Session A56: Kitaev Model Theory and Experiment

Pressure Induced Quantum Spin Liquids in Extended Kitaev Model

The Kitaev's Honeycomb lattice model has exactly solvable spin liquid ground states and has attracted lots of research interest. However, most Kitaev materials possess both Kitaev and non-Kitaev interactions, resulting in magnetically ordered ground states. A possible way to suppress the magnetic order and to drive the system to quantum spin liquid phases is exerting high pressure, assuming that the bond-dependent interaction strength can be adjusted by the external pressure. We illustrate this possibility by studying a (pressure caused) anisotropic spin model with variational Monte Carlo method. While the anisotropic pure Kitaev model contains only two phases, the presence of non-Kitaev interactions result in a much richer phase diagram and give rise to several gapless spin liquids whose low-energy spinon excitations contain different number of cones. We show that these gapless spin liquids can be distinguished experimentally. Furthermore, a small out-of-plane magnetic field opens a gap to these spin liquids and results in different chiral spin liquids, all of which are belonging to the Kitaev 16-fold classification.   

Transport and chaos in lattice Sachdev-Ye-Kitaev models

We compute the transport and chaos properties of lattices of quantum Sachdev-Ye-Kitaev islands coupled by single fermion hopping, and with the islands coupled to a large number of local, low energy phonons. We find two distinct regimes of linear-in-temperature (T) resistivity, and describe the crossover between them. When the electron-phonon coupling is weak, we obtain the “incoherent metal” regime, where there is near-maximal chaos with front propagation at a butterfly velocity v_B, and the associated diffusivity D_chaos = (v_B)² /(2πT) closely tracks the energy diffusivity. On the other hand, when the electron-phonon coupling is strong, and the linear resistivity is largely due to near-elastic scattering of electrons off nearly free phonons, we find that the chaos is far from maximal and spreads diffusively. We also describe the crossovers to low T regimes where the electronic quasiparticles are well defined.   

Low-rank Sachdev-Ye-Kitaev Models

Motivated by recent works on atom-cavity realizations of fast scramblers, and on Cooper pairing in non-Fermi liquids, we study a family of solvable variants of the (q=4) Sachdev-Ye-Kitaev model in which the rank and eigenvalue distribution of the coupling matrix J 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. More generic distributions give rise to "almost Fermi liquids'' with a scaling dimension Delta = 1/2, but which differ from a genuine Fermi-liquid in quasi-particle decay rate, quantum Lyapunov exponent and/or specific heat.   

Soft modes in the complex Sachdev-Ye-Kitaev model

We discuss soft modes in the Sachdev-Ye-Kitaev model for complex fermions with large N flavors and a global U(1) charge.
The conserved charge leads to a compact scalar field in 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.   

Dynamical and thermal magnetic properties of the Kitaev spin liquid candidate α-RuCl3

α-RuCl₃ is a promising Kitaev spin liquid candidate, but orders magnetically, the description of which necessitates additional interaction terms. The nature of these interactions, their magnitudes and even signs, remain an open question. In this work we investigate dynamical and thermal magnetic properties of proposed effective Hamiltonians. We calculate T=0 inelastic neutron scattering (INS) intensities using exact diagonalization, and magnetic specific heat, C(T), using a thermal pure quantum states method. We find that no single current model satisfactorily explains all observed phenomena of α-RuCl₃. In particular, we find that Hamiltonians derived from first principles can capture the experimentally observed high-temperature peak in C(T), while overestimating the magnon energy at q=0. In contrast, other models reproduce important features of the INS data, but do not adequately describe C(T). We propose a modified ab initio model that is consistent with both magnetic specific heat and low-energy features of INS data.   

