Session W22: Quantum Spin Liquids IV: Control, Manipulation and Quantum Information

Pump-Probe Spectroscopy for Anyon Braiding

Anyons are fractionalized quasiparticles with nontrivial braiding statistics that emerge in a variety of topologically ordered phases. Understanding and controlling the braiding of anyons in topological materials has been proposed as a route to realize fault tolerant quantum computation. Until now, signatures of anyon braiding have only been seen through interfering chiral edge modes of fractional quantum Hall states. Detection of anyons in quantum spin liquids instead requires a bulk spectroscopic technique. We present results of exact diagonalization and time-evolution block decimation calculations of a pump-probe experiment on the 1-dimensional quantum Ising chain and 2-dimensional Kitaev honeycomb model in a field perpendicular to the honeycomb lattice. We find that the nonlinear response function shows a distinct signature of long-time divergence, suppressed by a beat pattern due to the finite size of the simulated system. This behavior results from nontrivial braiding of quasiparticles induced by the pump pulse with those created by the probe pulse. We will further present results on the differences in the nonlinear response in the Abelian and non-Abelian Kitaev quantum spin liquid phases.   

Probing quantum spin liquids with a quantum twisting microscope

Quantum spin liquids are elusive states of matter that defy magnetic ordering down to zero temperature. Neutron scattering has been a powerful experimental tool to study the excitations of these states, but it is unsuitable for TMD monolayers, where these states have been recently predicted. Here, we propose a novel technique to image the fractionalized excitations in quantum spin liquids. Our approach is based on a tunneling spectroscopy setup composed of a planar tunneling junction with a magnetic insulator sandwiched between metallic layers. By tuning the relative angle and voltage difference between the metallic layers, we can extract the dynamical spin structure factor of the insulator with both energy and momentum resolution. Our technique offers a promising tool for the experimental identification and characterization of quantum spin liquids in monolayer systems.   

Generalized Kitaev Spin Liquid model andEmergent Twist Defect

The Kitaev spin liquid model on honeycomb lattice offers an intriguingfeature that encapsulates both Abelian and non-Abelian anyons. Recentstudies suggest that the comprehensive phase diagram of possible gener-alized Kitaev model largely depends on the specific details of the discretelattice, which somewhat deviates from the traditional understanding of"topological" phases. In this paper, we propose an adapted version of theKitaev spin liquid model on arbitrary planar lattices. Our revised modelrecovers the toric code model under certain parameter selections withinthe Hamiltonian terms. Our research indicates that changes in parame-ters can initiate the emergence of holes, domain walls, or twist defects.Notably, the twist defect, which presents as a lattice dislocation defect,exhibits non-Abelian braiding statistics upon tuning the coefficients of theHamiltonian on a standard translationally invariant lattice. Additionally,we illustrate that the creation, movement, and fusion of these defects canbe accomplished through natural time evolution by linearly interpolatingthe static Hamiltonian. These defects demonstrate the Ising anyon fusionrule as anticipated. Our findings hint at possible implementation in ac-tual physical materials owing to a more realistically achievable two-body interaction.   

Nonlocal spin correlation as a signature of Ising anyons trapped in vacancies of the non-Abelian Kitaev spin liquid

Determining the elementary excitations in α-RuCl3 under in-plane magnetic fields over 7T is the foremost challenge in Kitaev spin liquid research. While the thermal Hall conductance plateau observed in some experimental groups may be consistent with Kitaev's prediction for the chiral spin liquid phase, the origin of such conductance is still under debate. To conclusively confirm the existence of the non-Abelian Kitaev spin liquid in this candidate material, a direct probe of Ising anyons within the bulk is indispensable. This theoretical study aims to elucidate how nonlocal correlations of Ising anyons become discernible in observables [arXiv:2211.13884]. By constructing an analytical formula for nonlocal spin correlations between spin sites, each of which is adjacent to two isolated vacancies, we confirm that the nonlocality of Ising anyons manifests in specific long-range spin correlations within the spin liquid backgrounds. We also discover that the dynamical nonlocal spin correlation function is electrically detectable through the observation of nonzero nonlocal conductance in the Kitaev magnet/metallic substrate heterostructure. Our proposed setup can be employed to directly probe vacancy-trapped Ising anyons, thus confirming the existence of the Kitaev chiral spin liquid in α-RuCl3.   

