Bulletin of the American Physical Society
APS March Meeting 2014
Volume 59, Number 1
Monday–Friday, March 3–7, 2014; Denver, Colorado
Session J43: Interaction Effects in Topological Insulators: Theory |
Hide Abstracts |
Sponsoring Units: DCMP Chair: Feng Liu, University of Utah Room: Mile High Ballroom 4B |
Tuesday, March 4, 2014 2:30PM - 2:42PM |
J43.00001: Lattice construction of pseudopotential Hamiltonians for Fractional Chern Insulators Ching Hua Lee, Xiao-Liang Qi Fractional Chern insulators (FCIs) are new realizations of fractional quantum Hall states in lattice systems without orbital magnetic field. These states can be mapped onto conventional fractional quantum Hall states through the Wannier state representation (WSR) (Phys. Rev. Lett. 107, 126803 (2011)). In this talk, I shall show how the WSR can be used to construct FCIs pseudopotential Hamiltonians that are interaction Hamiltonians with certain ideal model wavefunctions as exact ground states. These pseudopotential Hamiltonians can be approximated by short-ranged interactions in FCIs, with the range minimized by an optimal gauge choice for the Wannier states. I will illustrate this lattice construction by showing the explicit form of the lowest pseudopotential for a few commonly used FCI models like the lattice Dirac model and the checkerboard model with Chern number C=1, and the d-wave model and triangular lattice model with C=2. The proposed pseudopotential Hamiltonians have the 1/3 Laughlin state as their ground-state when C=1, and a topological nematic (330) state as their groundstate when C=2. The proposed states can be verified by future numerical works, and in particular provide a model Hamiltonian for topological nematic states that have not yet been realized numerically. [Preview Abstract] |
Tuesday, March 4, 2014 2:42PM - 2:54PM |
J43.00002: Electron-Hole Entanglement in a Quantum Spin Hall Insulator Koji Sato, Mircea Trif, Yaroslav Tserkovnyak We demonstrate that entangled electron-hole pairs can be produced and detected in a quantum spin Hall insulator with a constriction that allows for a weak inter-edge tunneling. A violation of a Bell inequality, which can be constructed in terms of low-frequency nonlocal current-current correlations, serves as a detection of the entanglement. We show that the maximum violation of a Bell inequality can be naturally achieved in this setup, without a need to fine tune tunneling parameters. This may provide a viable route to producing spin entanglement in the absence of any correlations and pairing, where spin-to-charge conversion is enabled by the helical edge structure of a quantum spin Hall insulator. [Preview Abstract] |
Tuesday, March 4, 2014 2:54PM - 3:06PM |
J43.00003: correlation effects in topological phase transitions Hsiang-Hsuan Hung, Victor Chua, Lei Wang, Gregory Fiete We study topological insulators/trivial insulators topological phase transitions in the Kane-Mele-Hubbard model using the projective quantum Monte Carlo method. We numerically compute the topological invariants and study topological phase transitions under correlation. We find that quantum fluctuation effects from interactions can act both to stabilize and destabilize topological phases, depending on the details of the model. When the one-body terms break the lattice symmetry, e.g. bond dimerization breaks the rotational symmetry in the Kane-Mele model, the Hubbard interaction destabilizes the topological insulator phase. On the other hand, when the one-body terms (e.g. the third-nearest neighbor hopping) preserves the lattice symmetry, the interaction stabilizes the topological phase. [Preview Abstract] |
Tuesday, March 4, 2014 3:06PM - 3:18PM |
J43.00004: Gravitational responses and entanglement for 2-dimensional chiral topological states Roger Mong, Michael Zaletel, Xiao-Liang Qi Chiral topological phases in 2+1D, which have a gapped bulk and gapless chiral edges, can be characterized by their response to deformations of spacetime. The leading order `gravitational response' is encoded in the gravitational and torsional Chern-Simons terms, which result in a chiral central charge and Hall viscosity respectively; however, it is not clear which aspects of these responses remain universal for a model without microscopic Lorentz invariance. We demonstrate how the chiral central charge and Hall viscosity may be extracted via an entanglement measure in the bulk, giving evidence for the correctness of a subset of the predicted responses. We also discuss some physical interpretations of the thermal responses. As a concrete example, we explicitly calculate the relevant bulk thermal responses and entanglement properties of a p+ip superconductor. [Preview Abstract] |
