Bulletin of the American Physical Society
APS March Meeting 2014
Volume 59, Number 1
Monday–Friday, March 3–7, 2014; Denver, Colorado
Session B45: Topological Quantum Hall Phases |
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Sponsoring Units: FIAP Chair: Nickolas Bonesteel, Florida State University Room: Mile High Ballroom 4D |
Monday, March 3, 2014 11:15AM - 11:27AM |
B45.00001: Bulk-Edge Correspondence in 2+1-Dimensional Abelian Topological Phases Eugeniu Plamadeala, Meng Cheng, Michael Mulligan, Chetan Nayak, Jennifer Cano, Jon Yard The same bulk two-dimensional topological phase can have multiple distinct, fully-chiral edge phases. We show that this can occur in the integer quantum Hall and Abelian fractional quantum Hall states. We give a general criterion for the existence of multiple distinct chiral edge phases for the same bulk phase and discuss experimental consequences. We show that fermionic systems can have edge phases with only bosonic low-energy excitations and discuss a fermionic generalization of the relation between bulk topological spins and the central charge. The latter follows from our demonstration that every fermionic topological phase can be represented as a bosonic topological phase, together with some number of filled Landau levels. Our analysis shows that every Abelian topological phase can be decomposed into a tensor product of theories associated with prime numbers $p$ in which every quasiparticle has a topological spin that is a $p^n$-th root of unity for some $n$. [Preview Abstract] |
Monday, March 3, 2014 11:27AM - 11:39AM |
B45.00002: Distinguishing between edge phases of a bulk quantum Hall state Jennifer Cano, Meng Cheng, Michael Mulligan, Chetan Nayak, Eugeniu Plamadeala, Jon Yard The same bulk quantum Hall state can have multiple distinct, fully-chiral edge phases. This effect can occur at both integer and fractional quantum Hall states; examples include $\nu = 8$ and $12$ and the fractions $\nu = 8/7, 12/11, 8/15, 16/5$. This raises the question: given a quantum Hall device, how do we know which edge phase it is in? This is especially interesting when one edge phase has gapless fermionic excitations and the other does not. Since no bulk measurement can distinguish the states and their quasiparticles are identical, it is necessary to probe the edge directly. Here we discuss experimental probes that can distinguish between the possible edge phases. In addition, we consider interfaces between two edge phases and the localized zero energy modes that can reside at these interfaces. [Preview Abstract] |
Monday, March 3, 2014 11:39AM - 11:51AM |
B45.00003: Supersymmetry approach to delocalization transitions in a network model of the weak field quantum Hall effect and related models. Shanthanu Bhardwaj, Vagharsh Mkhitaryan, Ilya Gruzberg We consider a recently proposed network model of the integer quantum Hall (IQH) effect in a weak magnetic field. Using a supersymmetry approach, we reformulate the network model in terms of a superspin chain. A subsequent analysis of the superspin chain and the corresponding supersymmetric nonlinear sigma-model allows to establish the analytical form of the critical line of the weak-field IQH transition, which separates the Anderson insulator and the quantum Hall insulator phases. Our results also confirm the universality of the IQH transition, which is described by the same sigma model in strong and weak magnetic fields. [Preview Abstract] |
Monday, March 3, 2014 11:51AM - 12:03PM |
B45.00004: Loop Statistics in $SU(2)_k$ String-Net Models S.L. Sondhi, Vedika Khemani, Rahul Roy Topologically ordered quantum phases are often realized as condensates of highly-fluctuating, extended ``string-net'' degrees of freedom. We posit that the non-local quantum order in these phases manifests itself in universal, geometric properties of the underlying string-nets. In this work, we consider a mapping from the $SU(2)_k$ string-net models to generalized loop models and compute statistical properties of the resulting loops. In an appropriate classical limit, we find that the loop length distribution shows critical scaling with exponents that are independent of $k$. We also report loop-length scaling for the quantum $SU(2)_2$ and $SU(2)_3$ models. [Preview Abstract] |
Monday, March 3, 2014 12:03PM - 12:15PM |
B45.00005: Semiclassical theory of Hall viscosity Rudro Biswas Hall viscosity is an intriguing stress response in quantum Hall systems and is predicted to be observable via the conductivity in an inhomogeneous electric field. This has been studied extensively using a range of techniques, such as adiabatic transport, effective field theories, and Kubo formulae. All of these are, however, agnostic as to the distinction between strongly correlated quantum Hall states and non-interacting ones, where the effect arises due to the fundamental non-commuting nature of velocities and orbit positions in a magnetic field. In this talk I shall develop the semiclassical theory of quantized cyclotron orbits drifting in an applied inhomogeneous electric field and use it to provide a clear physical picture of how single particle properties in a magnetic field contribute to the Hall viscosity-dependence of the conductivity. [Preview Abstract] |
Monday, March 3, 2014 12:15PM - 12:27PM |
