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.

arXiv:2112.12827Dec 23, 20216 citations

Quantum dynamics in 1D lattice models with synthetic horizons

Corentin Morice, Dmitry Chernyavsky, Jasper van Wezel +2 more

Jan 1, 20220 citations

Synthetic gravitational horizons in low-dimensional quantum matter

Corentin Morice, Ali G. Moghaddam, Dmitry Chernyavsky +2 more

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 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.

arXiv:2104.03875Physical Review ResearchJun 9, 202135 citations

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

Ali G. Moghaddam, Viktor Könye, Lotte Mertens +2 more

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 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.

arXiv:2504.16194Physical review. B./Physical review. BApr 20, 20260 citations

Spontaneous Hawking Radiation from Dynamical Black-Hole Formation in Quantum Spin Systems

Shunichiro Kinoshita, Keiju Murata, Daisuke Yamamoto +1 more

We show that Hawking radiation spontaneously generated by dynamical black-hole formation can be realized in a local quantum spin model. Starting from the ground state corresponding to the early-time vacuum, with no initially prepared excitations, we follow the dynamics induced by the evolving geometry. In the corresponding continuum quantum field theory, Hawking particle creation is associated with nontrivial Bogoliubov mixing between the in- and out-mode decompositions. We derive the resulting renormalized local energy density in the continuum quantum field theory, which corresponds to an energy-weighted integral of the Hawking spectrum, and identify its counterpart as a local spin observable whose expectation value quantitatively reproduces the continuum prediction, including its dependence on the surface gravity. The agreement persists over a finite time window whose duration grows logarithmically with system size, revealing the crossover from universal continuum Hawking physics to lattice-cutoff dynamics. These results establish a microscopic route to quantum simulation of quantum field theory in curved spacetime, connecting field-theoretic particle creation directly to experimentally accessible many-body observables.We show that Hawking radiation spontaneously generated by dynamical black-hole formation can be realized in a local quantum spin model. Starting from the ground state corresponding to the early-time vacuum, with no initially prepared excitations, we follow the dynamics induced by the evolving geometry. In the corresponding continuum quantum field theory, Hawking particle creation is associated with nontrivial Bogoliubov mixing between the in- and out-mode decompositions. We derive the resulting renormalized local energy density in the continuum quantum field theory, which corresponds to an energy-weighted integral of the Hawking spectrum, and identify its counterpart as a local spin observable whose expectation value quantitatively reproduces the continuum prediction, including its dependence on the surface gravity. The agreement persists over a finite time window whose duration grows logarithmically with system size, revealing the crossover from universal continuum Hawking physics to lattice-cutoff dynamics. These results establish a microscopic route to quantum simulation of quantum field theory in curved spacetime, connecting field-theoretic particle creation directly to experimentally accessible many-body observables.

hep-thCross-listedarXiv:2610.07794Oct 7, 20260 citations

Emergent Spacetime in Quantum Lattice Models

Matthew D. Horner

Many quantum lattice models have an emergent relativistic description in their continuum limit. The celebrated example is graphene, whose continuum limit is described by the Dirac equation on a Minkowski spacetime. Not only does the continuum limit provide us with a dictionary of geometric observables to describe the models with, but it also allows one to solve models that were otherwise analytically intractable. In this thesis, we investigate novel features of this relativistic description for a range of quantum lattice models. In particular, we demonstrate how to generate emergent curved spacetimes and identify observables at the lattice level which reveal this emergent behaviour, allowing one to simulate relativistic effects in the laboratory. We first study carbon nanotubes, a system with an edge, which allows us to test the interesting feature of the Dirac equation that it allows for bulk states with support on the edges of the system. We then study Kitaev's honeycomb model which has a continuum limit describing Majorana spinors on a Minkowski spacetime. We show how to generate a non-trivial metric in the continuum limit of this model and how to observe the effects of this metric and its corresponding curvature in the lattice observables, such as Majorana correlators, Majorana zero modes and the spin densities. We also discuss how lattice defects and $\mathbb{Z}_2$ gauge fields at the lattice level can generate chiral gauge fields in the continuum limit and we reveal their adiabatic equivalence. Finally, we discuss a chiral modification of the 1D XY model which makes the model interacting and introduces a non-trivial phase diagram. We see that this generates a black hole metric in the continuum limit, where the inside and outside of the black hole are in different phases. We then demonstrate that by quenching this model we can simulate Hawking radiation.Many quantum lattice models have an emergent relativistic description in their continuum limit. The celebrated example is graphene, whose continuum limit is described by the Dirac equation on a Minkowski spacetime. Not only does the continuum limit provide us with a dictionary of geometric observables to describe the models with, but it also allows one to solve models that were otherwise analytically intractable. In this thesis, we investigate novel features of this relativistic description for a range of quantum lattice models. In particular, we demonstrate how to generate emergent curved spacetimes and identify observables at the lattice level which reveal this emergent behaviour, allowing one to simulate relativistic effects in the laboratory. We first study carbon nanotubes, a system with an edge, which allows us to test the interesting feature of the Dirac equation that it allows for bulk states with support on the edges of the system. We then study Kitaev's honeycomb model which has a continuum limit describing Majorana spinors on a Minkowski spacetime. We show how to generate a non-trivial metric in the continuum limit of this model and how to observe the effects of this metric and its corresponding curvature in the lattice observables, such as Majorana correlators, Majorana zero modes and the spin densities. We also discuss how lattice defects and $\mathbb{Z}_2$ gauge fields at the lattice level can generate chiral gauge fields in the continuum limit and we reveal their adiabatic equivalence. Finally, we discuss a chiral modification of the 1D XY model which makes the model interacting and introduces a non-trivial phase diagram. We see that this generates a black hole metric in the continuum limit, where the inside and outside of the black hole are in different phases. We then demonstrate that by quenching this model we can simulate Hawking radiation.

arXiv:2212.12548Dec 23, 20221 citation

\mathbb{Z}_2

gauge fields at the lattice level can generate chiral gauge fields in the continuum limit and we reveal their adiabatic equivalence. Finally, we discuss a chiral modification of the 1D XY model which makes the model interacting and introduces a non-trivial phase diagram. We see that this generates a black hole metric in the continuum limit, where the inside and outside of the black hole are in different phases. We then demonstrate that by quenching this model we can simulate Hawking radiation.