou, Rahul Nandkishore, Michael A Hermele, Leo R Radzihovsky Three dimensional topological insulators exhibit a bulk quantum anomaly that protects certain properties of their surface. For example, theoretical studies of weakly interacting strong and weak topological insulators show that their surface stays conducting, even with arbitrarily strong disorder, as long as the relevant symmetries are preserved on average. However, the combination of strong interactions and disorder offers theoretical questions which have not yet been addressed. Here we address this interplay and show that it can lead to a type of localized surface state, even while the disorder ensemble preserves all symmetries. We discuss how the quantum anomaly is manifested within the localized surface. These minimal manifestations of the quantum anomaly can constrain possible Lieb-Schultz-Mattis-type theorems for disordered systems. |
Wednesday, March 6, 2019 11:27AM - 11:39AM |
L07.00002: Free and Interacting SRE Phases of Fermions: Beyond the Ten-Fold Way Yu-An Chen, Anton Kapustin, Alex Turzillo, Minyoung You It is well-known that sufficiently strong interactions can destabilize some SPT phases of free fermions, while others remain stable even in the presence of interactions. It is also known that certain interacting phases cannot be realized by free fermions. We systematically study both of these phenomena in low dimensions and determine the map from free to interacting SPT phases for an arbitrary unitary symmetry G. In particular, in dimension zero and one we describe precisely which SPT phases can be realized by free fermions. We show that in dimension three there are no non-trivial free fermionic SPT phases with a unitary symmetry. We also describe how to compute invariants characterizing interacting phases for free band Hamiltonians with symmetry G (in any dimension) using only representation theory. |
Wednesday, March 6, 2019 11:39AM - 11:51AM |
L07.00003: Emergent Dirac fermions in Composite-Fermi-Liquids. Jie Wang, Edward H Rezayi, Frederick D Haldane Composite Fermi Liquids (CFLs) are compressible states that can occur for 2D interacting fermions in the lowest Landau level at 1/2m Landau level fillings when m is an integer. They have been understood as Fermi seas of electromagnetic-flux-attached fermions due to Halperin, Lee and Read. At 1/2 filling, an alternative particle-hole symmetric description based on Dirac fermions was proposed by Son. In this talk, we numerically examined the Berry phase associated with transporting one composite fermion around the Fermi sea at filling 1/2 and 1/4. At one-half, a PI Berry curvature singularity was observed [1,2], supporting Son’s effective theory. At one-quarter, we found a uniform Berry curvature and an additional PI strength at Fermi sea center. We explained the 1/4 phenomenon from CFL model wavefunctions. We also proposed a flux-attached Dirac fermion effective action [3], which generalized Son’s theory from 1/2 filling to all other filling fractions. The Fermi-sea in this new theory is interpreted as formed by internal-gauge-flux-attached Dirac fermions. |
Wednesday, March 6, 2019 11:51AM - 12:03PM |
L07.00004: Fragile topological phases in interacting systems Dominic Else, Hoi Chun Po, Haruki Watanabe Topological phases of matter are defined by their nontrivial patterns of ground-state quantum entanglement, which is irremovable so long as the excitation gap and the protecting symmetries, if any, are maintained. Recent studies on noninteracting electrons in crystals have unveiled a peculiar variety of topological phases, which harbors nontrivial entanglement that can be dissolved simply by the the addition of entanglement-free, but charged, degrees of freedom. Such topological phases have a weaker sense of robustness than their conventional counterparts, and are therefore dubbed "fragile topological phases." In this work, we show that fragile topology is a general concept prevailing beyond systems of noninteracting electrons. We identify the key ingredients for fragile topological phases, and demonstrate their existence not only in interacting systems of fermions, but also bosons. |
Wednesday, March 6, 2019 12:03PM - 12:15PM |
