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At least 217 records · Page 12
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DOE OSTI2022

Traversable wormhole dynamics on a quantum processor

The holographic principle, theorized to be a property of quantum gravity, postulates that the description of a volume of space can be encoded on a lower-dimensional boundary. The anti-de Sitter (AdS)/conformal field theory correspondence or duality is the principal example of holography. The Sachdev–Ye–Kitaev (SYK) model of N >> 1 Majorana fermions has features suggesting the existence of a gravitational dual in AdS 2 , and is a new realization of holography. Here, we invoke the holographic correspondence of the SYK many-body system and gravity to probe the conjectured ER=EPR relation between entanglement and spacetime geometry through the traversable wormhole mechanism as implemented in the SYK model. A qubit can be used to probe the SYK traversable wormhole dynamics through the corresponding teleportation protocol. This can be realized as a quantum circuit, equivalent to the gravitational picture in the semiclassical limit of an infinite number of qubits. Here we use learning techniques to construct a sparsified SYK model that we experimentally realize with 164 two-qubit gates on a nine-qubit circuit and observe the corresponding traversable wormhole dynamics. Despite its approximate nature, the sparsified SYK model preserves key properties of the traversable wormhole physics: perfect size winding, coupling on either side of the wormhole that is consistent with a negative energy shockwave, a Shapiro time delay, causal time-order of signals emerging from the wormhole, and scrambling and thermalization dynamics. Our experiment was run on the Google Sycamore processor. By interrogating a two-dimensional gravity dual system, our work represents a step towards a program for studying quantum gravity in the laboratory. Future developments will require improved hardware scalability and performance as well as theoretical developments including higher-dimensional quantum gravity duals and other SYK-like models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Majorana bound states with chiral magnetic textures

The aim of this Tutorial is to give a pedagogical introduction into realizations of Majorana fermions, usually termed as Majorana bound states (MBSs), in condensed matter systems with magnetic textures. We begin by considering the Kitaev chain model of “spinless” fermions and show how two “half” fermions can appear at chain ends due to interactions. By considering this model and its two-dimensional generalization, we emphasize intricate relation between topological superconductivity and possible realizations of MBS. We further discuss how “spinless” fermions can be realized in more physical systems, e.g., by employing the spin-momentum locking. Next, we demonstrate how magnetic textures can be used to induce synthetic or fictitious spin–orbit interactions, and, thus, stabilize MBS. We describe a general approach that works for arbitrary textures and apply it to skyrmions. We show how MBS can be stabilized by elongated skyrmions, certain higher order skyrmions, and chains of skyrmions. We also discuss how braiding operations can be performed with MBS stabilized on magnetic skyrmions. Furthermore, this Tutorial is aimed at students at the graduate level.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Fusion dynamics of Majorana zero modes

Braiding and fusion of Majorana zero modes are key elements of any future topological Majorana-based quantum computer. In this article, we investigate the fusion dynamics of Majorana zero modes in the spinless Kitaev model, as well as in a spinful model describing magnet-superconductor hybrid structures. We consider various scenarios allowing us to reproduce the fusion rules of the Ising anyon model. Particular emphasis is given to the charge of the fermion obtained after fusing two Majorana zero modes: as long as it remains on the superconductor, charge quantization is absent. When moving the fermion to a nonsuperconducting region, such as a quantum dot, nearly quantized charge can be measured. Our findings confirm for both platforms that fusion dynamics of Majorana zero modes can indeed be used for the readout of Majorana qubits.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Scaling behavior and giant field enhancement of the thermal conductivity in the honeycomb antiferromagnet BaCo 2⁢ (AsO 4 ) 2

The layered honeycomb material BaCo 2 (AsO 4 ) 2 is of topical interest because its magnetic state is related to that of the Kitaev magnet α-RuCl 3 . Using thermal transport to probe how magnetic excitations interact with phonons in the magnetically disordered regime, we have uncovered an unusually large enhancement of the thermal conductivity κ xx in an in-plane magnetic field H. Just above the Néel temperature T N , a field of 13 T increases κ xx by a factor of ∼ 211, which is very large compared to other magnetic insulators. Interestingly, κ xx (H, T) exhibits a scaling behavior in the entire magnetically disordered region that surrounds the ordered zigzag state. The ratio Δκ xx (H, T)/κ xx (13, T), measured throughout the disordered region, collapses to a one-parameter scaling function exp(−1/gx) (where x = μ B B/k B T and g is a constant).

