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DOE OSTI2023

Confinement of many-body Bethe strings

Based on the Bethe ansatz approach and inelastic neutron scattering experiments, we reveal the evolution of confinement of many-body Bethe strings in ordered regions of the quasi-one-dimensional antiferromagnet YbAlO 3 . In the antiferromagnetic phase, the spin dynamics is dominated by confined length-1 Bethe strings, whose dominancy in the high-energy branch of the excitation spectrum yields to confined length-2 Bethe strings when the material is tuned to the spin-density-wave phase. In the thermal-induced disordered region, the confinement effect disappears, and the system restores the conventional quantum integrable physics of the one-dimensional Heisenberg model. Finally, our results establish a unified picture based on a Bethe string for the spin dynamics in different magnetic phases of YbAlO 3 , and thus provide profound insight into many-body quantum magnetism.

1-dimensional spin chains↗

DOE OSTI2021

Dynamical properties of a driven dissipative dimerized $S$ =1/2 chain

We consider the dynamical properties of a gapped quantum spin system coupled to the electric field of a laser, which drives the resonant excitation of specific phonon modes that modulate the magnetic interactions. Here, we deduce the quantum master equations governing the time-evolution of both the lattice and spin sectors, by developing a Lindblad formalism with bath operators providing an explicit description of their respective phonon-mediated damping terms. We investigate the nonequilibrium steady states (NESS) of the spin system established by a continuous driving, delineating parameter regimes in driving frequency, damping, and spin-phonon coupling for the establishment of physically meaningful NESS and their related nontrivial properties. Focusing on the regime of generic weak spin-phonon coupling, we characterize the NESS by their frequency and wave-vector content, explore their transient and relaxation behavior, and discuss the energy flow, the system temperature, and the critical role of the type of bath adopted. Our study lays a foundation for the quantitative modeling of experiments currently being designed to control coherent many-body spin states in quantum magnetic materials.

1-dimensional spin chains↗

DOE OSTI2022

Demonstration of long-range correlations via susceptibility measurements in a one-dimensional superconducting Josephson spin chain

Abstract Spin chains have long been considered an effective medium for long-range interactions, entanglement generation, and quantum state transfer. In this work, we explore the properties of a spin chain implemented with superconducting flux circuits, designed to act as a connectivity medium between two superconducting qubits. The susceptibility of the chain is probed and shown to support long-range, cross-chain correlations. In addition, interactions between the two end qubits, mediated by the coupler chain, are demonstrated. This work has direct applicability in near term quantum annealing processors as a means of generating long-range, coherent coupling between qubits.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Chiral topologically ordered insulating phases in arrays of interacting integer quantum Hall islands

Here, we study networks of Coulomb-blockaded integer quantum Hall islands with even fillings ν = 2 k ( k being an integer), including cases with 2 k layers each of ν = 1 fillings. Allowing only spin-current interactions between the islands (i.e., without any charge transfer), we obtain solvable models leading to a rich set of insulating S U ( 2 ) k topologically ordered phases. The case with k = 1 is dual to the Kalmeyer-Laughlin phase, k = 2 to Kitaev's chiral spin liquid and the Moore-Read state, and k = 3 contains a Fibonacci anyon that may be utilized for universal topological quantum computation. Additionally, we show how the S U ( 2 ) k topological phases may be obtained also in an array of islands with ν = 2 k integer quantum Hall states and critical spin chains in a checkerboard pattern. The array and checkerboard constructions gap out the charge mode and additional “flavor” modes by virtue of their geometry. Furthermore, we find that a fine tuning of the system parameter is not needed in the checkerboard configuration and the ν = 2 case. We also discuss their bulk excitations, and show that their thermal Hall conductance is universal, reflecting the central charge c = 3 k / ( k + 2 ) of the chiral edge modes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Dynamics of nonequilibrium magnons in gapped Heisenberg antiferromagnets