Vacancy spectroscopy of non-Abelian Kitaev spin liquids

Spin vacancies in the non-Abelian Kitaev spin liquid are known to harbor Majorana zero modes, potentially enabling topological quantum computing at elevated temperatures. Here, we study the spectroscopic signatures of such Majorana zero modes in a scanning tunneling setup where a non-Abelian Kitaev spin liquid with a finite density of spin vacancies forms a tunneling barrier between a tip and a substrate. Our key result is a well-defined peak close to zero bias voltage in the derivative of the tunneling conductance whose voltage and intensity both increase with the density of vacancies. This 'quasi-zero-voltage peak' is identified as the closest analog of the zero-voltage peak observed in topological superconductors that additionally reflects the fractionalized nature of spin-liquid-based Majorana zero modes. We further highlight a single-fermion Van Hove singularity at a higher voltage that reveals the energy scale of the emergent Majorana fermions in the Kitaev spin liquid.   

Electric field control of a quantum spin liquid in weak Mott insulators

The triangular lattice Hubbard model at strong coupling, whose effective spin model contains both Heisenberg and ring exchange interactions, exhibits a rich phase diagram as the ratio of the hopping t to onsite Coulomb repulsion U is tuned. This includes a chiral spin liquid (CSL) phase. Nevertheless, this exotic phase remains challenging to realize experimentally because a given material has a fixed value of t/U that can difficultly be tuned with external stimuli. One approach to address this problem is applying a DC electric field, which renormalizes the exchange interactions as electrons undergo virtual hopping processes; in addition to creating virtual doubly occupied sites, electrons must overcome electric potential energy differences. Performing a small t/U expansion to fourth order, we derive the ring exchange model in the presence of an electric field and find that it not only introduces spatial anisotropy but also tends to enhance the ring exchange term compared to the dominant nearest-neighbor Heisenberg interaction. Thus, increasing the electric field serves as a way to increase the importance of the ring exchange at constant t/U. Through density matrix renormalization group calculations, we compute the ground state phase diagram of the ring exchange model for two different electric field directions. In both cases, we find that the electric field shifts the phase boundary of the CSL towards a smaller ratio of t/U. Therefore, the electric field can drive a magnetically ordered state into the CSL. This explicit demonstration opens the door to tuning other quantum spin systems into spin liquid phases via the application of an electric field.   

Majorana Fermion Mean-Field Theories of Kitaev Quantum Spin Liquid

We determine the phase diagrams of anisotropic Kitaev-Heisenberg models on the honeycomb lattice using parton mean-field theories based on different Majorana fermion representations of the S = 1/2 spin operators. Firstly, we use a two-dimensional Jordan-Wigner transformation (JWT) involving a semi-infinite snake string operator. In order to ensure that the fermionized Hamiltonian remains local we consider the limit of extreme Ising exchange anisotropy in the Heisenberg sector. Secondly, we use the conventional Kitaev representation in terms of four Majorana fermions subject to local constraints, which we enforce through Lagrange multipliers. For both representations we self- consistently decouple the interaction terms in the bond and magnetization channels and determine the phase diagrams as a function of the anisotropy of the Kitaev couplings and the relative strength of the Ising exchange. While both mean-field theories produce identical phase boundaries for the topological phase transition between the gapless and gapped Kitaev quantum spin liquids, the JWT fails to correctly describe the the magnetic instability and finite-temperature behavior. Our results show that the magnetic phase transition is first order at low temperatures but becomes continuous above a certain temperature.   

Effect of a magnetic field on the Kitaev model coupled to environment

Open quantum systems can display unusual phenomena not seen in closed systems such as new topological phases and skin effect. An interesting example was studied for the Kitaev model in the previous study [1]. An effective non-Hermitian Kitaev model, which incorporates dissipation effects, was shown to display a new gapless spin liquid state, in which the Dirac-like node in the Hermitian case splits into two exceptional points with square-root dispersions. However, the effect of a magnetic field on the model has not been clarified yet, even though the exceptional points may bring about unprecedented quantum phenomena. In this study, we investigate the effect of a magnetic field on the non-Hermitian Kitaev model based on the perturbation theory. We show that the exceptional points remain gapless up to a nonzero critical field, in stark contrast to the Hermitian case. We also show that the critical field diverges for some particular parameter regions. By calculating the winding number of the exceptional points, we find topological transitions caused by the magnetic field. In addition, in the system with the open boundary condition, we find that the edge states in the skin effect switch from one side to the other through the exceptional points. Our results provide a new possible route to stabilize topological quantum spin liquids under the magnetic field in the presence of dissipation. [1] K. Yang, S. C. Morampudi, and E. J. Bergholtz, Phys. Rev. Lett. 126, 077201 (2021).   

Response of Renyi entanglement entropies of perturbed quantum spin liquids

We study the behavior of Renyi entanglement entropies in various models including dimer models and fractional quantum hall models that are known to harbor a quantum spin liquid phase when an additional external perturbation $V(lambda)$ is present. 

