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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Robustness of Vacancy-Bound Non-Abelian Anyons in the Kitaev Model in a Magnetic Field

Non-Abelian anyons in quantum spin liquids (QSLs) provide a promising route to fault-tolerant topological quantum computation. In the exactly solvable Kitaev honeycomb model, such anyons of the QSL state can be bound to nonmagnetic spin vacancies and endowed with non-Abelian statistics by an infinitesimal magnetic field. Here, we investigate how this approach for stabilizing non-Abelian anyons extends to a finite magnetic field represented by a proper Zeeman term. Through large-scale density-matrix renormalization group simulations, we compute the vacancy-anyon binding energy as a function of magnetic field for both the ferromagnetic and antiferromagnetic Kitaev models. Here, we find that anyon binding remains robust within the entire QSL phase for the ferromagnetic Kitaev model but breaks down already inside this phase for the antiferromagnetic Kitaev model. To compute a binding energy several orders of magnitude below the magnetic energy scale, we introduce both a refined definition and an extrapolation scheme based on carefully tailored perturbations.

Xiao, Bo [Oak Ridge National Laboratory (ORNL), Oa↗
DOE OSTI2020

Notes on the complex Sachdev-Ye-Kitaev model

We describe numerous properties of the Sachdev-Ye-Kitaev model for complex fermions with N $\gg$ 1 flavors and a global U(1) charge. We provide a general definition of the charge in the ( G, Σ) formalism, and compute its universal relation to the infrared asymmetry of the Green function. The same relation is obtained by a renormalization theory. The conserved charge contributes a compact scalar field to the effective action, from which we derive the many-body density of states and extract the charge compressibility. We compute the latter via three distinct numerical methods and obtain consistent results. Finally, we present a two dimensional bulk picture with free Dirac fermions for the zero temperature entropy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Excitation spectra of quantum matter without quasiparticles. I. Sachdev-Ye-Kitaev models

Here, we study the low-frequency spectra of complex Sachdev-Ye-Kitaev models at general densities. The analysis applies also to SU(M) magnets with random exchange at large M. The spectral densities are computed by numerical analysis of the saddle-point equations on the real frequency ω axis at zero temperature T. The asymptotic low-ω behaviors are found to be in excellent agreement with the scaling dimensions of irrelevant operators which perturb the conformally invariant critical states. Of possible experimental interest is our computation of the universal spin spectral weight of the SU(M) magnets at low ω and T; this includes a contribution from the time reparametrization mode, which is the boundary graviton of the holographic dual. This analysis is extended to a random t-J model in the following paper [M. Tikhanovskaya et al., following paper, Phys. Rev. B 103, 075142 (2021)].

36 MATERIALS SCIENCE↗
DOE OSTI2021

Proximate ferromagnetic state in the Kitaev model material α-RuCl 3

α-RuCl 3 is a major candidate for the realization of the Kitaev quantum spin liquid, but its zigzag antiferromagnetic order at low temperatures indicates deviations from the Kitaev model. We have quantified the spin Hamiltonian of α-RuCl 3 by a resonant inelastic x-ray scattering study at the Ru L 3 absorption edge. In the paramagnetic state, the quasi-elastic intensity of magnetic excitations has a broad maximum around the zone center without any local maxima at the zigzag magnetic Bragg wavevectors. This finding implies that the zigzag order is fragile and readily destabilized by competing ferromagnetic correlations. The classical ground state of the experimentally determined Hamiltonian is actually ferromagnetic. The zigzag state is stabilized by quantum fluctuations, leaving ferromagnetism – along with the Kitaev spin liquid – as energetically proximate metastable states. The three closely competing states and their collective excitations hold the key to the theoretical understanding of the unusual properties of α-RuCl 3 in magnetic fields.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Low-rank Sachdev-Ye-Kitaev models

Motivated by recent proposals of experimental realization of fast scramblers, we study a family of solvable variants of the ($\textit{q}$ = 4) Sachdev-Ye-Kitaev model in which the rank and eigenvalue distribution of the coupling matrix $J_{ ij,kl}$ are tuneable. When the rank is proportional to the number of fermions, the low temperature behavior is sensitive to the eigenvalue distribution. We obtain a complete classification of the possible non-Fermi liquid quantum phases. These include two previously studied phases whose fermion scaling dimension depends continuously on the rank; we show that they are maximally chaotic, but necessitate an extensively degenerate or negative semidefinite coupling matrix. In this work, more generic distributions give rise to “almost Fermi liquids” with a scaling dimension Δ = 1/2, but which differ from a genuine Fermi liquid in quasiparticle decay rate, quantum Lyapunov exponent, and/or specific heat.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Phases of $ \mathcal{N} $ = 2 Sachdev-Ye-Kitaev models

