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Conference on Quark Confinement and the Hadron Spectrum (Confinement)

Quantum measurements and chiral magnetic effect

Vladimir I Shevchenko

Published May 21, 2013• 1 citation
Publisher

Abstract

The effect of anisotropy for fluctuations of electric currents in magnetic field is addressed within framework of quantum measurements theory.It is shown that for free fermions in uniform magnetic field the anisotropy is of the same sign as one expects for chiral magnetic effect and is related to triangle anomaly.The corresponding decoherence functional contains anomalous off-diagonal terms leading to correlation of fluctuations between observables of opposite P-parity.

DOI
10.22323/1.171.0082

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The effect of anisotropy for fluctuations of electric currents in magnetic field is addressed within framework of quantum measurements theory.It is shown that for free fermions in uniform magnetic field the anisotropy is of the same sign as one expects for chiral magnetic effect and is related to triangle anomaly.The corresponding decoherence functional contains anomalous off-diagonal terms leading to correlation of fluctuations between observables of opposite P-parity.
A century’s proliferation of Quantum Interpretations has been driven by an incomplete understanding of the measurement problem, by an incomplete understanding of the unobservable wavefunction and its unobservable interactions. Yet it remains that the observer effect - observing a phenomenon necessarily changes that phenomenon - is at the historical foundation of quantum mechanics. The semantic confusion, that wavefunction interactions are unobservable yet the observer effect is irrefutable, can be resolved by considering the difference between simple passive measurement and active transfer function measurement. In the first, one registers whatever lump of energy lands upon a sensor, and there is no observer effect. In the second, one excites the system of interest and measures the response, and there is an observer effect. Magnetic moment measurements are transfer function measurements. To measure an amplitude one must align the spin, applying a magnetic field to separate the energy eigenstates, and excite the system to measure their difference. A paper presented to Spin 2016 suggests that the measured anomaly is not an intrinsic property of the fermionic proton, but rather an observer effect. In our presentation to Spin 2018 we propose to extend the Spin 2016 interpretation to the neutron anomalous moment.
Dirac fermions coupled to gauge fields can exhibit the chiral anomaly even on a finite spatial lattice. A careful description of this phenomenon yields new insights into the nature of spin-charge relations and on-site symmetries (symmetries that are gauged by placing gauge fields on all links of the lattice). One notable result is that only sufficiently small symmetry groups can act on-site in a system with finitely many degrees of freedom. Symmetries that break this rule either cannot be gauged on an arbitrary lattice, or the gauging decouples the matter fields from gauge fields. These "anomalies" are not quantum in nature, and they are diagnosed geometrically, by the volume of the spatial manifold. The familiar particle number U(1){\mathrm U}(1)U(1) exhibits this kind of anomalous behavior in any finite fermion theory. The chiral anomaly in such a finite system instead manifests itself most simply after gauging the Z2{\mathbb Z}_2Z2​ fermion parity.
The quantum chiral anomaly enables a nearly dissipationless current in the presence of chirality imbalance and magnetic field -- this is the Chiral Magnetic Effect (CME), observed recently in Dirac and Weyl semimetals. Here we propose to utilize the CME for the design of qubits potentially capable of operating at THz frequency, room temperature, and the coherence time to gate time ratio of about 10410^4104. The proposed "Chiral Qubit" is a micron-scale ring made of a Weyl or Dirac semimetal, with the ∣0⟩|0\rangle∣0⟩ and ∣1⟩|1\rangle∣1⟩ quantum states corresponding to the symmetric and antisymmetric superpositions of quantum states describing chiral fermions circulating along the ring clockwise and counter-clockwise. A fractional magnetic flux through the ring induces a quantum superposition of the ∣0⟩|0\rangle∣0⟩ and ∣1⟩|1\rangle∣1⟩ quantum states. The entanglement of qubits can be implemented through the near-field THz frequency electromagnetic fields.
A magnetoelectric effect according to Katsura-Nagaosa-Balatsky mechanism in spin-1/2 XY chain in transverse magnetic field is considered. A spatial orientation of the electric field is chosen to provide an exact solution of the model in terms of free spinless fermions. The simplest model of quantum spin chain demonstrating a magnetoelectric effect, a zero temperature case of the spin-1/2 XX chain in a transverse magnetic field with Katsura-Nagaosa-Balatsky mechanism, is considered. The model has the simplest possible form of the magnetization, polarization and susceptibility functions, depending on electric and magnetic fields in a most simple form. For the case of arbitrary XY anisotropy, a non-monotonous dependence of magnetization on the XY anisotropy parameter is figured out. This non-uniform behaviour is governed by the critical point which is connected with the possibility to drive the system gapless or gapped by the electric field. Singularities of the magnetoelectric susceptibility at the critical value of system parameters are shown.