36 MATERIALS SCIENCE↗
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 OSTI2026

Concatenated dual displacement code for continuous-variable quantum error correction

The continuous-variable (CV) Gaussian no-go theorem fundamentally limits the suppression of Gaussian displacement errors using only Gaussian gates and states. Prior studies have employed Gottesman-Kitaev-Preskill (GKP) states as ancillary qumodes to suppress small Gaussian displacement errors. However, when the displacement magnitude becomes large, inevitable lattice-crossing errors arise beyond the correctable range of the GKP state. To address this issue, we concatenate the Gaussian-noise-suppression circuit with an outer analog Steane code that corrects such occasional lattice-crossing events as well as other abrupt displacement errors. Contrary to conventional concatenation, which primarily aims to reduce logical error rates, the Steane-GKP duality in encoding provides complementary protection against displacement errors at different scales: The inner GKP layer employs non-Gaussian resources to suppress continuous Gaussian noise and reduce residual variance, while the outer analog Steane code corrects discrete lattice-crossing events that exceed the GKP correctable range. It is precisely this separation of error-mitigation roles that enables CV error correction. In contrast to prior work on concatenating GKP and repetition codes to establish error correction for discrete qubit/qudit encoding, we provide correction in the continuous encoding space. Analytical studies show that, under infinite squeezing, the concatenated code suppresses the variance of Gaussian displacement errors acting on all qumodes by up to 50%, while enabling unbiased correction of lattice-crossing errors with a success probability determined by the ratio between the residual Gaussian error standard deviation and the lattice-crossing magnitude. Even with finite squeezing, the proposed architecture still provides Gaussian-error suppression and lattice-crossing correction. Moreover, the presence of the outer analog Steane code relaxes the squeezing requirement of the inner GKP states, indicating near-term experimental feasibility. This work establishes a viable route toward fault-tolerant continuous-variable quantum computation and provides insight into the design of concatenated CV error-correcting architectures.

quantum error correction↗
DOE OSTI2026

Understanding Majorana braiding in superconductors with a fixed total number of particles

Mean-field one-dimensional topological superconductors host edge Majorana zero modes (MZMs) that encode a topologically protected ground-state degeneracy and enable robust braiding operations within this subspace. Mean-field states lack definite particle number and thus cannot represent isolated systems. Nevertheless, projecting them onto fixed particle number can yield good approximations to an isolated superconductor ground state. In earlier work [Sajith et al., Phys. Rev. B 109, 184509 (2024)] we showed that the projected Kitaev wave function of a single wire preserves some important mean-field features, such as the zero-energy spectral peaks near the wire edges. However, uniqueness of the fixed-number ground state does not allow for any nontrivial operations in the ground-state subspace. To overcome this limitation, here we consider the case of multiple wires with a conserved total charge, using the same approach. In the limit of vanishing interwire coupling, this system has a macroscopic ground-state degeneracy. We show how this degeneracy is resolved by coherent single-particle tunneling, and identify special many-body states which play the same role as the MZM parity states in the mean field. In this work, we demonstrate how braiding operations can be implemented and discuss both intrinsic and extrinsic limits on their fidelity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Magic state distillation from entangled states

We report that magic can be distributed non-locally in many-body entangled states, such as the low energy states of condensed matter systems. Using the Bravyi-Kitaev magic state distillation protocol, we find that non-local magic is distillable and can improve the distillation outcome. We analyze a few explicit examples and show that spin squeezing can be used to convert non-distillable states into distillable ones. Our analysis also suggests that the conventional product input states assumed by magic distillation protocols are extremely atypical among general states with distillable magic. It further justifies the need for studying a diverse range of entangled inputs that yield magic states with high probability.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Determining topological order from infinite projected entangled pair states