B45.00006: Fractionally charged bound states of an impurity in a fractional quantum Hall system Kelly Patton, Michael Geller The single-particle spectral function for an incompressible fractional quantum Hall state of the lowest Landau level (LLL) in the presence of a short-ranged attractive impurity potential is calculated via exact diagonalization. In contrast to the noninteracting case, where only a single bound state below the LLL, electron-electron interactions strongly renormalize the impurity potential, effectively giving it a finite range, which supports many quasi-bound states (long-lived resonances). Averaging the spectral weights $Z$ of the quasi-bound states and extrapolating to the thermodynamic limit, for filling factor $\nu = 1/3$ we find evidence consistent with localized fractionally charged $e/3$ quasiparticles. For $\nu = 2/5$, the results are slightly more ambiguous, due to finite size effects and possible bunching of Laughlin-quasiparticles. [Preview Abstract] |
Monday, March 3, 2014 12:27PM - 12:39PM |
B45.00007: Monte-Carlo Study of Phase Transitions out of Symmetry-Enriched Topological phases of bosons in Two-dimensions Jong Yeon Lee, Olexei Motrunich, Scott Geraedts In this work, we studied a statistical mechanics model of two species of bosons with mutual statistics $\theta=2\pi/n$ in (2+1) dimensions. This is a model for quasi-particles in a symmetry-enriched topological quantum phase of bosons with charge fractionalization, and by studying condensation of the quasi-particles we can access nearby phases. Through a reformulation, sign problem was eliminated and we could perform Monte Carlo simulation of this model. We focused on the phase transition point between the topological insulator and trivial Mott insulator to study critical properties of the transition. By measuring correlations in terms of original variables and dual variables, with finite size scaling, we could narrow down the region of criticality, and concluded it is a continuous multi-critical point. We extracted critical exponents for the topological phase transition. [Preview Abstract] |
Monday, March 3, 2014 12:39PM - 12:51PM |
B45.00008: Analyzing pseudo potentials in ``guiding-center-only'' approach Alexander Seidel, Zohar Nussinov, Jorge Dukelsky, Gerardo Ortiz A variety of short-range interactions are known whose zero energy modes successfully describe the low energy properties of various interesting phases in the fractional quantum Hall regime. The theoretical analysis of Haldane-type pseudo potentials and their generalizations is usually based on a first quantized picture, deriving nice analytical properties of their first quantized zero mode wave functions, which have polynomial form in most standard geometries. Recently, however, the second quantized -or guiding center- form of these pseudo-potentials has enjoyed much interest, e.g., in flat band solids. In such a context, the embedding of the problem into the lowest Landau level of some larger Hilbert space is artificial, and with the construction of new models in mind, it seems beneficial to understand how to systematically ``solve'' known pseudo-potential problems in a purely second quantized picture. He we discuss some general theorems that apply to the second quantized forms of pseudo-potential Hamiltonians, and allow for the derivation of many known properties of zero modes, in particular ``squeezing'', in a second quantized language, starting from a second quantized Hamiltonian. [1] Phys. Rev. B 88, 165303 (2013) [Preview Abstract] |
Monday, March 3, 2014 12:51PM - 1:03PM |
B45.00009: Bulk/Boundary Relations in Hydrodynamics with Quantum Anomalies Gustavo Monteiro, Alexander Abanov It is well-known that Quantum Hall systems can be described as incompressible fluids. Their effective hydrodynamics description contains anomalous topological terms that reflect broken parity. These terms together with gauge symmetry generate topologically protected gapless states propagating on the boundary. We consider similar relations between quantum anomalous terms in hydrodynamics of two and one-dimensional systems. Our starting point is the relativistic hydrodynamics in 2+1 dimensions with parity odd terms [1, 2]. These terms are present due to quantum anomalies in the underlying field theory. We introduce domain walls to our system and derive the propagating mode along these domain walls. These edge modes are chiral and their effective action generalizes the one found in [3]. Furthermore, they are present even in the absence of external magnetic field and do persist at non-zero temperatures. As result, we find some relations between the anomalous transport in the bulk and at the boundary. We also discuss similar reductions in higher dimensional cases. [1] A. Nicolis and D. T. Son, arXiv:1103.2137 [2] F. M. Haehl and M. Rangamani, arXiv:1305.6968 [3] S. Dubovsky, L. Hui, and A. Nicolis, arXiv:1107.0732 [Preview Abstract] |
Monday, March 3, 2014 1:03PM - 1:15PM |
B45.00010: Bipartite fluctuations and entanglement spectrum in quantum Hall states Alexandru Petrescu, H. Francis Song, Stephan Rachel, Zoran Ristivojevic, Christian Flindt, Nicolas Laflorencie, Israel Klich, Nicolas Regnault, Karyn Le Hur We exploit a general relation between bipartite fluctuations of particle number or spin and the real space bipartite entanglement entropy and the entanglement R\'enyi entropies for free fermion systems [Phys. Rev. B \textbf{85}, 035409 (2012)]. We apply this method to derive the real space entanglement entropy and entanglement spectrum [Phys. Rev. Lett. \textbf{101}, 010504 (2008)] of integer quantum Hall systems and Chern insulators, focusing on continuum models, edge models at quantum point contacts and the role of sine-Gordon terms, and finite-sized lattice models. Numerical efforts will be addressed for fractional quantum Hall systems. [Preview Abstract] |