Nonequilibrium dynamics in spin systems is a topic currently under intense investigation as it provides fundamental insights into thermalization, universality, and exotic transport phenomena. While most of the studies have been focused on ideal closed quantum many-body systems such as ultracold atomic quantum gases and one-dimensional spin chains, driven-dissipative Bose gases in steady states away from equilibrium in classical systems also lead to intriguing nonequilibrium physics. Here, in this work, we theoretically investigate out-of-equilibrium dynamics of magnons in a gapped Heisenberg quantum antiferromagnet based on Boltzmann transport theory. We show that, by treating scattering terms beyond the relaxation-time approximation in the Boltzmann transport equation, energy and particle number conservation mandate that nonequilibrium magnons cannot relax to equilibrium, but decay to other nonequilibrium stationary states. The only decay channel for these stationary states back to equilibrium is through the nonconserving interactions (i.e., changing particle number and/or energy within the magnon system) such as boundary or magnon-phonon scattering. At low temperatures, these nonconserving interactions are much slower processes than intrinsic magnon-magnon interaction in a gapped spin system. Using magnon-phonon interaction as a quintessential type of nonconserving interaction, we then propose that nonequilibrium steady states of magnons can be maintained and tailored using periodic driving at frequencies faster than relaxation due to phonon interactions. These findings reveal a class of classical material systems that are suitable platforms to study nonequilibrium statistical physics and macroscopic phenomena such as classical Bose-Einstein condensation of quasiparticles and magnon supercurrents that are relevant for spintronic applications.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Floquet Engineering of Interactions and Entanglement in Periodically Driven Rydberg Chains

Neutral atom arrays driven into Rydberg states constitute a promising approach for realizing programmable quantum systems. Enabled by strong interactions associated with Rydberg blockade, they allow for simulation of complex spin models and quantum dynamics. We introduce a new Floquet engineering technique for systems in the blockade regime that provides control over novel forms of interactions and entanglement dynamics in such systems. Our approach is based on time-dependent control of Rydberg laser detuning and leverages perturbations around periodic many-body trajectories as resources for operator spreading. These time-evolved operators are utilized as a basis for engineering interactions in the effective Hamiltonian describing the stroboscopic evolution. As an example, we show how our method can be used to engineer strong spin exchange, consistent with the blockade, in a one-dimensional chain, enabling the exploration of gapless Luttinger liquid phases. In addition, we demonstrate that combining gapless excitations with Rydberg blockade can lead to dynamic generation of large-scale multipartite entanglement. Experimental feasibility and possible generalizations are discussed.

Floquet systems↗

DOE OSTI2021

Nonadiabatic Phase Transition with Broken Chiral Symmetry

We explore nonadiabatic quantum phase transitions in an Ising spin chain with a linearly time-dependent transverse field and two different spins per unit cell. Such a spin system passes through critical points with gapless excitations, which support nonadiabatic transitions. Nevertheless, we find that the excitations on one of the chain sublattices are suppressed in the nearly adiabatic regime exponentially. Furthermore, we reveal a coherent mechanism to induce exponentially large density separation for different quasiparticles.

1-dimensional spin chains↗

DOE OSTI2021

Exact results for nonlinear Drude weights in the spin-1/2 XXZ chain

Nonlinear Drude weight (NLDW) is a generalization of the linear Drude weight, which characterizes the nonlinear transport in quantum many-body systems. We investigate these weights for the spin-1/2 XXZ chain in the critical regime. The effects of the Dzyaloshinskii-Moriya interaction and an external magnetic field are also studied. Solving the Bethe equations numerically, we obtain these weights for very large system sizes and identify parameter regimes where the weights diverge in the thermodynamic limit. These divergences appear in all the orders studied in this Letter and can be regarded as a generic feature of the NLDWs. We study the origin of these divergences and reveal that they result from nonanalytic finite-size corrections to the ground-state energy. As a result, we compute closed-form expressions for several weights in the thermodynamic limit and find excellent agreement with the numerical results.