We study N = 2 supersymmetric Sachdev-Ye-Kitaev (SYK) models with com- plex fermions at non-zero background charge. Motivated by multi-charge supersymmetric black holes, we propose a new N = 2 SYK model with multiple U(1) symmetries, integer charges, and a non-vanishing supersymmetric index, realizing features not present in known SYK models. In both models, a conformal solution with a super-Schwarzian mode emerges at low temperatures, signaling the appearance of nearly AdS2/BPS physics. However, in contrast to complex SYK, the fermion scaling dimension depends on the background charge in the conformal limit. For a critical charge, we find a high to low entropy phase transition in which the conformal solution ceases to be valid. This transition has a simple interpretation– the fermion scaling dimension violates the unitarity bound. We offer some comments on a holographic interpretation for supersymmetric black holes.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Manipulating Growth and Propagation of Correlations in Dipolar Multilayers: From Pair Production to Bosonic Kitaev Models

Here, we study the nonequilibrium dynamics of dipoles confined in multiple stacked two-dimensional layers realizing a long-range interacting quantum spin 1/2 XXX model. We demonstrate that strong in-plane interactions can protect a manifold of collective layer dynamics. This then allows us to map the many-body spin dynamics to bosonic models. In a bilayer configuration we show how to engineer the paradigmatic two-mode squeezing Hamiltonian known from quantum optics, resulting in exponential production of entangled pairs and generation of metrologically useful entanglement from initially prepared product states. In multilayer configurations we engineer a bosonic variant of the Kitaev model displaying chiral propagation along the layer direction. Our study illustrates how the control over interactions, lattice geometry, and state preparation in interacting dipolar systems uniquely afforded by AMO platforms such as Rydberg and magnetic atoms, polar molecules, or trapped ions allows for the control over the temporal and spatial propagation of correlations for applications in quantum sensing and quantum simulation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Variational preparation of the thermofield double state of the Sachdev-Ye-Kitaev model

Here, we provide an algorithm for preparing the thermofield double (TFD) state of the Sachdev-Ye-Kitaev (SYK) model without the need for an auxiliary bath. Following previous work, the TFD can be cast as the approximate ground state of a Hamiltonian, H TFD . Using variational quantum circuits, we propose and implement a gradient-based algorithm for learning parameters that find this ground state, an application of the variational quantum eigensolver. Concretely, we find shallow quantum circuits that prepare the ground state of H TFD for the q = 4 SYK model for N = 8 Majoranas per side. For N = 12, we achieve a variational energy within 1% of the true ground-state energy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Two-magnon bound states in the Kitaev model in a [111] field

It is now well established that the Kitaev honeycomb model in a magnetic field along the [111] direction harbors an intermediate gapless quantum spin liquid (QSL) phase sandwiched between a gapped non-Abelian QSL at low fields $H < H_{c1}$ and a partially polarized phase at high fields $H > H_{c2}$. Here, we analyze the low-field and high-field phases and phase transitions in terms of single- and two-magnon excitations using exact diagonalization and density matrix renormalization group methods. In this work, we find that the energy to create a bound state of two-magnon $Δ_p$ becomes lower than the energy to create a single spin flip $Δ_s$ near $H_{c2}$. In the entire Kitaev spin liquid, $Δ_p < Δ_s$ and both gaps vanish at $H_{c2}$. We make testable predictions for magnon pairing that could be observable in Raman scattering measurements on Kitaev QSL candidate materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Superconductivity of incoherent electrons in the Yukawa Sachdev-Ye-Kitaev model