L07.00005: Gapped boundary theory of the twisted gauge theory model of three-dimensional topological orders Hongyu Wang, Yingcheng Li, Yuting Hu, Yidun Wan We extend the twisted gauge theory model of topological orders in three spatial dimensions to the case where the three spaces have two dimensional boundaries. We achieve this by systematically constructing the boundary Hamiltonians that are compatible with the bulk Hamiltonian. Given the bulk Hamiltonian defined by a gauge group G and a four-cocycle ω in the fourth cohomology group of G over U(1), we construct a gapped boundary Hamiltonian using {K, α}, with a subgroup K ⊆ G and a 3-cochain α of K over U(1), which satisfies the generalized Frobenius condition. The Hamiltonian is invariant under the topological renormalization group flow (via Pachner moves). Each solution {K, α} to the generalized Frobenius condition specifies a gapped boundary condition. We derive a closed-form formula of the ground state degeneracy of the model on a three-cylinder, which can |
Wednesday, March 6, 2019 12:15PM - 12:27PM |
L07.00006: SU(3) trimer resonating-valence-bond state on the square lattice Xiaoyu Dong, Ji-Yao Chen, Hong-Hao Tu We propose and study an SU(3) trimer resonating-valence-bond (tRVB) state with C4v point- group symmetry on the square lattice. By devising a projected entangled-pair state (PEPS) representation, we show that all (connected) correlation functions between local operators in this SU(3) tRVB state decay exponentially, indicating its gapped nature. We further calculate the modular S and T matrices by constructing all nine topological sectors on a torus and establish the existence of Z3 topological order in this SU(3) tRVB state. |
Wednesday, March 6, 2019 12:27PM - 12:39PM |
L07.00007: Quantum phase transitions between gapped topological phases: a percolation approach Xin Dai, Saad Khalid, Ilya A Gruzberg, Yuanming Lu We study continuous quantum phase transitions between two gapped topological orders, where a gapped boundary exists at the interface of the two phases. Using a percolation picture, we derive the effective Hamiltonian and the universality class of the quantum phase transition. |
Wednesday, March 6, 2019 12:39PM - 12:51PM |
L07.00008: Anyon exclusions statistics on surfaces with gapped boundaries Yingcheng Li, Yidun Wan, Hongyu Wang, Yuting Hu Anyon exclusion statistics, proposed by Haldane, generalizes the Bose-Einstein and Fermi-Dirac statistics. When fusion of anyons is involved, certain ‘pseudo-species’ anyons appear in the exotic statistical weights of non-Abelian anyon systems, whose meaning and significance remains an open problem. The relevant past studies had considered only anyon systems without any physical boundary. In this paper, we propose an extended anyon exclusion statistics on surfaces with gapped boundaries, introducing mutual exclusion statistics between anyons as well as the boundary components. We present a formula for the statistical weight of many-anyon states obeying the proposed statistics. We develop a systematic basis construction for non-Abelian anyons on any Riemann surfaces with gapped boundaries. The basis construction offers a standard way to read off a canonical set of statistics parameters and hence write down the extended statistical weight of the anyon system being studied. The basis construction reveals that a pseudo-species has different ‘excitation’ modes corresponding to good quantum numbers of subsystems of a non-Abelian anyon system. This is important because often (e.g., in topological quantum computing) we may be concerned about only the entanglement between such subsystems. |
Wednesday, March 6, 2019 12:51PM - 1:03PM |
L07.00009: Lattice model constructions for gapless domain walls between topological phases Chenfeng Bao, Shuo Yang, Chenjie Wang, Zhengcheng Gu Lattice models of gapless domain walls between twisted and untwisted gauge theories of finite group G are constructed systematically. As simple examples, we numerically studied the gapless domain walls between twisted and untwisted Z_N (with N<6) gauge models in 2+1D using the state-of-art loop optimization of tensor network renormalization algorithm. We also studied the physical mechanism for these gapless domain walls and obtained quantum field theory descriptions that agree perfectly with our numerical results. By taking the advantage of the systematic classification and construction of twisted gauge models using group cohomology theory, we systematically construct general lattice models to realize gapless domain walls for arbitrary finite symmetry group G. Such constructions can be generalized into arbitrary dimensions and might provide us with a systematical way to study gapless domain walls and topological quantum phase transitions. |
