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DOE OSTI2024

Determining the N -Representability of a Reduced Density Matrix via Unitary Evolution and Stochastic Sampling

The N-representability problem consists in determining whether, for a given p-body matrix, there exists at least one N-body density matrix from which the p-body matrix can be obtained by contraction, that is, if the given matrix is a p-body reduced density matrix (p-RDM). The knowledge of all necessary and sufficient conditions for a p-body matrix to be N-representable allows the constrained minimization of a many-body Hamiltonian expectation value with respect to the p-body density matrix and, thus, the determination of its exact ground state. However, the number of constraints that complete the N-representability conditions grows exponentially with system size, and hence, the procedure quickly becomes intractable for practical applications. This work introduces a hybrid quantum-stochastic algorithm to effectively replace the N-representability conditions. The algorithm consists of applying to an initial N-body density matrix a sequence of unitary evolution operators constructed from a stochastic process that successively approaches the reduced state of the density matrix on a p-body subsystem, represented by a p-RDM, to a target p-body matrix, potentially a p-RDM. The generators of the evolution operators follow the well-known adaptive derivative-assembled pseudo-Trotter method (ADAPT), while the stochastic component is implemented by using a simulated annealing process. The resulting algorithm is independent of any underlying Hamiltonian, and it can be used to decide whether a given p-body matrix is N-representable, establishing a criterion to determine its quality and correcting it. We apply the proposed hybrid ADAPT algorithm to alleged reduced density matrices from a quantum chemistry electronic Hamiltonian, from the reduced Bardeen–Cooper–Schrieffer model with constant pairing, and from the Heisenberg XXZ spin model. In all cases, the proposed method behaves as expected for 1-RDMs and 2-RDMs, evolving the initial matrices toward different targets.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Spin-strain interactions under hydrostatic pressure in α-RuCl 3

We investigate the effects of hydrostatic pressure on 𝛼−RuCl 3 , a prototypical material for the Kitaev spin model on a honeycomb lattice with a possible spin-liquid ground state. Using ultrasound measurements at pressures up to 1.16 GPa, we reveal significant modifications of the acoustic properties and the 𝐻−𝑇 phase diagram of this material. Hydrostatic pressure suppresses the three-dimensional magnetic order and induces a dimerization transition at higher pressures. At low pressures, the sound attenuation exhibits a linear temperature dependence, while above 0.28 GPa, it becomes nearly temperature independent, suggesting a shift in the phonon scattering regime dominated by Majorana fermions. These findings provide new insights into spin-strain interactions in Kitaev magnets and deliver a detailed characterization of the 𝐻−𝑇 phase diagram of 𝛼−RuCl 3 under hydrostatic pressure.

Focused ion beam↗

DOE OSTI2026

Krylov winding and emergent coherence in operator growth dynamics

The operator wavefunction provides a fine-grained description of quantum chaos and of the irreversible growth of simple operators into increasingly complex ones. Remarkably, at finite temperature this wavefunction can acquire a phase that increases linearly with the operator’s size, a phenomenon called . Although size winding occurs naturally in a holographic setting, the emergence of a coherent phase in a scrambled operator remains mysterious from the standpoint of a thermalizing quantum many-body system. Here, in this article, we elucidate this phenomenon by introducing the related concept of , whereby the operator wavefunction acquires a phase which winds linearly with the Krylov index. We show that Krylov winding is a generic feature of quantum chaotic systems and is a direct consequence of the universal operator growth bound hypothesis. It gives rise to size winding under two additional conditions: (i) a low-rank mapping between the Krylov and size bases, which ensures phase alignment among operators of the same size, and (ii) the saturation of the "chaos-operator growth" bound 𝜆 𝐿 ≤ 2⁢𝛼 (with 𝜆 𝐿 the Lyapunov exponent and 𝛼 the growth rate), which ensures a linear phase dependence on size. For systems which do not saturate this bound, with ℎ = 𝜆 𝐿 /2⁢𝛼 < 1, the winding with Pauli size ℓ becomes superliner, behaving as ℓ 1/ℎ . We illustrate these results with two classes of microscopic models: the Sachdev-Ye-Kitaev (SYK) model and its variants, and a disordered 𝑘-local spin model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Ground-state-based model reduction with unitary circuits

Here, we present a method to numerically obtain low-energy effective models based on a unitary transformation of the ground state. The algorithm finds a unitary circuit that transforms the ground state of the original model to a projected wavefunction with only the low-energy degrees of freedom. The effective model can then be derived using the unitary transformation encoded in the circuit. We test our method on the one-dimensional and two-dimensional square-lattice Hubbard model at half-filling, and obtain more accurate effective spin models than the standard perturbative approach.