1-dimensional systems↗

DOE OSTI2022

Quantum time dynamics employing the Yang-Baxter equation for circuit compression

Quantum time dynamics (QTD) is considered a promising problem for quantum supremacy on near-term quantum computers. However, QTD quantum circuits grow with increasing time simulations. This study focuses on simulating the time dynamics of one-dimensional (1D) integrable spin chains with nearest-neighbor interactions. We have proved the existence of a reflection symmetry in the quantum circuit employed for simulating the time evolution of certain classes of 1D Heisenberg model Hamiltonians by virtue of the quantum Yang-Baxter equation, and how this symmetry can be exploited to compress and produce a shallow quantum circuit. With this compression scheme, the depth of the quantum circuit becomes independent of step size and only depends on the number of spins. We show that the depth of the compressed circuit is rigorously a linear function of the system size for the studied Heisenberg model Hamiltonians in the present work. As a consequence, the number of CNOT gates in the compressed circuit only scales quadratically with the system size, which allows for the simulations of time dynamics of very large 1D spin chains. We derive the compressed circuit representations for different special cases of the Heisenberg Hamiltonian. We compare and demonstrate the effectiveness of this approach by performing simulations on quantum computers.

1-dimensional spin chains↗

DOE OSTI2020

Spinon excitations in the quasi-one-dimensional $S = \frac{1}{2}$ chain compound Cs 4 CuSb 2 Cl 12

The spin-$\frac{1}{2}$ Heisenberg antiferromagnetic chain is ideal for realizing one of the simplest gapless quantum spin liquids (QSLs), supporting a many-body ground state whose elementary excitations are fractional fermionic excitations called spinons. Here we report the discovery of such a one-dimensional (1D) QSL in Cs 4 CuSb 2 Cl 12 . Compared to previously reported $S = \frac{1}{2}$ 1D chains, this material possesses a wider temperature range over which the QSL state is stabilized. In this work, we identify spinon excitations extending at $\textit{T}$ > 0.8 K, with a large $\textit{T}$-linear contribution to the specific heat, γ = 31.5(2)mJ mol –1 K –2 , which contribute itinerantly to thermal transport up to temperatures as high as $\textit{T}$ = 35 K. At $\textit{T}$ = 0.7 K , we find a second-order phase transition that is unchanged by a $μ_0H = 5T$ magnetic field. Cs 4 CuSb 2 Cl 12 reveals new phenomenology deep in the 1D QSL regime, supporting a gapped QSL phase over a wide temperature range compared to many other experimental realizations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Deconfined classical criticality in the anisotropic quantum spin- 1 2 XY model on the square lattice

The anisotropic quantum spin- 1 2 XY model on a linear chain was solved by Lieb, Schultz, and Mattis [] and shown to display a continuous quantum phase transition at the O(2) symmetric point separating two gapped phases with competing Ising long-range order. For the square lattice, the following is known. The two competing Ising ordered phases extend to finite temperatures, up to a boundary where a transition to the paramagnetic phase occurs, and meet at the O(2) symmetric critical line along the temperature axis that ends at a tricritical point at the Berezinskii-Kosterlitz-Thouless transition temperature where the two competing phases meet the paramagnetic phase. We show that the first-order zero-temperature (quantum) phase transition that separates the competing phases as a function of the anisotropy parameter is smoothed by thermal fluctuations into deconfined classical criticality. Published by the American Physical Society 2025

Mudry, Christopher (ORCID:0000000340746758)↗

DOE OSTI2023

Quasi-one-dimensional Pb 5 Re 3 O 15 : A 5 d realization of the Heisenberg antiferromagnetic spin-1/2 chain

