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Physical Review Letters

Quantum Simulation of Motzkin Spin Chains with Rydberg Atoms

Anonymous, Hatem Barghathi, Adrian Del Maestro, Rick Mukherjee

Published Sep 23, 2026• 0 citations
Publisher

Abstract

The Motzkin spin chain is a well-known mathematical model with connections to symmetry-protected topological phases, such as the Haldane phase, as well as to concepts in the AdS/CFT correspondence. They exhibit highly entangled ground states that violate the area law and are exceptionally difficult to simulate with conventional numerical methods. Numerical simulations of the Motzkin ground state become further challenging at large system sizes due to their high-dimensional spin structure, rendering it a natural test bed for quantum simulation with ultracold systems. Here, we propose a Rydberg-atom based quantum simulation scheme that effectively realizes Motzkin spins using an experimentally accessible set of parameters. We show that the resulting effective Motzkin ground state reproduces the characteristic entanglement scaling and the block-structure properties of the reduced density matrix associated with the ideal Motzkin state. Our results establish a pathway toward a concrete experimental realization of Motzkin spins beyond purely mathematical constructions, opening avenues for exploring other similar exotic non-area-law entangled phases in programmable Rydberg simulators.

DOI
10.1103/ph91-6pg2

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The Motzkin spin chain is a well-known mathematical model with connections to symmetry-protected topological phases, such as the Haldane phase, as well as to concepts in the AdS/CFT correspondence. They exhibit highly entangled ground states that violate the area law and are exceptionally difficult to simulate with conventional numerical methods. Numerical simulations of the Motzkin ground state become further challenging at large system sizes due to their high-dimensional spin structure, rendering it a natural test bed for quantum simulation with ultracold systems. Here, we propose a Rydberg-atom based quantum simulation scheme that effectively realizes Motzkin spins using an experimentally accessible set of parameters. We show that the resulting effective Motzkin ground state reproduces the characteristic entanglement scaling and the block-structure properties of the reduced density matrix associated with the ideal Motzkin state. Our results establish a pathway toward a concrete experimental realization of Motzkin spins beyond purely mathematical constructions, opening avenues for exploring other similar exotic non-area-law entangled phases in programmable Rydberg simulators.
Motzkin spin chain is a well-known mathematical model with connections to symmetry-protected topological phases, such as the Haldane phase, as well as to concepts in the AdS/CFT correspondence. They exhibit highly entangled ground states that violate the area law and are exceptionally difficult to simulate with conventional numerical methods. Numerical simulations of the Motzkin ground state become further challenging at large system sizes due to their high-dimensional spin structure, rendering it a natural test bed for quantum simulation with ultra-cold systems. Here, we propose a Rydberg-atom based quantum simulation scheme that effectively realizes Motzkin spins using an experimentally accessible set of parameters. We show that the resulting effective Motzkin ground state reproduces the characteristic entanglement scaling and the block-structure properties of the reduced density matrix associated with the ideal Motzkin state. Our results establish a pathway toward a concrete experimental realization of Motzkin spins beyond purely mathematical constructions, opening avenues for exploring other similar exotic non-area-law entangled phases in programmable Rydberg simulators.
Abstract Topology in quantum many-body systems has profoundly changed our understanding of quantum phases of matter. The model that has played an instrumental role in elucidating these effects is the antiferromagnetic spin-1 Haldane chain 1,2 . Its ground state is a disordered state, with symmetry-protected fourfold-degenerate edge states due to fractional spin excitations. In the bulk, it is characterized by vanishing two-point spin correlations, gapped excitations and a characteristic non-local order parameter 3,4 . More recently it has been understood that the Haldane chain forms a specific example of a more general classification scheme of symmetry-protected topological phases of matter, which is based on ideas connected to quantum information and entanglement 5–7 . Here, we realize a finite-temperature version of such a topological Haldane phase with Fermi–Hubbard ladders in an ultracold-atom quantum simulator. We directly reveal both edge and bulk properties of the system through the use of single-site and particle-resolved measurements, as well as non-local correlation functions. Continuously changing the Hubbard interaction strength of the system enables us to investigate the robustness of the phase to charge (density) fluctuations far from the regime of the Heisenberg model, using a novel correlator.