In this work, we present a method of extracting information about the topological order from the ground state of a strongly correlated two-dimensional system computed with the infinite projected entangled pair state (iPEPS). For topologically ordered systems, the iPEPS wrapped on a torus becomes a superposition of degenerate, locally indistinguishable ground states. Projectors in the form of infinite matrix product operators onto states with well-defined anyon flux are used to compute topological S and T matrices (encoding mutual and self-statistics of emergent anyons). The algorithm is shown to be robust against a perturbation driving string-net toric code across a phase transition to a ferromagnetic phase. Our approach provides accurate results near quantum phase transition, where the correlation length is prohibitively large for other numerical methods. Moreover, we used numerically optimized iPEPS describing the ground state of the Kitaev honeycomb model in the toric code phase and obtained topological data in excellent agreement with theoretical prediction.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Magnetic anisotropy in ferromagnetic CrI 3

We use neutron scattering to show that ferromagnetic (FM) phase transition in the two-dimensional (2D) honeycomb lattice CrI 3 is a weakly first order transition and controlled by spin-orbit coupling (SOC) induced magnetic anisotropy, instead of magnetic exchange coupling as in a conventional ferromagnet. With increasing temperature, the magnitude of magnetic anisotropy, seen as a spin gap at the Brillouin zone center, decreases in a power law fashion and vanishes at T C , while the in-plane and c-axis spin-wave stiffnesses associated with magnetic exchange couplings remain robust at T C . We also compare parameter regimes where spin waves in CrI 3 can be described by a Heisenberg Hamiltonian with Dzyaloshinskii-Moriya interaction or a Heisenberg-Kitaev Hamiltonian. These results suggest that the SOC induced magnetic anisotropy plays a dominant role in stabilizing the FM order in single layer 2D van der Waals ferromagnets.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Competition between magnetic order and charge localization in Na 2 IrO 3 thin crystal devices thin crystal devices

Spin orbit assisted Mott insulators such as sodium iridate (Na 2 IrO 3 ) have been an important subject of study in recent years. In these materials, the interplay of electronic correlations, spin-orbit coupling, crystal field effects, and a honeycomb arrangement of ions bring exciting ground states, predicted in the frame of the Kitaev model. The insulating character of Na 2 IrO 3 has hampered its integration to an electronic device, desirable for applications, such as the manipulation of quasiparticles interesting for topological quantum computing. Here we show through electronic transport measurements supported by angle-resolved photoemission spectroscopy (ARPES) experiments, that electronic transport in Na 2 IrO 3 is ruled by variable range hopping and it is strongly dependent on the magnetic ordering transition known for bulk Na 2 IrO 3 , as well as on external electric fields. Furthermore, electronic transport measurements allow us to deduce a value for the localization length and the density of states in our Na 2 IrO 3 thin crystal devices, and offer an alternative approach to study insulating 2D-materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Scrambling versus relaxation in Fermi and non-Fermi liquids

In this work, we compute the Lyapunov exponent characterizing quantum scrambling in a family of generalized Sachdev- Ye-Kitaev models, which can be tuned between different low temperature states from Fermi liquids, through non-Fermi liquids, to fast scramblers. The analytic calculation, controlled by a small coupling constant and large $\textit{N}$, allows us to clarify the relations between the quasiparticle relaxation rate $\textit{1/τ}$ and the Lyapunov exponent $λ_L$ characterizing scrambling. In the Fermi liquid states we find that the quasiparticle relaxation rate dictates the Lyapunov exponent. In non-Fermi liquids, where $1/τ \gg T$, we find that $λ_L$ is always $\textit{T}$ linear with a prefactor that is independent of the coupling constant in the limit of weak coupling. Instead it is determined by a scaling exponent that characterizes the relaxation rate. $λ_L$ approaches the general upper bound 2$\textit{πT}$ at the transition to a fast scrambling state. Finally, in a marginal Fermi liquid state the exponent is linear in temperature with a prefactor that vanishes as a nonanalytic function ~$g\text{ln}(1/g)$ of the coupling constant $\textit{g}$.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Soluble limit and criticality of fermions in $\mathbb Z_2$ gauge theories

