Related papers: Tangent fermions can restore vacuum stability of discrete-time Dirac models

Tangent fermions can restore vacuum stability of discrete-time Dirac models

URL: http://arxiv.org/abs/2609.01029v1
Date: Tue, 01 Sep 2026 10:27:21 GMT
Title: Tangent fermions can restore vacuum stability of discrete-time Dirac models
Abstract summary: We show that an alternative discretization scheme, with a tangent rather than a sine dispersion relation, offers stability while retaining a single Dirac cone.<n>The key step is the Cayley transformation from the unit circle of Floquet eigenvalues $e-ivarepsilon$ to the real line of energies $E=2tan(varepsilon/2)$.<n>We compute the Schwinger effect (particle-hole pair creation in a uniform electric field) for tangent fermions and show that the pair-production rate agrees with the continuum result for a single Dirac cone
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License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: The Dirac quantum walk (a 1+1 dimensional space-time discretization of the Dirac equation) has a $2μ$ mass gap both at the center and at the corner of the quasi-energy-momentum Brillouin zone. Gupta and Short recently noted [Quantum 9, 1845 (2025)] that the Dirac vacuum can create a particle-hole pair at the zone corner with the release of an energy $2μ$ to the environment. They removed this vacuum instability at the expense of fermion doubling, the appearance of a second low-energy Dirac cone. Here we show that an alternative discretization scheme, with a tangent rather than a sine dispersion relation, offers stability while retaining a single Dirac cone. The key step is the Cayley transformation from the unit circle of Floquet eigenvalues $e^{-i\varepsilon}$ to the real line of unbounded energies $E=2\tan(\varepsilon/2)$. We compute the Schwinger effect (particle-hole pair creation in a uniform electric field) for tangent fermions and show that the pair-production rate agrees with the continuum result for a single Dirac cone. The zone corner is exactly decoupled if the scalar potential is coupled through the Hermitian generator of the quantum map. If it is coupled as a split operator, in order to preserve exact gauge invariance on the lattice, the corner does contribute - with a weight that vanishes quadratically with the lattice constants, in contrast to the Dirac quantum walk where the zone-corner instability survives the continuum limit.

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