Thermal and magnetoelastic properties of a-RuCl3 in the field-induced low temperature states

Magnetocaloric effect, thermal expansion, and magnetostriction measurements on single crystal α-RuCl₃ samples in applied magnetic fields are discussed. α-RuCl₃ has been established as a promising candidate for the sought-after physical realization of the Kitaev model, which describes S=1/2 spins on a honeycomb lattice with bond dependent Ising interactions, hosting Majorana fermions as well as a topological quantum spin liquid (QSL) ground state. Recent experimental data indicate signs of a QSL state that emerges in applied magnetic fields, once the antiferromagnetic (AFM) transition temperature T_N observed in zero field below 7K is suppressed. In order to identify the nature of the phase transitions below T_N and to map the phase diagram as a function of magnetic field, we conducted measurements of the magnetocaloric effect in pulse magnetic fields as well as thermal expansion and magnetostriction measurements in static fields up to 15 T. The results are discussed in the context of possible quantum critical and QSL behavior in α-RuCl₃.   

Multipartite Entanglement in the Kitaev Honeycomb Model

Quantum spin liquid (QSL) phases of matter have proven extremely elusive from both experimental and theoretical perspectives. In the theoretical domain, examining the topological entanglement entropy has been a primary tool for diagnosing whether or not a model exhibits QSL physics in its groundstate. We study the Kitaev honeycomb model, a prototype of QSL physics in two dimensions, using the quantum Fisher information (QFI), which is both experimentally accessible and well defined at finite temperature. We explore he behaviour of the QFI in both the gapped and gapless phases and in the regions around the transition.

  

Spin-one Kitaev-Heisenberg model on a two-dimensional honeycomb lattice

We study the Kitaev-Heisenberg model with a spin-1 local degree of freedom on a two-dimensional honeycomb lattice numerically by density matrix renormalization group method. We obtain the phase diagram with two spin liquid phases and four symmetry broken phases. We identify that the spin liquid is gapless and has short-ranged spin-spin correlations within the whole phase. Comparing to its spin-1/2 counterpart, the spin-1 spin liquid has more gapless modes.   

Microscopic route to magnetic anisotropy in higher-spin honeycomb lattice: application to CrI3

In the past decade transition metal (TM) compounds have generated a wealth of theoretical and experimental research on frustrated magnetism, especially TM compounds that host local 1/2 moments. Spin-orbit coupling (SOC) of the TM cation sites plays a key role for the appearance and dominance of frustrated terms such as the Kitaev spin-1/2 term. Very recently it has been recognized that SOC of the anion sites is a viable route to realizing frustrated higher spin model terms from super-exchange paths [1]. We present the microscopic origin of frustrated S=3/2 model terms in d³ systems. The appearance and competition of the Kitaev term with conventional spin model terms are presented. Applications of the theory to CrI₃ and related materials are also discussed.

[1] P. P. Stavropoulos, D. Pereira, and H.-Y. Kee, Phys. Rev. Lett. 123, 037203 (2019)   

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<Hc₁ and a partially polarized phase at high fields H>Hc₂. Here, we analyze the low field and high field phases and phase transitions in terms of single- and two-magnon excitations using exact diagonalization (ED) and density matrix renormalization group (DMRG) methods. We find that the energy to create a bound state of two-magnons Δ_p becomes lower than the energy to create a single spin flip Δ_s near Hc₂. In the entire Kitaev spin liquid Δ_p<Δ_s and both gaps vanish at Hc₂. We make testable predictions for magnon pairing that could be observable in Raman scattering measurements on Kitaev QSL candidate materials.   

Phase diagram of the spin-1/2 Kitaev-Gamma chain and emergent ``partial" SU(2) symmetry

We study the phase diagram of a one-dimensional version of the Kitaev spin-1/2 model with an extra ``$\Gamma$-term", using analytical, density matrix renormalization group and exact diagonalization methods. Two intriguing phases are found. In the gapless phase, the low energy theory is described by an emergent SU(2)$_1$ Wess-Zumino-Witten (WZW) model though the exact symmetry group is discrete. On the other hand, the relations between the local spin operators and the WZW currents and primary field contain SU(2) breaking coefficients. A modified nonabelian bosonization formula is proposed to capture such exotic emergent ``partial" SU(2) symmetry. In the ordered phase, there is numerical evidence for an $O_h\rightarrow D_8$ spontaneous symmetry breaking.   

