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arXiv:2610.10357

Quantum simulation of the Heisenberg XXZ model on a Rydberg atom array

Matthias Werner, Artur García-Sáez

quant-phcond-mat.quant-gascond-mat.str-elphysics.atom-phSubmitted Oct 7, 2026• Announced Oct 8, 2026• 0 citations
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Abstract

A major application of analog quantum hardware is quantum simulation, where a system evolves over time according to a given Hamiltonian. One challenge when implementing the Hamiltonian on a programmable quantum simulator is the availability of distinct coupling types, many of which go beyond the conventional ZZ-couplings found in Ising Hamiltonians that are naturally implemented by various platforms. In prior work, we have developed a method based on domain wall encoding to simulate one-dimensional spin chains using only Ising Hamiltonians, which would otherwise require XX+YY-couplings as well. Here, we implement the method on a commercially accessible Rydberg atom quantum device, and simulate the time evolution of the Heisenberg XXZ model with various anisotropies. We successfully probe the XY and Ising phases of the model and reproduce the qualitative behavior of several one- and two-body observables in both phases, as well as at the critical point. Our work augments the toolbox to simulate canonical quantum many-body systems on analog quantum simulators.

Comments
14 pages, 10 figures

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A major application of analog quantum hardware is quantum simulation, where a system evolves over time according to a given Hamiltonian. One challenge when implementing the Hamiltonian on a programmable quantum simulator is the availability of distinct coupling types, many of which go beyond the conventional ZZ-couplings found in Ising Hamiltonians that are naturally implemented by various platforms. In prior work, we have developed a method based on domain wall encoding to simulate one-dimensional spin chains using only Ising Hamiltonians, which would otherwise require XX+YY-couplings as well. Here, we implement the method on a commercially accessible Rydberg atom quantum device, and simulate the time evolution of the Heisenberg XXZ model with various anisotropies. We successfully probe the XY and Ising phases of the model and reproduce the qualitative behavior of several one- and two-body observables in both phases, as well as at the critical point. Our work augments the toolbox to simulate canonical quantum many-body systems on analog quantum simulators.
We use the resonant dipole-dipole interaction between Rydberg atoms and a periodic external microwave field to engineer XXZ spin Hamiltonians with tunable anisotropies.The atoms are placed in one-dimensional (1D) and two-dimensional (2D) arrays of optical tweezers.As illustrations, we apply this engineering to two iconic situations in spin physics: the Heisenberg model in square arrays and spin transport in 1D.We first benchmark the Hamiltonian engineering for two atoms and then demonstrate the freezing of the magnetization on an initially magnetized 2D array.Finally, we explore the dynamics of 1D domain-wall systems with both periodic and open boundary conditions.We systematically compare our data with numerical simulations and assess the residual limitations of the technique as well as routes for improvement.The geometrical versatility of the platform, combined with the flexibility of the simulated Hamiltonians, opens up exciting prospects in the fields of quantum simulation, quantum information processing, and quantum sensing.
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We investigate the magnetic-field dependence of the interaction between two Rydberg atoms, ∣nS1/2,mJ⟩|nS_{1/2}, m_J\rangle∣nS1/2​,mJ​⟩ and ∣(n+1)S1/2,mJ⟩|(n+1)S_{1/2}, m_J\rangle∣(n+1)S1/2​,mJ​⟩. In this setting, the effective spin-1/2 Hamiltonian takes the form of an {\it XXZ} model. We show that the anisotropy parameter of the {\it XXZ} model can be tuned by applying a magnetic field and, in particular, that it changes drastically near the Förster resonance points. Based on this result, we propose experimental realizations of spin-1/2 and spin-1 Heisenberg-type quantum spin models in Rydberg atom quantum simulators, without relying on Floquet engineering. Our results provide guidance for future experiments of Rydberg atom quantum simulators and offer insight into quantum many-body phenomena emerging in the Heisenberg model.
An important step towards a comprehensive understanding of far-from-equilibrium dynamics of quantum many-body systems is the identification of unifying features that are independent of microscopic details of the system. We experimentally observe such robust features in the magnetization relaxation dynamics of disordered Heisenberg XX, XXZ, and Ising Hamiltonians. We realize these Heisenberg spin models with tunable anisotropy parameter and power-law interactions in an ensemble of Rydberg atoms by encoding the spin in suitable Rydberg state combinations. We consistently observe stretched-exponential relaxation of magnetization for all considered spin models, collapsing onto a single curve after appropriate rescaling of time. This robust short-time relaxation behavior is explained by a perturbative treatment that exploits the strong disorder in pairwise couplings, which leads to a description in terms of approximately independent pairs of spins. In numerical simulations of small systems, we show that these pairs of spins constitute approximate local integrals of motion, which remain at least partially conserved on a timescale exceeding the duration of the relaxation dynamics of the magnetization. Published by the American Physical Society 2024
Programmable arrays of neutral Rydberg atoms are one of the leading platforms today for scalable quantum simulation and computation. In these systems, the dipole-dipole interactions between the individual atoms, or qubits, typically result in binary -- i.e., two-body -- couplings. In this work, we develop an experimentally accessible scheme for engineering three-body interactions in Rydberg lattices. Such strong three-body couplings can fundamentally modify the underlying physics compared to systems with only two-body interactions: we demonstrate this, in particular, by systematically investigating the effective many-body Hamiltonian and its emergent quantum phases. This capability paves the way for the quantum simulation of a broader class of correlated models of condensed matter and high-energy physics.
In recent years, analog quantum simulators have reached unprecedented quality, both in qubit numbers and coherence times. Most of these simulators natively implement Ising-type Hamiltonians, which limits the class of models that can be simulated efficiently. We propose a method to overcome this limitation and simulate the time evolution of a large class of spinless fermionic systems in one dimension (1D) using simple Ising-type Hamiltonians with local transverse fields. Our method is based on domain wall encoding, which is implemented via strong (anti)ferromagnetic couplings ∣J∣|J|∣J∣. We show that in the limit of strong ∣J∣|J|∣J∣, the domain walls behave like spinless fermions in 1D. The Ising Hamiltonians are one-dimensional chains with nearest-neighbor and, optionally, next-nearest-neighbor interactions. As a proof of concept, we perform numerical simulations of various 1D fermionic systems using domain wall evolution and accurately reproduce the systems' properties, such as topological edge states, Anderson localization, quantum chaotic time evolution, and time-reversal symmetry breaking via Floquet engineering. Our approach makes the simulation of a large class of fermionic many-body systems feasible on analog quantum hardware that natively implements Ising-type Hamiltonians with transverse fields.