Quasi-one-dimensional (1D) magnetic compounds connect the exact solutions of low-dimensional magnetic geometries, which promise quantum spin liquid behavior and exotic quasiparticles, with real-world materials, in which competing magnetic interactions affect their implementation in quantum information science. Here, the structural determination and quasi-1D magnetic behavior of a previously unreported compound, Pb 5 ⁢Re 3 ⁡O 15 , is presented. Like the anisotropic triangular A 3 ⁢ReO 5 ⁢Cl 2 (A = Ba, Sr, Ca) materials, Pb 5 ⁢Re 3 ⁡O 15 contains [ReO 5 ] square pyramids inserted into anion-centered quasi-two-dimensional layers and hosts spin-1/2 moments on the Re 6+ ions. Pb 5 ⁢Re 3 ⁡O 15 , however, has a more ideal quasi-1D geometry than the A 3 ⁢ReO 5 ⁢Cl 2 materials, with larger interchain distances and interlayer spacing. Quasi-1D magnetic behavior in Pb 5 ⁢Re 3 ⁡O 15 is confirmed by fitting the temperature-dependent magnetic susceptibility with the Bonner-Fisher model for a spin-1/2 antiferromagnetically coupled chain, yielding an intrachain coupling constant of |J|/k B =54.5K. Pb 5 ⁢Re 3 ⁡O 15 is highly insulating at room temperature, and heat capacity data below 10 K reveal a linear-T contribution that suggests the presence of low-temperature spinon excitations. Finally, with a lack of three-dimensional ordering down to at least 0.6 K, Pb 5 ⁢Re 3 ⁡O 15 is proposed as a model system for studying the quantum magnetism of quasi-1D Heisenberg chains in a real-world 5d 1 antiferromagnetic material.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Universality of Shallow Global Quenches in Critical Spin Chains

Measuring universal data in the strongly correlated regime of quantum critical points remains a fundamental objective for quantum simulators. In foundational work, Calabrese and Cardy demonstrated how these data govern the dynamics of certain global quenches to 1+1-dimensional conformal field theories. While the quasiparticle picture they introduce has been widely successful in both theory and experiment, their seminal prediction that the critical exponents are simply encoded in the relaxation rates of local observables is challenging to investigate experimentally. In this Letter, we examine the critical quench dynamics of local observables from two types of readily accessible initial conditions: ground states and finite-temperature ensembles. Here, we identify universal scaling collapses and scaling functions, utilizing a combination of conformal perturbation theory and tensor network numerics. For the finite-temperature quenches, we determine a regime in which the conformal field theory results are recovered, thereby allowing universal quantum critical data to be extracted from realistic quenches.

Quantum many-body systems↗

DOE OSTI2026

Superdiffusion resilience in Heisenberg chains with two-dimensional interactions on a quantum processor

Superdiffusive spin transport in the one-dimensional (1D) Heisenberg model is a key theoretical discovery in nonequilibrium quantum many-body physics. Although extensively studied in 1D systems, the breakdown and sustenance of superdiffusion in two-dimensional (2D) lattices with integrability-breaking terms, as found in real materials, remains an open question. To address this, we develop a toy model that extends the 1D Heisenberg model with a representative set of 2D interaction types and tunable strengths. Our model exhibits varying degrees of superdiffusion breakdown depending on the interaction type, spanning ballistic to diffusive regimes. We establish and justify a hierarchy of 2D interactions based on their resilience against superdiffusion breakdown: Heisenberg >𝑋⁢𝑋 > Ising. This precise control over the superdiffusive behavior also enables rigorous benchmarking of quantum hardware, and our simulations on IBM's Heron devices confirm the hardware's ability to accurately capture these many-body nonequilibrium phenomena. Overall, our results are relevant not only to simulating superdiffusion in real materials, such as the 1D Heisenberg compound KCuF3, which contains modest nonintegrable 2D terms, but also to extending superdiffusive behavior to larger 2D qubit lattices and other 2D materials.