We study a model of N fermions in a quantum dot, coupled to M bosons by a disorder-induced complex Yukawa coupling [Yukawa Sachdev-Ye-Kitaev (SYK) model], in order to explore the interplay between non-Fermi liquid and superconductivity in a strongly coupled, (quantum-)critical environment. We analyze the phase diagram of the model for an arbitrary complex interaction and arbitrary ratio of N/M, with special focus on the two regimes of non-Fermi-liquid behavior: an SYK-like behavior with a power-law frequency dependence of the fermionic self-energy and an impuritylike behavior with frequency independent self-energy. We show that the crossover between the two can be reached by varying either the strength of the fermion-boson coupling or the ratio M/N. We next argue that in both regimes the system is unstable to superconductivity if the strength of time-reversal-symmetry-breaking disorder is below a certain threshold. We show how the corresponding onset temperatures vary between the two regimes. We argue that the superconducting state is highly unconventional with an infinite set of minima of the condensation energy at T = 0, corresponding to topologically different gap functions. We discuss in detail similarities and differences between this model and the model of dispersion-full fermions tuned to a metallic quantum-critical point, with an effective singular dynamical interaction V(Ω) ∝ 1/|Ω| γ (the γ model).

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Spectral fluctuations in the Sachdev-Ye-Kitaev model

We present a detailed quantitative analysis of spectral correlations in the Sachdev-Ye-Kitaev (SYK) model. We find that the deviations from universal Random Matrix Theory (RMT) behavior are due to a small number of long-wavelength fluctuations (of the order of the number of Majorana fermions N ) from one realization of the ensemble to the next one. These modes can be parameterized effectively in terms of Q-Hermite orthogonal polynomials, the main contribution being due to scale fluctuations for which we give a simple analytical estimate. Our numerical results for N = 32 show that only the lowest eight polynomials are needed to eliminate the nonuniversal part of the spectral fluctuations. The covariance matrix of the coefficients of this expansion can be obtained analytically from low-order double-trace moments. We evaluate the covariance matrix of the first six moments and find that it agrees with the numerics. We also analyze the spectral correlations in terms of a nonlinear σ-model, which is derived through a Fierz transformation, and evaluate the one and two-point spectral correlation functions to two-loop order. The wide correlator is given by the sum of the universal RMT result and corrections whose lowest-order term corresponds to scale fluctuations. However, the loop expansion of the σ-model results in an ill-behaved expansion of the resolvent, and it gives universal RMT fluctuations not only for q= 4 or higher even q-body interactions, but also for the q= 2 SYK model albeit with a much smaller Thouless energy while the correct result in this case should have been Poisson statistics. In our numerical studies we analyze the number variance and spectral form factor for N = 32 and q = 4. We show that the quadratic deviation of the number variance for large energies appears as a peak for small times in the spectral form factor. After eliminating the long-wavelength fluctuations, we find quantitative agreement with RMT up to an exponentially large number of level spacings for the number variance or exponentially short times in the case of the spectral form factor.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Replica symmetry breaking for the integrable two-site Sachdev–Ye–Kitaev model

We analyze a two-body non-Hermitian two-site Sachdev–Ye–Kitaev (SYK) model with the couplings of one site complex conjugated to the other site. This model, with no explicit coupling between the sites, shows an infinite number of second-order phase transitions, which is a consequence of the factorization of the partition function into a product over Matsubara frequencies. We calculate the quenched free energy in two different ways: first in terms of the single-particle energies and second by solving the Schwinger–Dyson equations of the two-site model. The first calculation can be done entirely in terms of a one-site model. The conjugate replica enters due to non-analyticities when Matsubara frequencies enter the spectral support of the coupling matrix. The second calculation is based on the replica trick of the two-site partition function. Both methods give the same result. The free-fermion partition function can also be rephrased as a matrix model for the coupling matrix. Up to minor details, this model is the random matrix model that describes the chiral phase transition of QCD, and the order parameter of the two-body model corresponds to the chiral condensate of QCD. Comparing to the corresponding four-body model, we are able to determine which features of the free energy are due to the chaotic nature of the four-body model. The high-temperature phase of both models is entropy dominated, and in both cases, the free energy is determined by the spectral density. The chaotic four-body SYK model has a low-temperature phase whose free energy is almost temperature-independent, signaling an effective gap of the theory even though the actual spectrum does not exhibit a gap. On the other hand, the low-temperature free energy of the two-body SYK model is not flat; in fact, it oscillates to arbitrarily low temperature. This indicates a less desirable feature that the entropy of the two-body model is not always positive in the low-temperature phase, which most likely is a consequence of the non-hermiticity.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
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 OSTI2025

Anatomy of information scrambling and decoherence in the integrable Sachdev-Ye-Kitaev model