Hubbard model↗

DOE OSTI2023

Lower Bounds on Quantum Annealing Times

The adiabatic theorem provides sufficient conditions for the time needed to prepare a target ground state. While it is possible to prepare a target state much faster with more general quantum annealing protocols, rigorous results beyond the adiabatic regime are rare. Here, we provide such a result, deriving lower bounds on the time needed to successfully perform quantum annealing. The bounds are asymptotically saturated by three toy models where fast annealing schedules are known: the Roland and Cerf unstructured search model, the Hamming spike problem, and the ferromagnetic p-spin model. Our bounds demonstrate that these schedules have optimal scaling. Herein, our results also show that rapid annealing requires coherent superpositions of energy eigenstates, singling out quantum coherence as a computational resource.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Theoretical Studies of Polar Systems near Ferroelectrics Quantum Critical Points (Final Report)

The PI has studied emergent quantum phases near polar quantum critical points. A first challenge was to develop a theoretical description of the observation that many polar materials undergo classical first-order transitions while displaying quantum criticality. The possibility of novel metallic states near polar quantum critical points was then studied; identification and characterization of a non-Fermi liquid phase was made in a multiband system. In dilute quantum critical polar metals, electronic coupling to polar energy fluctuations was shown to result in attractive electron-electron interactions and to superconductivity. A spin-phonon resonance measurement in applied magnetic field was proposed to determine the magnitude of spin-orbit mediated electron-phonon coupling; furthermore in the polar phase new field-induced phonon collective modes were identified with specific signatures for experiment. In order to keep current, the PI has also worked on other types of strongly correlated problems. With experimental groups, she has developed phenomenologies to identify and explain observed dynamical critical behaviors. The PI has studied the interplay of topology, fractionalization and deconfinement in a minimalist spin model. An emergent phase transition in a 1 + 1 frustrated spin nanotube has also been identified and characterized. The PI has also begun exploring criticality out of equilibrium, characterizing rich dynamical phases associated with photoinduced polar transitions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Simulating Meson Scattering on Spin 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.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

State preparation and measurement in a quantum simulation of the $O(\mathrm{3})$ sigma model

Recently, Singh and Chandrasekharan [Phys. Rev. D 100, 054505 (2019)] showed that fixed points of the nonlinear O ( 3 ) sigma model can be reproduced near a quantum phase transition of a spin model with just two qubits per lattice site. In a paper by the NuQS Collaboration [Phys. Rev. Lett. 123, 090501 (2019)], the proposal is made to simulate such field theories on a quantum computer using the universal properties of a similar model. In this paper, following that direction, we demonstrate how to prepare the ground state of the model from Singh and Chandrasekharan and measure a dynamical quantity of interest, the O ( 3 ) Noether charge, on a quantum computer. In particular, we apply Trotter methods to obtain results for the complexity of adiabatic ground state preparation in both the weak-coupling and quantum-critical regimes and use shadow tomography to measure the dynamics of local observables. Finally, we then present and analyze a quantum algorithm based on nonunitary randomized simulation methods that may yield an approach suitable for intermediate-term noisy quantum devices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Application of the variational autoencoder to detect the critical points of the anisotropic Ising model

We generalize the previous study on the application of variational autoencoders to the two-dimensional Ising model to a system with anisotropy. Due to the self-duality property of the system, the critical points can be located exactly for the entire range of anisotropic coupling. This presents an excellent test bed for the validity of using a variational autoencoder to characterize an anisotropic classical model. Furthermore, we reproduce the phase diagram for a wide range of anisotropic couplings and temperatures via a variational autoencoder without the explicit construction of an order parameter. Considering that the partition function of ($d$ + 1)-dimensional anisotropic models can be mapped to that of the $d$-dimensional quantum spin models, the present study provides numerical evidence that a variational autoencoder can be applied to analyze quantum systems via the quantum Monte Carlo method.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Kitaev model on a quantum computer using VQE with Majorana fermions

We study the simulation of the Kitaev spin model on quantum computers. In particular we focus on the models defined on the honeycomb, and square-octagon lattices. Using a fermionic language to describe these models reveals a region of the parameter space that is exactly solvable. We explore an ansatz that is capable of expressing the ground state in the exactly solvable region of the parameter space and extend it outside this region with good accuracy. Doing the calculation using fermions, while requiring the introduction of a non-local map from the fermionic Hilbert space to that of qubits, offers the potentially interesting application of realizing non-abelian anyons on quantum computers, and can also lead to a reduction in the number of qubits required by half.

