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arXiv:2207.08840 · Physical Review Letters

Chiral Spin-Chain Interfaces Exhibiting Event-Horizon Physics

Matthew D. Horner, Andrew Hallam, Jiannis K. Pachos

Published Jan 3, 2023• 10 citations
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Abstract

The interface between different quantum phases of matter can give rise to novel physics, such as exotic topological phases or nonunitary conformal field theories. Here we investigate the interface between two spin chains in different chiral phases. Surprisingly, the mean field theory approximation of this interacting composite system is given in terms of Dirac fermions in a curved space-time geometry. In particular, the interface between the two phases represents a black hole horizon. We demonstrate that this representation is faithful both analytically, by employing bosonization to obtain a Luttinger liquid model, and numerically, by employing matrix product state methods. A striking prediction from the black hole equivalence emerges when a quench, at one side of the interface between two opposite chiralities, causes the other side to thermalize with the Hawking temperature for a wide range of parameters and initial conditions.

DOI
10.1103/physrevlett.130.016701

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The interface between different quantum phases of matter can give rise to novel physics, such as exotic topological phases or nonunitary conformal field theories. Here we investigate the interface between two spin chains in different chiral phases. Surprisingly, the mean field theory approximation of this interacting composite system is given in terms of Dirac fermions in a curved space-time geometry. In particular, the interface between the two phases represents a black hole horizon. We demonstrate that this representation is faithful both analytically, by employing bosonization to obtain a Luttinger liquid model, and numerically, by employing matrix product state methods. A striking prediction from the black hole equivalence emerges when a quench, at one side of the interface between two opposite chiralities, causes the other side to thermalize with the Hawking temperature for a wide range of parameters and initial conditions.
In this paper we explore the properties of a one-dimensional spin chain in the presence of chiral interactions, focusing on the system's transition to distinct chiral phases for various values of the chiral coupling. By employing the mean-field theory approximation we establish a connection between this chiral system and a Dirac particle in the curved spacetime of a black hole. Surprisingly, the black-hole horizon coincides with the interface between distinct chiral phases. We examine the chiral properties of the system for homogeneous couplings and in scenarios involving position-dependent couplings that correspond to black-hole geometries. To determine the significance of interactions in the chiral chain we employ bosonization techniques and derive the corresponding Luttinger liquid model. Furthermore, we investigate the classical version of the model to understand the impact of the chiral operator on the spins and gain insight into the observed chirality. Our findings shed light on the behavior of the spin chain under the influence of the chiral operator, elucidating the implications of chirality in various contexts, including black-hole physics.
There is currently significant interest in emulating the essential characteristics of black holes, such as their Hawking radiation or their optimal scrambling behavior, using condensed matter models. In this article, we investigate a chiral spin-chain, whose mean field theory effectively captures the behavior of Dirac fermions in the curved spacetime geometry of a black hole. We find that within the region of the chain that describe the interior of the black hole, strong correlations prevail giving rise to many-body chaotic dynamics. Employing out-of-time-order correlations as a diagnostic tool, we numerically compute the associated Lyapunov exponent. Intriguingly, we observe a linear increase in the Lyapunov exponent with temperature within the black hole's interior at low temperatures, indicative of optimal scrambling behavior. This contrasts with the quadratic temperature dependence exhibited by the spin-chain on the region outside the black hole. Our findings contribute to a deeper understanding of the interplay between black hole geometry and quantum chaos, offering insights into fundamental aspects of quantum gravity.
Type-II Weyl fermions may emerge behind the event horizon of black holes. We employ the Painlevé-Gullstrand metric to study the surface of the Lifshitz transition at the horizon, equivalent to the interface separating the type-I and type-II Weyl states. We find several analogies between the black hole horizon and the transformation of type-I to type-II Weyl fermions through the Dirac line. We analyze the symmetry-protected topological order at the Lifshitz transition originating in semimetals. The emergence of Hawking radiation in Weyl semimetals is discussed. We show that the transition state from type-I to type-II Dirac fermions can be viewed as a black-hole horizon, which exhibits unique characteristics, including a Dirac-line Fermi surface with a nontrivial topological invariant and a critical chiral anomaly effect.
We investigate the apparent thermality of Hawking radiation in the semi-classical limit of quantum black holes using the mean-field limit of a chiral spin-chain simulator, which models fermions propagating on a black hole space-time in the continuum. In this free-theory regime, no genuine thermalisation occurs. Nevertheless, we show that a bipartition across the event horizon yields a reduced density matrix whose mode occupations follow an apparent thermal Fermi-Dirac distribution. In contrast, partitions away from the horizon do not exhibit such thermal distributions, reflecting the absence of thermal behaviour. Our results demonstrate that Hawking radiation appears thermal only with respect to horizon bipartitions in free theories, with genuine thermal behaviour expected to emerge only in the presence of strong interactions deep in the black hole interior, a study of which we leave for future work.
We implement a chiral spin-chain black hole simulator on IBM superconducting quantum hardware and probe, within a common microscopic framework, both semiclassical horizon physics and interacting quantum scrambling. We first measure the dispersion relation across the exterior, horizon and over-tilted interior regimes, reproducing the predicted evolution of the effective light-cone structure. To probe Hawking thermality, we prepare a localised excitation inside the horizon and monitor its density response at an exterior site, observing the predicted inverse relation between the peak arrival time and the surface gravity, thereby establishing a calibrated dynamical estimator of the Hawking temperature. Beyond the semiclassical regime, we continuously tune the interactions and distinguish non-exponential operator spreading in the free-fermion limit from Lyapunov-like OTOC decay in the strongly interacting chiral regime. These measurements use observable-specific Floquet circuits derived from the same parent chiral model, including its mean-field and coordinate-equivalent XY descriptions, to reduce circuit depth while preserving the physics relevant to each probe. Our results provide a unified programmable platform for studying horizon geometry, Hawking thermality and interacting scrambling on quantum hardware.
We investigate the emergence and detection of Hawking radiation (HR) in a 1D chiral spin chain model, where the gravitational collapse is simulated by a sudden quantum quench that triggers a horizon-inducing phase transition. While our previous work [33] established that this model mimics black hole (BH) formation conditions even when the Hoop conjecture is seemingly violated, we here focus on the resulting stationary radiation spectrum and its detectability. By mapping the spin chain dynamics to a Dirac fermion in a curved ( 1 + 1 ) -dimensional spacetime, we analyze the radiation using two complementary approaches: field-theoretic modes and operational quantum sensors. First, using localized Gaussian wave packets to model realistic detectors, we find that the radiation spectrum exhibits deviations from the ideal Planckian form, while retaining robust Poissonian statistics that signal the loss of formation-scale information. Second, we introduce a qubit coupled globally to the chiral spin chain. Rather than acting as a localized point detector (which would break translational invariance), the qubit couples to the collective chiral excitations of the analogue spacetime, functioning as a global quantum sensor. We demonstrate that the decoherence dynamics of this macroscopic probe faithfully encode the thermal nature of the HR in the weak-coupling limit, while strong-coupling dynamics reveal non-Markovian memory effects driven by the horizon. These results provide a clear operational protocol for distinguishing genuine analog HR from environmental noise in quantum simulation platforms.