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arXiv:2204.05641 · PRX Quantum

Dynamical Hadron Formation in Long-Range Interacting Quantum Spin Chains

Joseph Vovrosh, Rick Mukherjee, Alvise Bastianello, Johannes Knolle

Published Oct 19, 2022• 26 citations
arXivHTMLPDF

Abstract

The study of confinement in quantum spin chains has seen a large surge of interest in recent years.It is not only important for understanding a range of effective one-dimensional condensed-matter realizations but it also shares some of the nonperturbative physics with quantum chromodynamics (QCD), which makes it a prime target for current quantum simulation efforts.In analogy to QCD, the confinementinduced two-particle bound states that appear in these models are dubbed mesons.Here, we study scattering events due to meson collisions in a quantum spin chain with long-range interactions such that two mesons have an extended interaction.We show how novel hadronic bound states, e.g., with four constituent particles akin to tetraquarks, may form dynamically in fusion events.In a natural collision their signal is weak, as elastic meson scattering dominates.However, we propose two controllable protocols that allow for a clear observation of dynamical hadron formation.We discuss how this physics can be simulated in trapped-ion or Rydberg-atom setups.

DOI
10.1103/prxquantum.3.040309

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The study of confinement in quantum spin chains has seen a large surge of interest in recent years.It is not only important for understanding a range of effective one-dimensional condensed-matter realizations but it also shares some of the nonperturbative physics with quantum chromodynamics (QCD), which makes it a prime target for current quantum simulation efforts.In analogy to QCD, the confinementinduced two-particle bound states that appear in these models are dubbed mesons.Here, we study scattering events due to meson collisions in a quantum spin chain with long-range interactions such that two mesons have an extended interaction.We show how novel hadronic bound states, e.g., with four constituent particles akin to tetraquarks, may form dynamically in fusion events.In a natural collision their signal is weak, as elastic meson scattering dominates.However, we propose two controllable protocols that allow for a clear observation of dynamical hadron formation.We discuss how this physics can be simulated in trapped-ion or Rydberg-atom setups.
The phenomenon of confinement is well known in high-energy physics and can also be realized for low-energy domain-wall excitations in one-dimensional quantum spin chains. A bound state consisting of two domain walls can behave like a meson, and recently, Vovrosh et al. [PRX Quantum 3, 040309 (2022)] demonstrated that a pair of mesons could dynamically form a metastable confinement-induced bound state (consisting of four domain walls) akin to a hadronic state. However, the protocol discussed by Vovrosh et al. involving the use of interactions with characteristically nonmonotonic distance dependence is not easy to come by in nature, thus posing a challenge for its experimental realization. In this regard, Rydberg atoms can provide the required platform for simulating confinement-related physics. We exploit the flexibility offered by interacting Rydberg-dressed atoms to engineering modified spin-spin interactions for the one-dimensional transverse-field Ising model. Our numerical simulations show how Rydberg-dressed interactions can give rise to a variety of effective potentials that are suitable for hadron formation, which opens the possibility of simulating confinement physics with Rydberg platforms as a viable alternative to current trapped-ion experiments.
Studying high-energy collisions of composite particles, such as hadrons and nuclei, is an outstanding goal for quantum simulators. However, preparation of hadronic wave packets has posed a significant challenge, due to the complexity of hadrons and the precise structure of wave packets. This has limited demonstrations of hadron scattering on quantum simulators to date. Observations of confinement and composite excitations in quantum spin systems have opened up the possibility to explore scattering dynamics in spin models. In this article, we develop two methods to create entangled spin states corresponding to wave packets of composite particles in analog quantum simulators of Ising spin Hamiltonians. One wave-packet preparation method uses the blockade effect enabled by beyond-nearest-neighbor Ising spin interactions. The other method utilizes a quantum-bus-mediated exchange, such as the native spin-phonon coupling in trapped-ion arrays. With a focus on trapped-ion simulators, we numerically benchmark both methods and show that high-fidelity wave packets can be achieved in near-term experiments. We numerically study scattering of wave packets for experimentally realizable parameters in the Ising model and find inelastic-scattering regimes, corresponding to particle production in the scattering event, with prominent and distinct experimental signals. Our proposal, therefore, demonstrates the potential of observing inelastic scattering in near-term quantum simulators.