Jahin, Ammar↗

DOE OSTI2023

NaRuO2: Kitaev-Heisenberg exchange in triangular-lattice setting

Abstract Kitaev exchange, a new paradigm in quantum magnetism research, occurs for 90° metal-ligand-metal links, $${t}_{2g}^{5}$$ t 2 g 5 transition ions, and sizable spin-orbit coupling. It is being studied in honeycomb compounds but also on triangular lattices. While for the former it is known by now that the Kitaev intersite couplings are ferromagnetic, for the latter the situation is unclear. Here we pin down the exchange mechanisms and determine the effective coupling constants in the $${t}_{2g}^{5}$$ t 2 g 5 triangular-lattice material NaRuO 2 , recently found to host a quantum spin liquid ground state. We show that, compared to honeycomb compounds, the characteristic triangular-lattice cation surroundings dramatically affect exchange paths and effective coupling parameters, changing the Kitaev interactions to antiferromagnetic. Quantum chemical analysis combined with subsequent effective spin model simulations provide perspective onto the nature of the experimentally observed quantum spin liquid—it seemingly implies fairly large antiferromagnetic second-neighbor isotropic exchange, and the atypical proximity to ferromagnetic order is related to ferromagnetic nearest-neighbor Heisenberg coupling.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Sunny.jl

Sunny is a Julia package designed to serve the needs of the quantum magnetism community. It supports the specification of a very broad class of spin models and a diverse suite of numerical solvers. These include powerful methods for simulating spin dynamics both in and out of equilibrium. Uniquely, it features a broad generalization of classical and semiclassical approaches to SU(N) coherent states, which is useful for studying systems exhibiting strong spin-orbit coupling or local entanglement effects. Sunny also offers a well-developed framework for calculating the dynamical spin structure factor, enabling direct comparison with scattering experiments. Ease of use is a priority, with tools for symmetry-guided modeling and interactive visualization.

Dahlbom, David↗

DOE OSTI2025

Sunny.jl: A Julia Package for Spin Dynamics

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Quantitative and interpretable order parameters for phase transitions from persistent homology

Here, we apply modern methods in computational topology to the task of discovering and characterizing phase transitions. As illustrations, we apply our method to four two-dimensional lattice spin models: the Ising, square ice, XY, and fully frustrated XY models. In particular, we use persistent homology, which computes the births and deaths of individual topological features as a coarse-graining scale or sublevel threshold is increased, to summarize multiscale and high-point correlations in a spin configuration. We employ vector representations of this information called persistence images to formulate and perform the statistical task of distinguishing phases. For the models we consider, a simple logistic regression on these images is sufficient to identify the phase transition. Interpretable order parameters are then read from the weights of the regression. This method suffices to identify magnetization, frustration, and vortex-antivortex structure as relevant features for phase transitions in our models. We also define “persistence” critical exponents and study how they are related to those critical exponents usually considered.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Quantum phases in the honeycomb-lattice J 1 – J 3 ferro-antiferromagnetic model

The significant role of quantum effects in magnets with competing interactions remains at the forefront of condensed matter physics for over 50 years, inspiring a multitude of quests for exotic states, models that can realize them, and real materials that can host them. The elusive spin-liquid states with strong entanglement are but one example; others include valence-bond phases with spatial symmetry breaking, quantum spin nematics that are quantum analogues of liquid crystals, and an especially extensive class of unconventional magnetically ordered phases that do not appear in the classical solutions of the underlying spin models. It is the latter group of phenomena that creates a broader context for the research effort in the present work concerning the search for and an identification of the novel ground states of quantum magnets. In this work, we have studied one of the paradigmatic models in quantum magnetism that is also attracting a significant recent interest because it appears to be providing a tantalizingly close description for many of the newly synthesized materials. We demonstrated that the phase diagram of the quantum ferro-antiferromagnetic model on the honeycomb lattice differs dramatically from the classical one. It hosts the double-zigzag and Ising-z phases as unexpected intermediaries between ferromagnetic and zigzag states that are also extended beyond their classical regions of stability. In broad agreement with quantum order-by-disorder arguments, these collinear phases completely supersede the classical spiral state.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Electronic structure, magnetic properties, spin orientation, and doping effect in Mn 3 Si 2 Te 6