Tuesday, March 4, 2014 3:18PM - 3:30PM |
J43.00005: Numerical studies of band geometry of fractional topological insulators Thomas Jackson, Abishek Roy, Gunnar M\"oller, Rahul Roy One of the chief motivations behind the current interest in topological insulators is the possibility that they may offer an alternate, more experimentally accessible venue for studying fractional quantum Hall effect (FQHE) physics, as well as possible novel states arising from the larger phase space relative to the lowest Landau level. Roy [1] identified several sufficient conditions on the single-particle Berry curvature and quantum metric for the algebra of projected density operators to be isomorphic to the Girvin-MacDonald-Platzman algebra of the FQHE. Here, we study the influence of these conditions in determining the stability of topological phases arising from density-density interactions in fractionally filled Chern bands. We present numerical results on the correlations between single-particle band geometry and the gaps in the energy and entanglement spectra for the corresponding interacting many-body state in a variety of lattice models exhibiting fractional Chern insulator phases. There is a key geometrical distinction between two- and multiple-band models. We also discuss extensions of the $W_{\infty}$ algebra and explore connections between the quantum metric and Hall viscosity.\\[0pt] [1] R. Roy, arXiv:1208.2055. [Preview Abstract] |
Tuesday, March 4, 2014 3:30PM - 3:42PM |
J43.00006: A symmetry-protected many-body Aharonov-Bohm effect Luiz Santos, Juven Wang It is known as a purely quantum effect that a magnetic flux affects the real physics of a particle, such as the energy spectrum, even if the flux does not interfere with the particle's path - the Aharonov-Bohm effect. We examine an Aharonov-Bohm effect on a many-body wavefunction. Specifically, we study this many-body effect on the gapless edge states of a two dimensional bulk gapped phase protected by a global symmetry - the symmetry-protected topological (SPT) states. The many-body analogue of spectral shifts, the twisted wavefunction and the twisted boundary realization are identified in this SPT state. An explicit lattice construction of SPT edge states is derived, and a challenge of gauging its non-onsite symmetry is overcome. Agreement is found in the twisted spectrum between a numerical lattice calculation and a conformal field theory prediction. Talk based on arXiv:1310.8291 [Preview Abstract] |
Tuesday, March 4, 2014 3:42PM - 3:54PM |
J43.00007: Classification and Description of Bosonic Symmetry Protected Topological Phases with semiclassical Nonlinear Sigma models Zhen Bi, Alex Rasmussen, Cenke Xu Symmetry protected topological (SPT) phases are a new type of quantum disordered phases with certain symmetry G, which is intrinsically different from a trivial direct product state. Well-known examples include topological insulators, topological superconductors and the Haldane phase of spin-1 chain. We focus on the field theory description of Bosonic SPT phases in all physical spatial dimensions. We propose that many bosonic SPT phases with different symmetries on a d-dimensional lattice can be described and classified by the same O(d+2) Nonlinear Sigma Model (NLSM) of a semiclassical Landau order parameter field in (d+1)-dimensional space-time, with a topological $\Theta$-term. Our classification based on topological NLSMs is completely identical to the Group Cohomology Classification of bosonic SPT phases. Besides that, NLSMs formalism also allow us to describe explicit physical properties of SPT phases, such as the bulk wave functions and boundary theories. [Preview Abstract] |
Tuesday, March 4, 2014 3:54PM - 4:06PM |
J43.00008: Gapped symmetric boundaries of topological insulators Dung-Hai Lee, Yuan-Ming Lu Topological insulators (TIs) are gapped quantum phases which host symmetry-protected gapless boundary excitations. On the other hand, the boundary states can be gapped by spontaneously breaking symmetry. We show that topological defects on the symmetry-broken boundary cannot proliferate due to their fractional statistics. A gapped symmetric boundary, however, can be achieved between a TI phase and certain fractionalized phase by condensing the bound state of a topological defect and an anyon. Such a hybrid structure containing TI and fractionalized phase generally support ground state degeneracy on torus. [Preview Abstract] |
