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arXiv:2504.16194 · Physical review. B./Physical review. B

Synthetic horizons in an atomic chain: Horizon-induced effects and connections to quantum Hall systems

Ali G. Moghaddam, Viktor Könye, Lotte Mertens, Jasper van Wezel, Jeroen van den Brink

Published Apr 20, 2026• 0 citations
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Abstract

We investigate the sine model, a one-dimensional tight-binding Hamiltonian with position-dependent sinusoidal hopping, and demonstrate the formation of synthetic horizons where electronic wave packets exhibit exponential slowdown. Interestingly, using the exact transformation between this model and the Harper equation, we find that analogous semiclassical horizons can emerge in a quantum Hall setup within the Harper-equation representation and at half-filling for specific values of the magnetic flux. The Harper equation describes the eigenstates of a square-lattice tight-binding model subjected to a perpendicular magnetic field, as a family of one-dimensional problems parametrized by a conserved transverse quasi-momentum. We demonstrate the correspondence between the sine and Harper models by comparing their semiclassical phase-space portraits and by numerically studying wave-packet dynamics in both models. Furthermore, by applying sudden quenches to the sine model's hopping profile, we observe the emergence of states with an effective thermal Fermi-Dirac distribution characterized by a corresponding Unruh temperature. Our numerical calculations reveal a non-universal behavior of this temperature, suggesting the involvement of mechanisms beyond a simple low-energy description.

DOI
10.1103/znlq-8k2p

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We investigate the sine model, a one-dimensional tight-binding Hamiltonian with position-dependent sinusoidal hopping, and demonstrate the formation of synthetic horizons where electronic wave packets exhibit exponential slowdown. Interestingly, using the exact transformation between this model and the Harper equation, we find that analogous semiclassical horizons can emerge in a quantum Hall setup within the Harper-equation representation and at half-filling for specific values of the magnetic flux. The Harper equation describes the eigenstates of a square-lattice tight-binding model subjected to a perpendicular magnetic field, as a family of one-dimensional problems parametrized by a conserved transverse quasi-momentum. We demonstrate the correspondence between the sine and Harper models by comparing their semiclassical phase-space portraits and by numerically studying wave-packet dynamics in both models. Furthermore, by applying sudden quenches to the sine model's hopping profile, we observe the emergence of states with an effective thermal Fermi-Dirac distribution characterized by a corresponding Unruh temperature. Our numerical calculations reveal a non-universal behavior of this temperature, suggesting the involvement of mechanisms beyond a simple low-energy description.
We investigate the wave packet dynamics and eigenstate localization in recently proposed generalized lattice models whose low-energy dynamics mimics a quantum field theory in (1+1)D curved spacetime with the aim of creating systems analogous to black holes. We identify a critical slowdown of zero-energy wave packets in a family of 1D tight-binding models with power-law variation of the hopping parameter, indicating the presence of a horizon. Remarkably, wave packets with non-zero energies bounce back and reverse direction before reaching the horizon. We additionally observe a power-law localization of all eigenstates, each bordering a region of exponential suppression. These forbidden regions dictate the closest possible approach to the horizon of states with any given energy. These numerical findings are supported by a semiclassical description of the wave packet trajectories, which are shown to coincide with the geodesics expected for the effective metric emerging from the considered lattice models in the continuum limit.
Synthetic horizons in models for quantum matter provide an alternative route to explore fundamental questions of modern gravitational theory. Here we apply these concepts to the problem of emergence of thermal quantum states in the presence of a horizon, by studying ground-state thermalization due to instantaneous horizon creation in a gravitational setting and its condensed matter analog. By a sudden quench to position-dependent hopping amplitudes in a one-dimensional lattice model, we establish the emergence of a thermal state accompanying the formation of a synthetic horizon. The resulting temperature for long chains is shown to be identical to the corresponding Unruh temperature, provided that the postquench Hamiltonian matches the entanglement Hamiltonian of the prequench system. Based on detailed analysis of the outgoing radiation we formulate the conditions required for the synthetic horizon to behave as a purely thermal source, paving a way to explore this interplay of quantum-mechanical and gravitational aspects experimentally.
We investigate the wave packet dynamics and eigenstate localization in recently proposed generalized lattice models whose low-energy dynamics mimics a quantum field theory in (1+1)D curved spacetime with the aim of creating systems analogous to black holes. We identify a critical slowdown of zero-energy wave packets in a family of 1D tight-binding models with power-law variation of the hopping parameter, indicating the presence of a horizon. Remarkably, wave packets with non-zero energies bounce back and reverse direction before reaching the horizon. We additionally observe a power-law localization of all eigenstates, each bordering a region of exponential suppression. These forbidden regions dictate the closest possible approach to the horizon of states with any given energy. These numerical findings are supported by a semiclassical description of the wave packet trajectories, which are shown to coincide with the geodesics expected for the effective metric emerging from the considered lattice models in the continuum limit.
We investigate the wave packet dynamics and eigenstate localization in recently proposed generalized lattice models whose low-energy dynamics mimics a quantum field theory in (1+1)D curved spacetime with the aim of creating systems analogous to black holes. We identify a critical slowdown of zero-energy wave packets in a family of 1D tight-binding models with power-law variation of the hopping parameter, indicating the presence of a horizon. Remarkably, wave packets with non-zero energies bounce back and reverse direction before reaching the horizon. We additionally observe a power-law localization of all eigenstates, each bordering a region of exponential suppression. These forbidden regions dictate the closest possible approach to the horizon of states with any given energy. These numerical findings are supported by a semiclassical description of the wave packet trajectories, which are shown to coincide with the geodesics expected for the effective metric emerging from the considered lattice models in the continuum limit.
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 [(1+1)D] gravitational backgrounds, including (anti-)de Sitter space-time.Wave packets propagating on the lattice exhibit an eternal slowdown for power-law positiondependent hopping integrals t (x) ∝ x γ when γ 1, signaling the formation of black hole event horizons.For γ < 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 space-times as they appear in certain gravity theories.
We propose and study systems of coupled atomic wires in a perpendicular synthetic magnetic field as a platform to realize exotic phases of quantum matter. This includes (fractional) quantum Hall states in arrays of many wires inspired by the pioneering work [C. L. Kane et al., Phys. Rev. Lett. 88, 036401 (2002)], as well as Meissner phases and vortex phases in double wires. With one continuous and one discrete spatial dimension, the proposed setup naturally complements recently realized discrete counterparts, i.e., the Harper-Hofstadter model and the two-leg flux ladder, respectively. We present both an in-depth theoretical study and a detailed experimental proposal to make the unique properties of the semicontinuous Harper-Hofstadter model accessible with cold-atom experiments. For the minimal setup of a double wire, we explore how a subwavelength spacing of the wires can be implemented. This construction increases the relevant energy scales by at least an order of magnitude compared to ordinary optical lattices, thus rendering subtle many-body phenomena such as Lifshitz transitions in Fermi gases observable in an experimentally realistic parameter regime. For arrays of many wires, we discuss the emergence of Chern bands with readily tunable flatness of the dispersion and show how fractional quantum Hall states can be stabilized in such systems. Using for the creation of optical potentials Laguerre-Gauss beams that carry orbital angular momentum, we detail how the coupled atomic wire setups can be realized in nonplanar geometries such as cylinders, disks, and tori.