The growth of information scrambling, captured by out-of-time-order correlation functions (OTOCs), is a central indicator of the nature of many-body quantum dynamics. Here, we compute analytically the complete time dependence of the OTOC for an integrable Sachdev-Ye-Kitaev (SYK) model, 𝑁 Majoranas with random two-body interactions of infinite range, coupled to a Markovian bath at finite temperature. In the limit of no coupling to the bath, the time evolution of scrambling experiences different stages. For 𝑡≲√𝑁, after an initial polynomial growth, the OTOC approaches saturation in a power-law fashion with oscillations superimposed. At 𝑡∼√𝑁, the OTOC reverses trend and starts to decrease linearly in time. The reason for this linear decrease is that, despite being a subleading 1/𝑁 effect, the OTOC in this region is governed by the spectral form factor of the antisymmetric couplings of the SYK model. The linear decrease stops at 𝑡∼2⁢𝑁, the Heisenberg time, where saturation occurs. The effect of the environment is an overall exponential decay of the OTOC for times longer than the inverse of the coupling strength to the bath. Here, the oscillations at 𝑡≲√𝑁 indicate lack of thermalization—a desired feature for better performance of quantum information devices.

Open quantum systems & decoherence↗
DOE OSTI2022

Theory of the Kitaev model in a [111] magnetic field

Recent numerical studies indicate that the antiferromagnetic Kitaev honeycomb lattice model undergoes a magnetic-field-induced quantum phase transition into a new spin-liquid phase. This intermediate-field phase has been previously characterized as a gapless spin liquid. By implementing a recently developed variational approach based on the exact fractionalized excitations of the zero-field model, we demonstrate that the field-induced spin liquid is gapped and belongs to Kitaev’s 16-fold way. Specifically, the low-field non-Abelian liquid with Chern number C = ±1 transitions into an Abelian liquid with C = ±4. The critical field and the field-dependent behaviors of key physical quantities are in good quantitative agreement with published numerical results. Furthermore, we derive an effective field theory for the field-induced critical point which readily explains the ostensibly gapless nature of the intermediate-field spin liquid.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Sachdev-Ye-Kitaev models and beyond: Window into non-Fermi liquids

In this work is a review of the Sachdev-Ye-Kitaev (SYK) model of compressible quantum many-body systems without quasiparticle excitations, and its connections to various theoretical studies of non-Fermi liquids in condensed matter physics. The review is placed in the context of numerous experimental observations on correlated electron materials. Strong correlations in metals are often associated with their proximity to a Mott transition to an insulator created by the local Coulomb repulsion between the electrons. The phase diagrams of a number of models of such a local electronic correlation are explored, employing a dynamical mean-field theory in the presence of random spin exchange interactions. Numerical analyses and analytical solutions, using renormalization group methods and expansions in large spin degeneracy, lead to critical regions that display SYK physics. The models studied include the single-band Hubbard model, the t–J model, and the two-band Kondo-Heisenberg model in the presence of random spin exchange interactions. Also examined are non-Fermi liquids obtained by considering each SYK model with random four-fermion interactions to be a multiorbital atom, with the SYK atoms arranged in an infinite lattice. Connections are made to theories of sharp Fermi surfaces without any low-energy quasiparticles in the absence of spatial disorder, obtained by coupling a Fermi liquid to a gapless boson; a systematic large-N theory of such a critical Fermi surface, with SYK characteristics, is obtained by averaging over an ensemble of theories with random boson-fermion couplings. Finally, an overview of the links between the SYK model and quantum gravity is presented, and the review ends with an outlook on open questions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Sixfold Way of Traversable Wormholes in the Sachdev-Ye-Kitaev Model

In the infrared limit, a nearly anti–de Sitter spacetime in two dimensions ( AdS 2 ) perturbed by a weak double trace deformation and a two-site ( q > 2 )-body Sachdev-Ye-Kitaev (SYK) model with N Majoranas and a weak 2 r -body intersite coupling share the same near-conformal dynamics described by a traversable wormhole. We exploit this relation to propose a symmetry classification of traversable wormholes depending on N , q , and r , with q > 2 r , and confirm it by a level statistics analysis using exact diagonalization techniques. Intriguingly, a time-reversed state never results in a new state, so only six universality classes occur—A, AI, BDI, CI, C, and D—and different symmetry sectors of the model may belong to distinct universality classes. Published by the American Physical Society 2024

Physics↗