Tuesday, March 4, 2014 4:06PM - 4:18PM |
J43.00009: Chasing the Hofstadter Butterfly Indu Satija The experimental observation of the Hofstadter butterfly, the fascinating quantum fractal that also encodes the Chern numbers associated with quantum Hall state, continues to remain a challenging task. It may be possible to observe the fine structure of the butterfly, consisting of small gaps of the spectrum characterized by topological invariants greater than unity, with a resolution matching that of the Chern-$1$ gaps that form the skeleton of the butterfly. The tiny gaps of the butterfly emanating from a rational flux $p/q$ are found to be associated with infinity of possible solutions (of Diophantine equation )for the rational flux. Not supported by the simple square lattice nearest-neighbor hopping model of the Hofstadter system, these solutions are found to be hiding in neighborhood of these fluxes. By perturbing this simple system, it is possible to ``amplify'' these small gaps corresponding to higher Chern states where they replace the Chern $1$ gap of the Hofstadter butterfly. In other words, by tuning a parameter, it is possible to induce topological quantum phase transitions where the finer gaps become the new major gaps that dominate the spectrum. This may provide a possible pathway to see the topological landscape of the Hofstadter butterfly fractal in its entirety. [Preview Abstract] |
Tuesday, March 4, 2014 4:18PM - 4:30PM |
J43.00010: Precision of the quantum anomalous Hall effect in magnetic topological insulators Karin Everschor-Sitte, Matthias Sitte, Allan MacDonald The quantum Hall effect normally refers to quantized Hall conductivity due to Landau quantization, as observed in 2D electron systems. To produce a Hall effect, one has to break time-reversal symmetry which is conveniently accomplished by applying an external magnetic field. The precision of the quantized Hall effect which occurs near integer Landau level filling factors has been verified to more than 8 figures. There are no known limitations to the accurary of the effect in the limit of zero temperature. The internal magnetization of a system in combination with spin-orbit coupling can also break time-reversal symmetry \emph{without} a magnetic field and can lead to a quantum anomalous Hall effect (QAHE). Recently, the QAHE has been observed experimentally in thin films of chromium-doped (Bi,Sb)$_2$Te$_3$, a magnetic topological insulator, where at zero magnetic field the Hall resistance reaches the predicted quantized value of $h/e^2$ [1]. We address the precision of the QAHE focussing on the role of quantum and thermal fluctuations of the magnetization.\\[0.2em] \noindent [1] C. Chang \textit{et al.}, Science \textbf{340}, 167--170 (2013). [Preview Abstract] |
Tuesday, March 4, 2014 4:30PM - 4:42PM |
J43.00011: Phases of correlated spinless fermions on the honeycomb lattice Martin Hohenadler, Maria Daghofer We use exact diagonalization and cluster perturbation theory to address the role of strong interactions and quantum fluctuations for spinless fermions on the honeycomb lattice. We find quantum fluctuations to be very pronounced both at weak and strong interactions. A weak second-neighbor Coulomb repulsion $V_2$ induces a tendency toward an interaction-generated quantum anomalous Hall phase, as borne out in mean-field theory. However, quantum fluctuations prevent the formation of a stable quantum Hall phase before the onset of the charge-modulated phase predicted at large $V_2$ by mean-field theory. Consequently, the system undergoes a direct transition from the semimetal to the charge-modulated phase. For the latter, charge fluctuations also play a key role. While the phase, which is related to pinball liquids, is stabilized by the repulsion $V_2$, the energy of its low-lying charge excitations scales with the kinetic energy $t$, as in a band insulator. [Preview Abstract] |
Tuesday, March 4, 2014 4:42PM - 4:54PM |