Monday, March 3, 2014 1:15PM - 1:27PM |
B45.00011: Fractional quantum Hall droplet on a lattice Martin Claassen, Thomas Devereaux In analogy to the fractional quantum Hall (FQH) liquid on a disk, we study droplets of interacting electrons in a fractional Chern insulator, in a dispersionless band with non-zero Chern number $\mathcal{C}$. We describe how the quantum geometry of such a band naturally defines a basis of momentum-space Landau levels, with radially-localized wave functions that preserve lattice rotational symmetries, in direct analogy to the lowest Landau level in the continuum. This new approach permits a direct description of the interacting droplet in terms of Haldane pseudopotentials on the disk. We then provide numerical results for the formation of a FQH liquid. We deform the host lattice model via local adiabatic modifications to ideal models with flat Berry curvature and analyze the ground state wavefunction. For $\mathcal{C} >$ 1, we discuss generalizations of the FQH droplet as multicomponent FQH systems. [Preview Abstract] |
Monday, March 3, 2014 1:27PM - 1:39PM |
B45.00012: Multi-layer fractional quantum Hall states in lattice systems Layla Hormozi We study fractional quantum Hall states of interacting particles in lattice systems subject to external magnetic fields. When the number of flux quanta per lattice plaquette is close to a rational fraction, the lowest energy states can be mapped to degenerate lowest Landau levels in the continuum, where particles carry an extra degree of freedom -- a pseudospin or layer-index. We find a class of multi-layer fractional quantum Hall states that can form in these systems with different inter- and intra-layer interactions and show that topological and spectral properties of these states can be derived from different conformal field theories that are related by a condensation/orbifolding mechanism. [Preview Abstract] |
Monday, March 3, 2014 1:39PM - 1:51PM |
B45.00013: 2D electrons in a magnetic field. Linear responses to curvature and e/m fields Alexander Abanov, Andrey Gromov Two-dimensional electron gas in a quantizing magnetic field plays an important role in condensed matter physics. At the integer filling factor its linear responses to weak e/m fields are known as expansions in wave vectors and frequencies. We generalize these known results to gravitational and mixed responses considering the system in weakly curved background. Using the obtained expansions to all orders in wave vectors and frequencies we verify the exact relations between linear response functions following from the Galilean symmetry of the model [1-2] as well as phenomenological expressions derived in [3]. We present examples of the linear responses such as charge accumulation around a disclination defect (conic singularity), non-dissipative current perpendicular to the gradient of the scalar curvature, stress in the medium produced by the inhomogeneous e/m field, etc. \\[4pt] [1] C. Hoyos, D. T. Son: `` Hall viscosity from electromagnetic response'' \newline [2] B. Bradlyn, M. Goldstein, N. Read: ``Kubo formulas for viscosity: Hall viscosity, Ward identities, and the relation with conductivity'' \newline [3] A. Abanov: ``On the effective hydrodynamics of FQHE'' [Preview Abstract] |
Monday, March 3, 2014 1:51PM - 2:03PM |
B45.00014: Topological gaps without masses in driven graphene-like systems Thomas Iadecola, Titus Neupert, Claudio Chamon We illustrate the possibility of realizing band gaps in graphene-like systems that fall outside the existing classification of gapped Dirac Hamiltonians in terms of masses. As our primary example we consider a band gap arising due to time-dependent distortions of the honeycomb lattice. By means of an exact, invertible, and transport-preserving mapping to a time-independent Hamiltonian, we show that the system exhibits Chern-insulating phases with quantized Hall conductivities $\pm e^2/h$. The chirality of the corresponding gapless edge modes is controllable by both the frequency of the driving and the manner in which sublattice symmetry is broken by the dynamical lattice modulations. We demonstrate that, while these phases are in the same topological sector as the Haldane model, they are nevertheless separated from the latter by a gap-closing transition unless an extra parameter is added to the Hamiltonian. Finally, we discuss a promising possible realization of this physics in photonic lattices. [Preview Abstract] |
Monday, March 3, 2014 2:03PM - 2:15PM |
B45.00015: Majorana fermion qubit states and non-Abelian braiding statistics in quenched inhomogeneous spin ladders Yan Chen, Yinchen He In studying Majorana fermions (MFs) in a spin ladder model, we numerically show that their qubit state can be read out by measuring fusion excitations in quenched inhomogeneous spin ladders. We construct an exactly solvable T-junction spin ladder model that can be used to implement MF braid operations. With braiding simulated numerically as non-equilibrium quench processes, we verify that the MFs in our spin ladder model obey non-Abelian braiding statistics. Our scheme provides a promising platform to study exotic properties of MFs and a broad range of applications in topological quantum computation. [Preview Abstract] |
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