Previous work in Phys. Rev. Lett. 110, 210602 (2013) has shown that the derivative of the n-th entanglement entropy $delta_{lambda}S_{n}$ with $n in {0.3, ldots, 2.0}$ displays characteristic so-called splitting behavior connected to the quantum information notion of differential local convertibility. Possible relations of the splitting behavior to various phenomena such as a nonflat entanglement spectrum or the presence of anyons are presented.    

Inverse Hamiltonian design of highly-entangled quantum many-body systems

Solving inverse problems to identify Hamiltonians with desired properties is promising for the discovery of new principles. In quantum many-body systems, quantum entanglement plays a pivotal role in not only the characterization of quantum matter but also future quantum computing. However, an efficient way to create Hamiltonians exhibiting large quantum entanglement remains unclear. Here, we apply the inverse design framework using automatic differentiation [1] to quantum many-body systems to create Hamiltonians with large quantum entanglement. Our method can automatically construct the Kitaev spin models on both honeycomb and square-octagon lattices, whose ground states are exactly shown to be quantum spin liquids [2,3]. On triangular and maple-leaf lattices with geometrical frustration, we find spatially inhomogeneous models, while we can derive a symmetric model on the maple-leaf case. We demonstrate that anisotropic interactions contribute to enhancing quantum entanglement. The method can be combined with numerical methods such as tensor networks, paving the way for the automatic design of new quantum systems.

[1] K. Inui and Y. Motome, Commun. Phys. 6, 37 (2023). [2] A. Kitaev, Ann. Phys. 321, 2 (2006). [3] S. Yang et. al., Phys. Rev. B 76, 180404 (2007).    

Kitaev-type spin liquid on a quasicrystal

We develop an exactly solvable model with Kitaev-type interactions and study its phase diagram on the dual lattice of the quasicrystalline Ammann-Beenker lattice. Our construction is based on the Γ-matrix generalization of the Kitaev model and utilizes the cut-and-project correspondence between the four-dimensional simple cubic lattice and the Ammann-Beenker lattice to designate four types of bonds. We obtain a rich phase diagram with gapped (chiral and abelian) and gapless spin liquid phases via Monte Carlo simulations and variational analysis. We show that the ground state can be further tuned by the inclusion of an onsite term that selects 21 different vison configurations while maintaining the integrability of the model. Our results highlight the rich physics at the intersection of quasicrystals and quantum magnetism.   

Topological Quantum Dimers Emerging from Kitaev Spin Liquid Bilayer: Anyon Condensation Transition

Quantum Spin Liquids (QSLs) are many-body quantum entangled states supporting anyon quasiparticles, proposed as one of the best platforms for quantum science and technology. In particular, Kitaev Spin Liquid (KSL) and Resonating Valence Bond (RVB) states are active subjects of research, stimulated by recent advances in experimental platforms including the quantum magnet RuCl3, quantum processors, and Rydberg atom arrays.

Transition mechanism between distinct QSLs is one of the outstanding problems in the field of topological quantum matter. Anyon condensation was theoretically proposed as a mechanism for such transitions, providing global insights on how a variety of topological phases can be connected via anyon condensation transitions. However, it has been elusive to confirm the mechanism in quantum spin systems because of the scarcity of appropriate microscopic models and the difficulty with defining an order parameter for anyon condensation in terms of local spin operators.

In this work, I introduce a bilayer spin model that illuminates the mechanism of anyon condensation transition. KSL bilayer state and RVB state are stabilized in different limits of the model, connected by an anyon condensation transition. By performing explicit calculations of the order parameter, this work provides numerical evidence for the anyon condensation and uncovers an intimate connection between the KSL bilayer and RVB states.   

Magnetic excitons in a topological Kondo insulator candidate YbB12

We employed time-of-flight inelastic neutron scattering to investigate magnetic excitations in the topological Kondo insulator (TKI) candidate YbB₁₂. Covering the entire Brillouin zone, our data reveal two resonant modes and a continuum all with weak dispersion and a pronounced Q-dependent oscillator strength. The Q-dependence of the intensity of the resonant modes at hω ≈ 40 meV and hω ≈ 15 meV, corresponds to dynamic antiferromagnetic correlations between the nearest and next-nearest Yb neighbors, respectively. Neither mode exhibits intensity at the Γ point. The resonant modes appear to represent collective excitons within the d-f hybridization gap. We utilized the Anderson lattice model with phenomenological tight-binding band structures to simulate the Q-dependence of these magnetic excitons to obtain an experimental measure of the electronic band structure. We also report the field dependence or the 15 meV exciton for fields along the [110].