Quantum information theory and strongly correlated electron systems share a common theme of macroscopic quantum entanglement. In both topological error correction codes and theories of quantum materials (spin liquid, heavy fermion and high-$T_c$ systems), entanglement is implemented by means of an emergent gauge symmetry. Inspired by these connections, in this paper we introduce a simple model for fermions moving in the deconfined phase of a $\mathbb Z_2$ gauge theory by coupling Kitaev's toric code to mobile fermions. This permits us to exactly solve the ground state of this system and map out its phase diagram. Reversing the sign of the plaquette term in the toric code permits us to tune the ground state between an orthogonal metal and an orthogonal semimetal in which gapless quasiparticles survive despite a gap in the spectrum of original fermions. The small-to-large Fermi surface transition between these two states occurs in a stepwise fashion with multiple intermediate phases. By using a diagrammatic technique, we are able to explore physics beyond the integrable point to examine various instabilities of the deconfined phase and to derive the critical theory at the transition between deconfined and confined phases. We outline how the fermionic toric code can be implemented as a quantum circuit, thus providing an important link between quantum materials and quantum information theory.

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 OSTI2021

Excitation spectra of quantum matter without quasiparticles. II. Random t - J models

Here, we present numerical solutions of the spectral functions of large dimension t -J models with random nearest neighbor exchange and global SU(M) spin rotation symmetry. The solutions are obtained from the saddle-point equations of the large dimension limit, followed by the large M limit. The same saddle point equations also apply to the model with all-to-all and random hopping and exchange. Such a t -J model realizes a deconfined critical state proposed as a model for the optimally doped cuprates. The large M theory involves Green’s functions for fractionalized spinons and holons carrying emergent U(1) gauge charges, obeying relations similar to those of the Sachdev-Ye-Kitaev (SYK) models. The low frequency spectral functions are compared with an analytic analysis of the operator scaling dimensions with good agreement. We also compute the low frequency and temperature behavior of experimentally observable gauge-invariant observables: the electron Green’s function, the local spin susceptibility and the optical conductivity, along with the temperature dependence of the d.c. resistivity. The time reparameterization soft mode (equivalent to the boundary graviton in holographically dual models of two-dimensional quantum gravity) makes important contributions to all observables and provides a linear-in-temperature contribution to the d.c. resistivity.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Dynamics of local magnetic moments induced by itinerant Weyl electrons

We derive the effective interactions between local magnetic moments which are mediated by Weyl electrons in magnetic topological semimetals. The resulting spin dynamics is governed by the induced Heisenberg, Kitaev, and Dzyaloshinskii-Moriya (DM) interactions with extended range and oscillatory dependence on the distance between the spins. These interactions are realized in multiple competing channels shaped by the multitude of Weyl nodes in the electron spectrum. Microscopic spins need to be spatially modulated with a channel-dependent wave vector in order to take advantage of the interactions. The DM vector is parallel to the displacement between the two interacting spins, and requires the presence of Weyl electron Fermi surfaces. Here, we also derive the Weyl-induced chiral three-spin interaction in the presence of an external magnetic field. This interaction has an extended range as well, and acts upon the spatially modulated spins in various channels. Its tendency is to produce a skyrmion lattice or a chiral spin liquid which exhibits topological Hall effect. Ultimately, the theory developed here addresses magnetic dynamics in relativistic metals even when chiral magnetism is microscopically precluded. We discuss insights into the ordered state of the magnetic Weyl semimetal NdAlSi.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Field-induced intermediate ordered phase and anisotropic interlayer interactions in α-RuCl 3

In α-RuCl 3 , an external magnetic field applied within the honeycomb plane can induce a transition from a magnetically ordered state to a disordered state that is potentially related to the Kitaev quantum spin liquid. In zero field, single crystals with minimal stacking faults display a low-temperature state with in-plane zigzag antiferromagnetic order and a three-layer periodicity in the direction perpendicular to the honeycomb planes. In this work, we present angle-dependent magnetization, ac susceptibility, and thermal transport data that demonstrate the presence of an additional intermediate-field ordered state at fields below the transition to the disordered phase. Neutron-diffraction results show that the magnetic structure in this phase is characterized by a six-layer periodicity in the direction perpendicular to the honeycomb planes. Theoretically, the intermediate ordered phase can be accounted for by including spin-anisotropic couplings between the layers in a three-dimensional spin model. Together, this demonstrates the importance of interlayer exchange interactions in α-RuCl 3 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