Wednesday, March 6, 2019 1:03PM - 1:15PM |
L07.00010: Effect of Electron-Phonon Interactions on Dirac Fermions Yuxi Zhang, George Batrouni, Wei-ting Chiu, Natanael de Carvalho Costa, Huaiming Guo, Richard Theodore Scalettar The effect of electron-electron interactions on Dirac fermions, and the possibility of an intervening spin liquid phase between the semi-metal and antiferromagnetic (AF) regimes, has been a focus of intense quantum simulation effort over the last five years. We use determinant quantum Monte Carlo (DQMC) to study the Holstein model on Honeycomb lattice and pi-flux lattice and explore the role of electron-phonon interactions on Dirac fermions. We show that they give rise to charge density wave (CDW) order, and present evidence that this occurs only above a finite critical interaction strength. We evaluate the temperature for the transition into the CDW which, unlike the AF transition, can occur at finite values owing to the discrete nature of the broken symmetry. |
Wednesday, March 6, 2019 1:15PM - 1:27PM |
L07.00011: Charge-Density-Wave Transitions of Dirac Fermions Coupled to Phonons Chuang Chen, Xiao Yan Xu, Zi Yang Meng, Martin Hohenadler The spontaneous generation of charge-density-wave order in a Dirac fermion system via the natural mechanism of electron-phonon coupling is studied in the framework of the Holstein model on the honeycomb lattice. Using two independent and unbiased quantum Monte Carlo methods, the phase diagram as a function of temperature and coupling strength is determined. It features a quantum critical point as well as a line of thermal critical points. Finite-size scaling appears consistent with fermionic Gross-Neveu-Ising universality for the quantum phase transition, and bosonic Ising universality for the thermal phase transition. The critical temperature has a maximum at intermediate couplings. Our findings motivate experimental efforts to identify or engineer Dirac systems with sufficiently strong and tunable electron-phonon coupling. |
Wednesday, March 6, 2019 1:27PM - 1:39PM |
L07.00012: Diagnosing fractionalization and anyonic statistics in magnetic insulators via noise magnetometry with spin qubits Shubhayu Chatterjee, Joaquin Rodriguez Nieva, Eugene Demler Two-dimensional magnetic insulators exhibit a plethora of competing ground states, such as ordered (anti)ferromagnets, quantum spin liquids with topological order and anyonic excitations, and random singlet phases emerging in the presence of disorder and frustration. We propose that single spin qubits, which interact directly with the low-energy excitations of magnetic insulators, can be used as a diagnostic of magnetic ground states. Experimentally tunable parameters, such as qubit level splitting, sample temperature, and qubit-sample distance, can be used to measure spin correlations with energy and wavevector resolution. Such resolution can be exploited to distinguish between fractionalized excitations in spin liquids and spin waves in magnetically ordered states, or to detect anyonic statistics in systems with a finite energy gap. |
Wednesday, March 6, 2019 1:39PM - 1:51PM |
L07.00013: Chiral Tricritical Point: A New Universality Class in Dirac Systems Shuai Yin, Shao-Kai Jian, Hong Yao Tricriticality, as a sister of criticality, is a fundamental and absorbing issue in condensed-matter physics. It has been verified that the bosonic Wilson-Fisher universality class can be changed by gapless fermionic modes at criticality. However, the counterpart phenomena at tricriticality have rarely been explored. In this Letter, we study a model in which a tricritical Ising model is coupled to massless Dirac fermions. We find that the massless Dirac fermions result in the emergence of a new tricritical point, which we refer to as the chiral tricritical point (CTP), at the phase boundary between the Dirac semimetal and the charge-density wave insulator. From functional renormalization group analysis of the effective action, we obtain the critical behaviors of the CTP, which are qualitatively distinct from both the tricritical Ising universality and the chiral Ising universality. We further extend the calculations of the chiral tricritical behaviors of Ising spins to the case of Heisenberg spins. The experimental relevance of the CTP in two-dimensional Dirac semimetals is also discussed. |
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