A no-go theorem for regularizing chiral fermions

Nielsen, Holger Bech; Ninomiya, M.

doi:10.1016/0370-2693(81)91026-1

Cited by 878 publications

(702 citation statements)

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“…If one wants a trial state which breaks parity and time-reversal symmetry, one is naturally lead to consider chiral fermions. It is a notoriously difficult problem to construct lattice models which give rise to chiral fermions [83]. Working directly in the continuum allows to circumvent such problems.…”

Section: Discussion: Entanglement Trial Wavefunctions Conformal mentioning

confidence: 99%

Edge-state inner products and real-space entanglement spectrum of trial quantum Hall states

2012

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We consider the trial wavefunctions for the fractional quantum Hall effect that are given by conformal blocks, and construct their associated edge excited states in full generality. The inner products between these edge states are computed in the thermodynamic limit, assuming generalized screening (i.e. short-range correlations only) inside the quantum Hall droplet, and using the language of boundary conformal field theory (boundary CFT). These inner products take universal values in this limit: they are equal to the corresponding inner products in the bulk 2d chiral CFT which underlies the trial wavefunction. This is a bulk/edge correspondence; it shows the equality between equal-time correlators along the edge and the correlators of the bulk CFT up to a Wick rotation.This approach is then used to analyze the entanglement spectrum of the ground state obtained with a bipartition A ∪ B in real-space. Starting from our universal result for inner products in the thermodynamic limit, we tackle corrections to scaling using standard field-theoretic and renormalization group arguments. We prove that generalized screening implies that the entanglement Hamiltonian HE = − log ρA is isospectral to an operator that is local along the cut between A and B. We also show that a similar analysis can be carried out for particle partition. We discuss the close analogy between the formalism of trial wavefunctions given by conformal blocks and Tensor Product States, for which results analogous to ours have appeared recently. Finally, the edge theory and entanglement spectrum of px ± ipy paired superfluids are treated in a similar fashion in the appendix.

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Section: Discussion: Entanglement Trial Wavefunctions Conformal mentioning

confidence: 99%

Edge-state inner products and real-space entanglement spectrum of trial quantum Hall states

2012

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“…This class of materials is called Weyl semimetals and many three-dimensional Weyl semimetals have been predicted theoretically and confirmed experimentally 70 graphene is a two-dimensional version 71 . There are always an equal number of Weyl fermions with positive and negative chiralities in the band structure 72 . There must also be a surface state that connects them, known as a Fermi arc 73 .…”

Section: Berry Phase Engineeringmentioning

confidence: 99%

Emergent functions of quantum materials

2017

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Materials can harbour quantum many-body systems, most typically in the form of strongly correlated electrons in solids, that lead to novel and remarkable functions thanks to emergence-collective behaviours that arise from strong interactions among the elements. These include the Mott transition, high-temperature superconductivity, topological superconductivity, colossal magnetoresistance, giant magnetoelectric e ect, and topological insulators. These phenomena will probably be crucial for developing the next-generation quantum technologies that will meet the urgent technological demands for achieving a sustainable and safe society. Dissipationless electronics using topological currents and quantum spins, energy harvesting such as photovoltaics and thermoelectrics, and secure quantum computing and communication are the three major fields of applications working towards this goal. Here, we review the basic principles and the current status of the emergent phenomena and functions in materials from the viewpoint of strong correlation and topology.E mergence is a concept developed for many-body systems, indicating the properties, phenomena, and functions that never appear in the individual elements but are realized only when a huge number of elements get together 1 . Inside materials, emergent phenomena are often seen due to the interaction of electronic states; with recent developments on electronic states in solids schematically summarized in Fig. 1a. Electrons in solids have several degrees of freedom: charge, spin and orbital, and are characterized by the topological nature determined by the atomic potential on the crystal lattice structure, as schematically shown in Fig. 1b. These five attributes are coupled together and determine the overall responses to stimuli, which appear as materials' electrical, magnetic, optical, thermal, and mechanical properties.These collective electrons demonstrate various macroscopic quantum phenomena, the representative example of which is superconductivity. One of the big challenges in condensed matter physics is to increase the temperature (T c ) at which superconductivity can be observed to above room temperature. However, there are many other macroscopic quantum phenomena that are already observable above room temperature. One is magnetism (by the Bohr-van Leeuwen theorem), and the other is ferroelectricity 2,3 . Remarkably, there are common features of these three macroscopic quantum phenomena: the order parameter, which is of quantum origin, behaves as a classical quantity, and the quantum topology plays a crucial role.The topological nature of the electronic states is the key concept in the most recent developments in understanding quantum materials. The quantum Hall effect, topological insulators, and topological superconductors are all characterized by nontrivial topologies in Hilbert space. The Berry phase, which describes the connection and curvature of the subspace of Hilbert space, plays the central role in the unified principle to describe this topological nature 4 . ...

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“…The finite lattice spacing, a, serves as an ultraviolet cutoff, and a valid lattice formulation must respect all of the features of QCD in the limit a → 0. Technical challenges arise as spurious fermion states can be produced in this limit as lattice artifacts [42,43]. This can be mitigated, although not completely removed, while maintaining chiral symmetry, by introducing staggered fermions [44].…”

Section: Non-perturbative Dynamicsmentioning

confidence: 99%