Alagarsamy Manikandan, Keerthi Kumaran [ORNL]↗

DOE OSTI2026

Spontaneously Broken Noninvertible Symmetries in Transverse-Field Ising Qudit Chains

Recent developments have revealed that symmetries need not form a group, but instead can be noninvertible. Here we use analytical arguments and numerical evidence to illuminate how spontaneous symmetry breaking of a noninvertible symmetry is similar yet distinct from ordinary, invertible, symmetry breaking. We consider one-dimensional chains of group-valued qudits, whose local Hilbert space is spanned by elements of a finite group 𝐺 (reducing to ordinary qubits when 𝐺=ℤ 2 ). We construct Ising-type transverse-field Hamiltonians with Rep⁡(𝐺) symmetry whose generators multiply according to the tensor product of irreducible representations (irreps) of the group 𝐺 . For non-Abelian 𝐺 , the symmetry is noninvertible. In the symmetry broken phase there is one ground state per irrep on a closed chain. The symmetry breaking can be detected by local order parameters but, unlike the invertible case, different ground states have distinct entanglement patterns. We show that for each irrep of dimension greater than one the corresponding ground state exhibits string order, entanglement spectrum degeneracies, and has gapless edge modes on an open chain—features usually associated with symmetry-protected topological order. Consequently, domain wall excitations behave as one-dimensional non-Abelian anyons with nontrivial internal Hilbert spaces and fusion rules. Our Letter identifies properties of noninvertible symmetry breaking that existing quantum hardware can probe.

1-dimensional spin chains↗

DOE OSTI2023

Variational quantum simulation of the critical Ising model with symmetry averaging

Here we investigate the use of deep multiscale entanglement renormalization ansatz (DMERA) circuits as a variational ansatz. We use the exactly solvable one-dimensional critical transverse-field Ising model as a test bed. Numerically exact simulation of the quantum circuit ansatz can in this case be carried out to hundreds of qubits by exploiting efficient classical algorithms for simulating matchgate circuits. We find that, for this system, the DMERA strongly outperforms a standard quantum approximate optimization algorithm (QAOA)–style ansatz, and that a major source of systematic error in correlation functions approximated using the DMERA is the breaking of the translational and Kramers-Wannier symmetries of the transverse-field Ising model. We are able to reduce this error by up to four orders of magnitude by symmetry averaging, without incurring additional cost in qubits or circuit depth. Here, we propose that this technique for mitigating systematic error could be applied to noisy intermediate-scale quantum (NISQ) simulations of physical systems with other symmetries.

1-dimensional spin chains↗

DOE OSTI2023

Realizing symmetry-protected topological phases in a spin-1/2 chain with next-nearest-neighbor hopping on superconducting qubits

Quantum simulation on near-term quantum hardware is a topic of intense interest. The preparation of novel quantum states of matter provides a quantitative assessment of the capabilities of near-term digital quantum computers to implement circuits with structure of relevance to quantum simulation. Here, we conduct a benchmark study by realizing symmetry-protected topological (SPT) phases of a spin-1/2 Hamiltonian with next-nearest-neighbor hopping on up to 11 qubits on a programmable superconducting quantum processor using adiabatic state preparation. Using recompilation techniques to reduce the gate count to around 50 two-qubit gates, we observe clear signatures of the two distinct SPT phases, such as excitations localized to specific edges and finite string-order parameters. Finally, we identify a parasitic phase associated with the two-qubit gate as the dominant imperfection that limits the depth of the circuits, indicating a research topic of interest for future hardware development.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Quantum many-body scars in a Landau level on a thin torus

We review a kinetically constrained pair-hopping model that arises within a Landau level in the quantum Hall effect. At filling ν = 1/3, the model exactly maps onto the so-called “PXP model,” a constrained model for the Rydberg atom chain that is numerically known to exhibit ETH-violating states in the middle of the spectrum or quantum many-body scars. Indeed, particular charge density wave configurations exhibit the same revivals seen in the PXP model. We generalize the mapping to fillings factors ν = p/(2p+1), and show that the model is equivalent to nonintegrable spin chains within particular constrained Krylov Hilbert spaces. These lead to new examples of quantum many-body scars which manifest as revivals and slow thermalization of particular charge density wave states. Finally, we investigate the stability of the quantum scars under certain Hamiltonian perturbations motivated by the fractional quantum Hall physics.

1-dimensional spin chains↗