Ab initio quantum chemical study of magnetic interactions in the honeycomb Kitaev-Heisenberg systems Cu2IrO3 and H3LiIr2O6

The magnetic interactions in honeycomb iridium oxide compounds are studied using quantum chemical wavefunction-based methods. Mapping the results onto the corresponding effective spin model shows the crucial dependence of the anisotropic magnetic couplings, in particular Kitaev exchange, on the precise position of inter-layer species and on additional geometrical factors such as Ir-O-Ir bond angles and Ir-O bond lengths. While the latter define the actual superexchange path between magnetic centers, the former may come into play through strong out-of-plane polarization of ligand 2p orbitals mediating intersite hopping [1,2].
(1) R. Yadav, R. Ray, M. S. Eldeeb, S. Nishimoto, L. Hozoi, and J. van den Brink, Phys. Rev. Lett. 121, 197203 (2018).
(2) R. Yadav, M. S. Eldeeb, R. Ray, S. Aswartham, M. I.Sturza, S. Nishimoto, J. van den Brink, and L. Hozoi, Chem. Sci. 10, 1866 (2019).   

Kitaev material candidates beyond the Iridates

Na2MO3 (M = a tetravalent metal) based Mott insulators have been studied recently as potential candidates to realize Kitaev spin model. 4d5 or 5d5 systems on a Honeycomb lattice exhibit spinorbit assisted Mott insulating ground states. At the strong SOC regime, the ground state for these ions in an octahedral crystal field is dominated by Jeff=1/2 states resulting in bond-dependent anisotropic magnetic exchange in the plane, essential to realize the Kitaev spin model. However, candidates to realize the Kitaev spin model are not limited to 4d/5d systems. Lanthanide elements with significant SOC and inherent anisotropy can also be considered in this context. In this talk, I will present our work on a new lanthanide-based, Kitaev material candidate with a potential Jeff=1/2 ground state. Synthesis and structure of the material will be discussed. Physical property measurements coupled with inelastic neutron scattering results will be utilized to understand the single-ion characteristics of the lanthanide and to unveil the rich low-temperature physics of the material.   

Ferrimagnetism and anisotropic phase tunability by magnetic fields in Na2Co2TeO6

Na2Co2TeO6 is a honeycomb-lattice compound with a zigzag antiferromagnetic order [1,2]. It has recently been proposed to be a Kitaev-like magnet based on high-spin d7 electron configuration [3,4]. To assess how close it is to realizing Kitaev quantum spin liquids, we have measured magnetization and specific heat on high-quality single crystals in magnetic fields applied along high-symmetry directions [5]. With small training fields, we find a canonical ferrimagnetic behavior below 27 K, which reveals additional Neel-type order of canted moments. Moreover, moderate fields in the honeycomb plane can suppress the thermal transition at 27 K, and seem to partly reverse the moment-canting when applied perpendicular to the zigzag chains. In contrast, out-of-plane fields leave the transition largely unaffected, but promotes another transition below 10 K, possibly also related to canting reversal. Our study indicates the magnetism of Na2Co2TeO6 is highly anisotropic and close to tipping points between competing phases.

[1] Lefrancois et al., Phys. Rev. B 94, 214416 (2016).
[2] Bera et al., Phys. Rev. B 95, 094424 (2017).
[3] Liu et al., Phys. Rev. B 97, 014407 (2018).
[4] Sano et al., Phys. Rev. B 97, 014408 (2018).
[5] Yao et al., arXiv:1908.09427.   

magnetic structures and excitations in the series of A2PrO3 (A: alkali metals)

We study magnetic structures and excitations in the series of A2PrO3 (A: alkali metals) by performing
neutron scattering experiments. In these compounds, tetravalent
praseodymium ions reside in edge-sharing PrO6 octahedra and the 4 f1 electrons
exhibit Jeff=1/2 ground state doublet which result from a strong spin-orbital
coupling and a weak octahedral crystal field. Furthermore, it was proposed that for
A=Li, Na, the interactions are anti-ferromagnetic and dominantly Kitaev-type and
therefore offer a potential playground for quantum spin liquid. We show evidence of
anti-ferromagnetic phase transitions in such materials and provide possible effective
Hamiltonians that will guide further searches for Kitaev spin liquids in rare earth compounds.