The layered material Mn 3 Si 2 Te 6 , with alternating stacking honeycomb and triangular layers, is attracting considerable attention due to its rich physical properties. Here, in this study, using density functional theory and classical Monte Carlo (MC) methods, we systematically study this system with the 3d 5 electronic configuration. Near the Fermi level, the states are mainly contributed by Te 5p orbitals hybridized with Mn 3d orbitals, resembling a charge-transfer system. Furthermore, the spin orientations of the ferrimagnetic (FiM) ground state display different conductive behaviors when along the ab plane or out-of-plane directions: insulating vs metallic states. The energy difference between the FiM [110] insulating and FiM [001] metallic phases is very small (~0.71 meV/Mn) . Changing the angle θ of spin orientation from in-plane to out-of-plane directions, the band gaps of this system are gradually reduced, leading to an insulator-metal transition, resulting in an enhanced electrical conductivity, related to the colossal angular magnetoresistance (MR) effect. Although the three main magnetic couplings were found to be antiferromagnetic, overall the ground state is FiM. In addition, we also constructed the magnetic phase diagram using the classical XY spin model studied with the MC method. Three magnetic phases were obtained, including antiferromagnetic order, noncollinear spin patterns, and FiM order. Moreover, we also investigated the Se and Ge doping into the Mn 3 Si 2 Te 6 system: the FiM state has the lowest energy among the magnetic candidates for both Se- and Ge-doped cases. The magnetic anisotropy energy (MAE) decreases in the Se-doped case because the Mn orbital moment is reduced as the doping x increases. Due to the small spin-orbit-coupling effect of Se, the insulator-metal transition caused by the spin orientation disappears in the Se-doped case, resulting in an insulating phase in the FiM [001] phase. This causes a reduced colossal angular MR. However, both the MAE and the band gap of the Ge-doped case do not change much with increasing doping x . Our results for Mn 3 Si 2 Te 6 could provide guidance to experimentalists and theorists working on this system or related materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

A windowed mean trajectory approximation for condensed phase dynamics

We propose a trajectory-based quasi-classical method for approximating dynamics in condensed phase systems. Building upon the previously developed optimized mean trajectory approximation that has been used to compute linear and nonlinear spectra, we borrow some ideas from filtering trajectory methods to obtain a novel semiclassical method for the dynamical propagation of density matrices. This new approximation is tested rigorously against standard multistate electronic models, spin-boson models, and models of the Fenna–Matthews–Olson complex. For dissipative systems, the current method is significantly better or as good as many other semiclassical methods available, especially at low temperatures and for off-diagonal density matrix elements, whereas for scattering models, the current method bears similar limitations as mean-field propagation schemes. All results are tested against the numerically exact hierarchical equations of motion method. In conclusion, the new method shows excellent agreement across various parameter regimes with numerically exact results, highlighting the robustness and accuracy of our approach.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Kondo Lattice Model of Magic-Angle Twisted-Bilayer Graphene: Hund’s Rule, Local-Moment Fluctuations, and Low-Energy Effective Theory

For this work, we apply a generalized Schrieffer-Wolff transformation to the extended Anderson-like topological heavy fermion (THF) model for the magic-angle (θ=1.05°) twisted bilayer graphene (MATBLG) [Phys. Rev. Lett. 129, 047601 (2022)], to obtain its Kondo lattice limit. In this limit localized $\mathcal{f}$ electrons on a triangular lattice interact with topological conduction $\mathcal{c}$ electrons. By solving the exact limit of the THF model, we show that the integer fillings ν=0, ±1, ±2 are controlled by the heavy $\mathcal{f}$ electrons, while ν=±3 is at the border of a phase transition between two $\mathcal{f}$-electron fillings. For ν=0, ±1, ±2, we then calculate the Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions between the $\mathcal{f}$ moments in the full model and analytically prove the SU(4) Hund’s rule for the ground state which maintains that two $\mathcal{f}$ electrons fill the same valley-spin flavor. Our (ferromagnetic interactions in the) spin model dramatically differ from the usual Heisenberg antiferromagnetic interactions expected at strong coupling. We show the ground state in some limits can be found exactly by employing a positive semidefinite “bond-operators” method. We then compute the excitation spectrum of the $\mathcal{f}$ moments in the ordered ground state, prove the stability of the ground state favored by RKKY interactions, and discuss the properties of the Goldstone modes, the (reason for the accidental) degeneracy of (some of) the excitation modes, and the physics of their phase stiffness. We develop a low-energy effective theory for the $\mathcal{f}$ moments and obtain analytic expressions for the dispersion of the collective modes. We discuss the relevance of our results to the spin-entropy experiments in TBG.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