Bulletin of the American Physical Society
APS March Meeting 2017
Volume 62, Number 4
Monday–Friday, March 13–17, 2017; New Orleans, Louisiana
Session X24: Transport, Geometry and Entanglement in Fractional Quantum Hall EffectInvited
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Sponsoring Units: DCMP Chair: Jainendra Jain, Pennsylvania State University Room: New Orleans Theater C |
Friday, March 17, 2017 8:00AM - 8:36AM |
X24.00001: Microscopic studies of geometry in the fractional quantum Hall effect Invited Speaker: Zlatko Papic Recently, there has been renewed interest in the fractional quantum Hall effect due to emerging connections between topological order, geometry and broken symmetry. Incompressible fluids, like Laughlin states, have been shown to have intrinsic degrees of freedom that can be viewed as "quantum geometry". These degrees of freedom play an important role in the low-energy physics of incompressible fluids, but they are also tied to the breaking of rotational invariance, which allows for the co-existence of topological order and broken symmetry in the form of "nematic" quantum Hall states. In this talk, I will present an overview of the microscopic studies of geometry in the fractional quantum Hall effect focusing on its physical probes, such as the band mass anisotropy and tilted magnetic field. I will also introduce a generalization of the Haldane pseudopotentials to the case where rotational symmetry is explicitly broken. This approach not only facilitates the numerical description of anisotropic quantum Hall systems, but also reveals new types of bound “molecular” states. Some applications of generalized Haldane pseudopotentials will be discussed, including systems with tilted magnetic field, the nematic quantum Hall effect, and fractional Chern insulators where the anisotropy is intrinsically present due to the underlying lattice structure. [Preview Abstract] |
Friday, March 17, 2017 8:36AM - 9:12AM |
X24.00002: Theory of Nematic Fractional Quantum Hall State Invited Speaker: Yizhi You Rotation symmetry can be spontaneously broken in the background of fractional quantum Hall fluids. The resulting nematic state is characterized by an order parameter that represents these quadrupolar fluctuations, which play the role of fluctuations of the local geometry of the quantum fluid. We demonstrate that the low-energy effective theory of the nematic order parameter has z=2 dynamical scaling exponent, due to a Berry phase term of the order parameter, which is related to the nondissipative Hall viscosity. By investigating the spectrum of collective excitations, we demonstrate that the mass gap of the Girvin-MacDonald-Platzman mode collapses at the isotropic-nematic quantum phase transition. An interesting feature of the nematic phase is that it has topological defects known as disclinations that act as local center of spatial curvature for the electronic degrees of freedom. The effective field theory provides a full description of the response of the quantum fluid to external electromagnetic probes and to local deformations of the underlying crystal. Although the theory is specific for fractional quantum Hall states, these ideas and mechanisms are of general interest to understanding the behavior of geometric fluctuations in other topological phases in condensed matter, including half-filled Landau Level and Chern insulators. [Preview Abstract] |
Friday, March 17, 2017 9:12AM - 9:48AM |
X24.00003: Interplay of Topology and Geometry in Fractional Quantum Hall Liquids Invited Speaker: Kun Yang Fractional Quantum Hall Liquids (FQHL) are the ultimate strongly correlated electron systems, and the birth place of topological phase of matter. Early theoretical work has emphasized the universal or topological aspects of quantum Hall physics. More recently it has become increasingly clear that there is very interesting bulk dynamics in FQHL, associated with an internal geometrical degree of freedom, or metric. The appropriate quantum theory of this internal dynamics is thus expected to take the form of a “quantum gravity”, whose elementary excitations are spin-2 gravitons. After briefly reviewing the topological aspect of FQHL, I will discuss in this talk how to couple and probe the presence of this internal geometrical degree of freedom experimentally in the static limit [1], and detect the graviton excitation in a spectroscopic measurement [2]. [1] Kun Yang, Geometry of compressible and incompressible quantum Hall States: Application to anisotropic composite-fermion liquids, Phys. Rev. B 88, 241105 (2013). [2] Kun Yang, Acoustic Wave Absorption as a Probe of Dynamical Gravitational Response of Fractional Quantum Hall Liquids, Phys. Rev. B 93, 161302 (2016). [Preview Abstract] |
Friday, March 17, 2017 9:48AM - 10:24AM |
X24.00004: Disorder Driven Fractional Quantum Hall To Insulator Transitions Invited Speaker: Ravindra Bhatt It is well known that disorder plays a key role in determining the stability of quantum Hall states and thus the extent of quantum Hall plateaus. As a result, there have been several numerical studies of plateau transitions in the integer quantum Hall regime for non-interacting electrons in two dimensions. By contrast, studies of interacting electrons with disorder in two dimensions in the fractional quantum Hall regime have received relatively less attention in numerical studies, because of computational complexity. After reviewing previous attempts at addressing this numerically challenging issue [1-2], I will describe our recent investigation [3] of the effect of disorder on quantum entanglement properties of the Laughlin state at $\nu =1/3$ filling. We find that a suitably defined entanglement entropy function serves as a good diagnostic of the transition from the fractional topological state to an Anderson insulator, and provides a numerically more efficient method of locating the transition than previous approaches. Further, it enables a study of the critical behavior, not obtainable previously. Studies of entanglement eigenvalue statistics [3], as well as extension to disorder-driven transitions from other fractional states [4] will also be described. REFERENCES: [1] D. N. Sheng, X. Wan, E. H. Rezayi, K. Yang, R. N. Bhatt and F. D. M. Haldane, Phys. Rev. Lett. 90, 256802 (2003); [2] X. Wan, D. N. Sheng, E. H. Rezayi, K. Yang, R. N. Bhatt and F. D. M. Haldane, Phys. Rev. B 72, 075325 (2005); [3] Zhao Liu and R. N. Bhatt, Phys. Rev. Lett. 117, 206801 (2016) – Editor’s Suggestion; [4] Zhao Liu and R. N. Bhatt (in preparation). [Preview Abstract] |
Friday, March 17, 2017 10:24AM - 11:00AM |
X24.00005: Spin-dependent tunneling and particle-hole symmetry breaking in 2D electron systems in the fractional quantum Hall regime Invited Speaker: James Eisenstein At high magnetic field the tunneling rate between two parallel two-dimensional electron systems is profoundly influenced by both inter- and intra-layer electron-electron interactions. In addition to a pronounced pseudo-gap at the Fermi level, the tunneling current-voltage characteristics vividly expose the broadening of the Landau levels due to these interactions. In this talk I will discuss recent tunneling experiments which are sensitive to the spin configuration of the 2D electron systems. In particular, a new technique, based on density-imbalanced bilayer 2D systems, has been developed which allows for a spin-selective study of the underlying electronic spectral functions in the two layers. This technique provides an estimate of the net spin polarization of the 2D systems at filling factors 5/2 and 7/2 in the first excited Landau level, and sheds new light on the breakdown of particle-hole symmetry between filling factors 1/2 and 3/2 in the ground Landau level. This work represents a collaboration with L.N. Pfeiffer and K.W. West and was supported, in part, by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center with support of the Gordon and Betty Moore Foundation through Grant No. GBMF1250. [Preview Abstract] |
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