Quantum simulators hold the promise of probing central questions of high-energy physics in tunable condensed matter platforms, for instance, the physics of confinement. Local defects can be an obstacle in these setups, harming their simulation capabilities. However, defects in the form of impurities can also be useful as probes of many-body correlations and may lead to fascinating new phenomena themselves. Here, we investigate the interplay between impurity and confinement physics in a basic spin chain setup, showing the emergence of exotic excitations as impurity-meson bound states with a long lifetime. For weak confinement, semiclassical approximations can describe the capture process in a meson-impurity scattering event. In the strong-confining regime, intrinsic quantum effects are visible through the quantization of the emergent bound state energies which can be readily probed in quantum simulators.
Studying high-energy collisions of composite particles, such as hadrons and nuclei, is an outstanding goal for quantum simulators. However, preparation of hadronic wave packets has posed a significant challenge, due to the complexity of hadrons and the precise structure of wave packets. This has limited demonstrations of hadron scattering on quantum simulators to date. Observations of confinement and composite excitations in quantum spin systems have opened up the possibility to explore scattering dynamics in spin models. In this article, we develop two methods to create entangled spin states corresponding to wave packets of composite particles in analog quantum simulators of Ising spin Hamiltonians. One wave-packet preparation method uses the blockade effect enabled by beyond-nearest-neighbor Ising spin interactions. The other method utilizes a quantum-bus-mediated exchange, such as the native spin-phonon coupling in trapped-ion arrays. With a focus on trapped-ion simulators, we numerically benchmark both methods and show that high-fidelity wave packets can be achieved in near-term experiments. We numerically study scattering of wave packets for experimentally realizable parameters in the Ising model and find inelastic-scattering regimes, corresponding to particle production in the scattering event, with prominent and distinct experimental signals. Our proposal, therefore, demonstrates the potential of observing inelastic scattering in near-term quantum simulators.
We study the quasiparticle excitation and quench dynamics of the one-dimensional transverse-field Ising model with power-law (1/r^{α}) interactions. We find that long-range interactions give rise to a confining potential, which couples pairs of domain walls (kinks) into bound quasiparticles, analogous to mesonic states in high-energy physics. We show that these quasiparticles have signatures in the dynamics of order parameters following a global quench, and the Fourier spectrum of these order parameters can be exploited as a direct probe of the masses of the confined quasiparticles. We introduce a two-kink model to qualitatively explain the phenomenon of long-range-interaction-induced confinement and to quantitatively predict the masses of the bound quasiparticles. Furthermore, we illustrate that these quasiparticle states can lead to slow thermalization of one-point observables for certain initial states. Our work is readily applicable to current trapped-ion experiments.
Confinement describes the phenomenon when the attraction between two particles grows with their distance, most prominently found in quantum chromodynamics (QCD) between quarks. In condensed matter physics, confinement can appear in quantum spin chains, for example, in the one dimensional transverse field Ising model (TFIM) with an additional longitudinal field, famously observed in the quantum material cobalt niobate or in optical lattices. Here, we establish that state-of-the-art quantum computers have reached capabilities to simulate confinement physics in spin chains. We report quantitative confinement signatures of the TFIM on an IBM quantum computer observed via two distinct velocities for information propagation from domain walls and their mesonic bound states. We also find the confinement induced slow down of entanglement spreading by implementing randomized measurement protocols for the second order Rényi entanglement entropy. Our results are a crucial step for probing non-perturbative interacting quantum phenomena on digital quantum computers beyond the capabilities of classical hardware.