Synthetic gravitational horizons in low-dimensional quantum matter

Abstract

We propose a class of lattice models realizable in a wide range of setups whose low-energy dynamics exactly reduces to Dirac fields subjected to (1+1)-dimensional gravitational backgrounds, including (anti-)de Sitter spacetime. Wave-packets propagating on the lattice exhibit an eternal slowdown for power-law position-dependent hopping integrals $t(x)\propto x^{\gamma }$ when $\gamma \ge 1$, signalling the formation of black hole event horizons. For $\gamma <1$ instead the wave-packets behave radically different and bounce off the horizon. We show that the eternal slowdown relates to a zero-energy spectral singularity of the lattice model and that the semiclassical wave packets trajectories coincide with the geodesics on (1+1)D dilaton gravity, paving the way for new and experimentally feasible routes to mimic black hole horizons and realize (1+1)D spacetimes as they appear in certain gravity theories.

arXiv comment6 pages, 5 figures

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Cited by in corpus (15)

• Hawking fragmentation and Hawking attenuation in Weyl semimetals
• Selberg trace formula in hyperbolic band theory
• Artificial event horizons in Weyl semimetal heterostructures and their non-equilibrium signatures
• Type-II Weyl semimetal vs gravastar
• Thermalization by a synthetic horizon
• Horizon physics of quasi-one-dimensional tilted Weyl cones on a lattice
• Black hole mirages: electron lensing and Berry curvature effects in inhomogeneously tilted Weyl semimetals
• Anisotropic optics and gravitational lensing of tilted Weyl fermions
• Engineering spectral properties of non-interacting lattice Hamiltonians
• Floquet engineered inhomogeneous quantum chaos in critical systems
• Analogue Hawking radiation as a tunneling in a two-level $\mathcal{P}\mathcal{T}$-symmetric system
• Anderson Localization and Swing Mobility Edge in Curved Spacetime
• Optimally scrambling chiral spin-chain with effective black hole geometry
• Quantum dynamics in 1D lattice models with synthetic horizons
• Synthetic horizons in an atomic chain: Horizon-induced effects and connections to quantum Hall systems