We present a protocol to implement a spin-1 chain in Rydberg systems using three Rydberg states close to a Förster resonance. In addition to dipole-dipole interactions, strong van der Waals interactions naturally appear due to the presence of the Förster resonance and give rise to a highly tunable Hamiltonian. The resulting phase diagram is studied using the infinite density-matrix renormalization group and reveals a highly robust Haldane phase—a prime example of a symmetry-protected topological phase. We find experimentally accessible parameters to probe the Haldane phase in current Rydberg systems, and demonstrate an efficient adiabatic preparation scheme. This paves the way to probe the remarkable properties of spin fractionalization in the Haldane phase.
Quantum phases with topological order, such as quantum spin liquids, have been the focus of explorations for several decades. Such phases feature a number of remarkable properties including long-range quantum entanglement. Moreover, they can be potentially exploited for the realization of robust quantum computation, as exemplified by the paradigmatic toric code model. While some indications that such phases may be present in frustrated condensed matter systems have been previously reported, so far quantum spin liquids have eluded direct experimental detection. In this talk, I will show how a programmable quantum simulator based on Rydberg atom arrays can be used to realize and probe quantum spin liquid states. In our approach, atoms are placed on the links of a kagome lattice and coherent evolution under Rydberg blockade enables the transition into frustrated quantum states with no local order. We detect the onset of a quantum spin liquid phase of the toric code type by measuring topological string operators in two complementary bases. The properties of this state are further revealed using a lattice with non-trivial topology, representing a step towards the realization of a topological qubit. Our observations open the door to the controlled experimental exploration of topological quantum matter, and could enable the investigation of new methods for topologically protected quantum information processing.
Abstract The interplay between many-body interactions and the kinetic energy gives rise to rich phase diagrams hosting, among others, interaction-induced topological phases. These phases are characterized by both a local order parameter and a global topological invariant, and can exhibit exotic ground states such as self-trapped polarons and interaction-induced edge states. In this work, we investigate a realistic scenario for the quantum simulation of such systems using cold Rydberg-dressed atoms in optical lattices. We consider spinless fermions on a checkerboard lattice, interacting via the tunable-range effective potential induced by the Rydberg dressing. We perform a detailed analysis of the phase diagram at half- and incommensurate fillings, in the mean-field approximation. We furthermore study the stability of the phases with respect to temperature within the mean-field approximation and with respect to quantum fluctuations using the density matrix renormalization group method. Finally, we propose an implementation protocol, and in particular identify attainable regimes of experimental parameters in which the topological properties of the model become accessible. Our work thereby opens a realistic pathway to the outstanding experimental observation of this predicted phase in state-of-the-art cold atom quantum simulators.
The interplay between many-body interactions and the kinetic energy gives rise to rich phase diagrams hosting, among others, interaction-induced topological phases. These phases are characterized by both a local order parameter and a global topological invariant, and can exhibit exotic ground states such as self-trapped polarons and interaction-induced edge states. In this work, we investigate a realistic scenario for the quantum simulation of such systems using cold Rydberg-dressed atoms in optical lattices. We consider spinless fermions on a checkerboard lattice, interacting via the tunable-range effective potential induced by the Rydberg dressing. We perform a detailed analysis of the phase diagram at half- and incommensurate fillings, in the mean-field approximation. We furthermore study the stability of the phases with respect to temperature within the mean-field approximation and with respect to quantum fluctuations using the density matrix renormalization group method. Finally, we propose an implementation protocol, and in particular identify attainable regimes of experimental parameters in which the topological properties of the model become accessible. Our work, thereby, opens a realistic pathway to the outstanding experimental observation of this predicted phase in state-of-the-art cold atom quantum simulators.