J43.00012: Helical topological exciton condensates Paolo Michetti, Jan C. Budich, Bj\"orn Trauzettel We investigate a bilayer system of critical HgTe quantum wells each featuring a spin-degenerate pair of massless Dirac fermions. In the presence of an electrostatic inter-layer Coulomb coupling, we determine the exciton condensate order parameter of the system self-consistently. Calculating the bulk topological Z2 invariant of the resulting mean field Hamiltonian, we discover a novel time reversal symmetric topological exciton condensate state coined the helical topological exciton condensate. We argue that this phase can exist for experimentally relevant parameters. Interestingly, due to its multi-band nature, the present bilayer model exhibits a nontrivial interplay between spontaneous symmetry breaking and topology: Depending on which symmetry the condensate order parameter spontaneously picks in combined orbital and spin space, stable minima in the free energy corresponding to both trivial and nontrivial gapped states can be found. [Preview Abstract] |
Tuesday, March 4, 2014 4:54PM - 5:06PM |
J43.00013: Ferromagnetism and quantum anomalous Hall effect in half-saturated germanene Shin-Ming Huang, Chung-Yu Mou, Shi-Ting Lee Owing to the buckled structure of germanene, saturating one sublattice of atoms is workable. After studying cases of different percentages of saturation, we confirm that a narrow band always exist at the chemical potential which makes flat-band ferromagnetism possible. As the vacancy density increases, ferromagnetism becomes weaker. The magnetization of the ferromagnetism is directly relates to the saturation percentage, which makes ferromagnetic gap controllable. Importantly, we observe quantum anomalous Hall (QAH) states with Chern number one or two depending on the magnetization in the 1/4-saturation system. Our finding provides a potent method in the pursuit of room-temperature QAH effect. [Preview Abstract] |
Tuesday, March 4, 2014 5:06PM - 5:18PM |
J43.00014: Fractional Topological Phases in Generalized Hofstadter Bands with Arbitrary Chern Numbers Kai Sun, Yinghai Wu, Jainendra Jain We examine similarities and differences between topological flat bands with Chern numbers $C > 1$ and conventional quantum Hall multi-layers. By constructing generalized Hofstadter models that possess ``color-entangled'' flat bands, we provide an intuitive understanding of certain puzzling properties of $C > 1$ flat bands, which can effectively be mapped either to a single-layer or to a multi-layer model depending on the lattice configuration. We identify interacting systems in which the ground state degeneracy depends on whether the system consists of an even or odd number of unit cells along one particular direction, and discuss the relation between these observations and the previously proposed ``topological nematic states.'' Our study also provides a systematic way of stabilizing various fractional topological states in $C > 1$ flat bands. [Preview Abstract] |
Tuesday, March 4, 2014 5:18PM - 5:30PM |
J43.00015: Weak symmetry breaking in two dimensional topological insulators Chenjie Wang, Michael Levin We show that there exist 2D time reversal invariant fractionalized insulators with the property that both their boundary with the vacuum and their boundary with a topological insulator can be fully gapped without breaking any symmetries. This result leads us to an apparent paradox: we consider a geometry in which a disk-like region made up of a topological insulator is surrounded by an annular strip of a fractionalized insulator, which is in turn surrounded by the vacuum. If we gap both boundaries of the strip, we naively obtain an example of a gapped interface between a topological insulator and the vacuum that does not break any symmetries -- an impossibility. The resolution of this paradox is that this system spontaneously breaks time reversal symmetry in an unusual way, which we call weak symmetry breaking. In particular, we find that the only order parameters that are sensitive to the symmetry breaking are nonlocal operators that describe quasiparticle tunneling processes between the two edges of the strip; expectation values of local order parameters vanish exponentially in the limit of a wide strip. Also, we find that the symmetry breaking comes with a ground state degeneracy, but the degeneracy is topologically protected, rather than symmetry protected. [Preview Abstract] |
Follow Us |
Engage
Become an APS Member |
My APS
Renew Membership |
Information for |
About APSThe American Physical Society (APS) is a non-profit membership organization working to advance the knowledge of physics. |
© 2024 American Physical Society
| All rights reserved | Terms of Use
| Contact Us
Headquarters
1 Physics Ellipse, College Park, MD 20740-3844
(301) 209-3200
Editorial Office
100 Motor Pkwy, Suite 110, Hauppauge, NY 11788
(631) 591-4000
Office of Public Affairs
529 14th St NW, Suite 1050, Washington, D.C. 20045-2001
(202) 662-8700