Reentrant violation of special relativity in the low-energy corner

Abstract

In the effective relativistic quantum field theories the energy region, where the special relativity holds, can be sandwiched from both the high and low energies sides by domains where the special relativity is violated. An example is provided by 3 He-A where the relativistic quantum field theory emerges as the effective theory. The reentrant violation of the special relativity in the ultralow energy corner is accompanied by the redistribution of the momentum-space topological charges between the fermionic flavors. At this ultralow energy an exotic massless fermion with the topological charge N3 = 2 arises, whose energy spectrum mixes the classical and relativistic behavior. This effect can lead to neutrino oscillations if neutrino flavors are still massless at this energy scale.Introduction. The condensed matter analogy supports an idea that the special and general relativity might be emergent properties of quantum vacuum, which arise gradually in the low energy corner [1][2][3]. If this is true one can expect that the Lorentz invariance of our low-energy world is violated at high energy. The condensed matter provides examples of how this violation can occur. Here we demonstrate one generic example which is realized in superfluid 3 He-A, where the effective special relativity and gravity do arise in the low energy corner together with the chiral fermions and effective gauge fields [3]. It suggests that if the effective Lorentz invariance is violated in the extreme limit of "Planckian" scale, it becomes violated also in the opposite extreme limit of ultralow energy. The energy scale where the reentrant violation of the special relativity occurs is also dictated by the "trans-Planckian" physics. If there are still fermions which remain chiral and massless when approaching this ultralow energy scale, the reentrant violation of the Lorentz invariance leads to the crucial reconstruction of their energy spectrum. Thus the trans-Planckian physics can be probed in the limit of low energies.In this example two flavors of chiral left-handed fermions, the two are hybridized producing one massive fermion with the relativistic spectrum E 2 = c 2 p 2 + m 2 c 4 and one exotic gapless fermion whose spectrum mixes the classical and relativistic behavior: E 2 = c 2 p 2 + (p

Topological invariants for standard model: From semi-metal to topological insulator

“…In 3D condensed matter systems these parameters correspond to a non-quantized part of the intrinsic Hall conductivity [61,25]. Reentrant violation of Lorentz symmetry which occurs at low energy leads to formation of exotic massless fermions with nontrival momentum space topology: fermions with quadratic dispersion at low energy and semi-Dirac fermions with linear dispersion in one direction and quadratic dispersion in the other [72,23]. Examples of such fermions in condensed matter are in Refs.…”

Analogue gravity from field theory normal modes?

“…In particular we view this particular hurdle as the single biggest issue facing the "induced gravity" proposal, though some particular implementations of this idea may skirt the issue. For instance, consider Volovik's proposals to extract the dynamics of Einstein gravity from condensed matter quasiparticle excitations [39]: Volovik essentially argues that certain theories might exhibit "one-loop dominance" in the sense that the one-loop physics dominates over the zero loop physics. In contrast, Sakharov implicitly assumes that whatever the microphysics is, it has effectively decoupled from the low energy effective metric.…”

Quenching through Dirac and semi-Dirac points in optical lattices: Kibble-Zurek scaling for anisotropic quantum critical systems

“…Similarly, two interpenetrating square-lattices can lead to Quadratic Band Crossing [24] and either a deformed Honeycomb system [25,26], or a 3-band system can lead to semi-Dirac points [27], where the spectrum is linear along one axis and quadratic along another. Anisotropic quantum critical points associated with spectra that are linear in some directions and quadratic in others arise in systems as diverse as semiconductor hetero-structures [28] and He 3 [29]. We will calculate a generalized Kibble-Zurek scaling for such anisotropic Quantum critical systems.…”