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Register a new userA Personal History of the Hastings-Michalakis Proof of Hall Conductance Quantization
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M. B. Hastings
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This is a personal history of the Hastings-Michalakis proof of quantum Hall conductance quantization.
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The goal of this paper is to explain how the views of Albert Einstein, John Bell and others, about nonlocality and the conceptual issues raised by quantum mechanics, have been rather systematically misunderstood by the majority of physicists.
The quest for non-Abelian quasiparticles has inspired decades of experimental and theoretical efforts, where the scarcity of direct probes poses a key challenge. Among their clearest signatures is a thermal Hall conductance with quantized half-integer value in natural units $ pi^2 k_B^2 T /3 h$ ($T$ is temperature, $h$ the Planck constant, $k_B$ the Boltzmann constant). Such a value was indeed recently observed in a quantum-Hall system and a magnetic insulator. We show that a non-topological thermal metal phase that forms due to quenched disorder may disguise as a non-Abelian phase by well approximating the trademark quantized thermal Hall response. Remarkably, the quantization here improves with temperature, in contrast to fully gapped systems. We provide numerical evidence for this effect and discuss its possible implications for the aforementioned experiments.
In contrast to the case of ordinary quantum Hall effect, the resistance of ballistic helical edge channels in typical quantum spin-Hall experiments is non-vanishing, additive and poorly quantized. Here we present a simple argument connecting this qualitative difference with a spin relaxation in the current/voltage leads in an experimentally relevant multi-terminal bar geometry. Both the finite lead resistance and the spin relaxation contribute to a non-vanishing four-terminal edge resistance, explaining poor quantization quality. We show that corrections to the four-terminal and two-terminal resistances in the limit of strong spin relaxation are opposite in sign, making a measurement of the spin relaxation resistance feasible, and estimate the magnitude of the effect in HgTe-based quantum wells.
In this paper we describe the history of the LHCb experiment over the last three decades, and its remarkable successes and achievements. LHCb was conceived primarily as a b-physics experiment, dedicated to CP violation studies and measurements of very rare b decays, however the tremendous potential for c-physics was also clear. At first data taking, the versatility of the experiment as a general-purpose detector in the forward region also became evident, with measurements achievable such as electroweak physics, jets and new particle searches in open states. These were facilitated by the excellent capability of the detector to identify muons and to reconstruct decay vertices close to the primary pp interaction region. By the end of the LHC Run 2 in 2018, before the accelerator paused for its second long shut down, LHCb had measured the CKM quark mixing matrix elements and CP violation parameters to world-leading precision in the heavy-quark systems. The experiment had also measured many rare decays of b and c quark mesons and baryons to below their Standard Model expectations, some down to branching ratios of order 10-9. In addition, world knowledge of b and c spectroscopy had improved significantly through discoveries of many new resonances already anticipated in the quark model, and also adding new exotic four and five quark states.
We provide a short proof of the quantisation of the Hall conductance for gapped interacting quantum lattice systems on the two-dimensional torus. This is not new and should be seen as an adaptation of the proof of [1], simplified by making the stronger assumption that the Hamiltonian remains gapped when threading the torus with fluxes. We argue why this assumption is very plausible. The conductance is given by Berrys curvature and our key auxiliary result is that the curvature is asymptotically constant across the torus of fluxes.
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