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arXiv:2104.12887 · Physical review. B./Physical review. B

Spin transport in a quantum spin orbital liquid

Zekun Zhuang, John Bradley Marston

Published Aug 4, 2021• 8 citations
arXivHTMLPDF

Abstract

Quantum spin orbital liquids (QSOLs) are a novel phase of matter, similar to quantum spin liquids, with quantum fluctuations in both spin and orbital degrees of freedom. We use nonequilibrium Green's function theory to study out-of-equilibrium spin transport in an exactly solvable QSOL model put forward by Yao and Lee. We find that the spin transport problem can be mapped to that of a free fermion problem with effective fermionic baths that have a rapidly varying density of states. In the gapless phase, the spin current ${I}_{s}\text{\ensuremath{-}}{V}_{s}$ relation is thus highly nonlinear, while in the chiral gapped phase, the spin current conductance is quantized to be $1/2\ensuremath{\pi}$ provided that the contacts are sufficiently wide. The quantized conductance is a signature of the topological nature of the chiral gapped QSOL.

DOI
10.1103/physrevb.104.l060403

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Quantum spin orbital liquids (QSOLs) are a novel phase of matter, similar to quantum spin liquids, with quantum fluctuations in both spin and orbital degrees of freedom. We use nonequilibrium Green's function theory to study out-of-equilibrium spin transport in an exactly solvable QSOL model put forward by Yao and Lee. We find that the spin transport problem can be mapped to that of a free fermion problem with effective fermionic baths that have a rapidly varying density of states. In the gapless phase, the spin current Is\ensuremath-Vs{I}_{s}\text{\ensuremath{-}}{V}_{s}Is​\ensuremath-Vs​ relation is thus highly nonlinear, while in the chiral gapped phase, the spin current conductance is quantized to be 1/2\ensuremathπ1/2\ensuremath{\pi}1/2\ensuremathπ provided that the contacts are sufficiently wide. The quantized conductance is a signature of the topological nature of the chiral gapped QSOL.
ABSTRACT Quantum spin liquids (QSLs) are magnetically frustrated phases characterized by spin fractionalization, emergent gauge fields, and long‐range entanglement. Quantum spin–orbital liquids (QSOLs) form a subset of QSLs with fluctuating orbital degrees of freedom, normally adding a layer of complexity to an already involved research field. This topical review provides guidelines for understanding a specific type of QSOL in which the orbital operators facilitate the analysis of quantum liquids, thereby providing adequate starting points for /exploring these phases. Such models are extensions of the spin‐1/2 Kitaev honeycomb model (KHM), in the sense that their exact solutions depend on an extensive number of conserved quantities, combined with a mapping to a problem of Majorana fermions hopping on a static gauge field. The starting points to understand such models are classical Hamiltonians characterized by bond‐dependent Ising interactions. Such classical models are exactly solvable in spin basis thanks to their extensive symmetries and can be directly connected to classical spin ice (CSI) systems that satisfy a Gauss law. QSOLs are easily stabilized in these models by applying a transverse field or introducing other exchange mechanisms that preserve the conserved local operators. The theory of such Ising QSOLs bridges the KHM to specific types of CSIs, thus providing further insight into paradigmatic forms of spin liquids. Furthermore, bond‐dependent Ising models are related to minimal Hamiltonians describing Rydberg‐atom simulations, which provide experimental grounds for investigating them.
Abstract Quantum spin liquid (QSL) has become an exciting topic in interacting spin systems that do not order magnetically down to the lowest experimentally accessible temperature; however, conclusive experimental evidence remains lacking. Motivated by the recent surge of theoretical and experimental interest in a half-filled Hubbard model on the triangular lattice, where chiral QSL can be stabilized, we investigate the electromagnetic signature of the chiral QSL to aid experimental detection. We systematically studied the electrical charge and orbital electrical current associated with a spinon excitation in the chiral QSL based on parton mean-field theory and unbiased density-matrix renormalization group calculations. We then calculated both longitudinal and transverse optical conductivities below the Mott gap. We also conduct quantum field theory analysis to unravel the connection between spinon excitation and emergent and physical gauge fields. Our results show that the chiral QSL phase has a clear electromagnetic response even in a Mott insulator regime, which can facilitate the experimental detection of this long-sought-after phase.
Quantum spin liquids may be considered 'quantum disordered' ground states of spin systems, in which zero-point fluctuations are so strong that they prevent conventional magnetic long-range order. More interestingly, quantum spin liquids are prototypical examples of ground states with massive many-body entanglement, which is of a degree sufficient to render these states distinct phases of matter. Their highly entangled nature imbues quantum spin liquids with unique physical aspects, such as non-local excitations, topological properties, and more. In this review, we discuss the nature of such phases and their properties based on paradigmatic models and general arguments, and introduce theoretical technology such as gauge theory and partons, which are conveniently used in the study of quantum spin liquids. An overview is given of the different types of quantum spin liquids and the models and theories used to describe them. We also provide a guide to the current status of experiments in relation to study quantum spin liquids, and to the diverse probes used therein.
Quantum spin liquids (QSLs) are strongly correlated systems displaying fascinating phenomena like long-range entanglement and fractionalized excitations. The research on these states has since its beginning followed trends generated by the synthesis of new compounds and the construction of new theoretical tools. In coherence with this history, a manifold of new results about QSLs were established during the past decade due to studies on the integrable Kitaev model on the honeycomb lattice. This j = 1/2 model displays bond-dependent and anisotropic exchanges that are essential to stabilize its QSL ground state with Majorana fermion excitations and emergent Z2 gauge field. Even more interestingly, this model is relevant to understand the magnetism of a certain class of 4/5d5 Mott insulators with specific lattice constraints, t2g orbital degeneracy and strong spin-orbit coupling (SOC). This mechanism defining these so-called Kitaev materials can be applied to similar compounds based on transition metal ions in different electronic configurations. In this thesis, I investigate minimal models for two types of 4/5d1 Mott insulators: the ones on the ordered double perovskite structure (ODP) and the ones isostructural to the Kitaev materials. Their effective models generically show bond-dependent and anisotropic interactions involving multipoles of an effective j = 3/2 angular momentum. Such degrees of freedom are conveniently written in terms of pseudospin s and pseudo-orbital τ operators resembling spin and orbital operators of Kugel-Khomskii models with twofold orbital degeneracy. Despite their anisotropy, the two realistic models display continuous global symmetries in the limit of vanishing Hund\'s coupling enhancing quantum fluctuations and possibly stabilizing a QSL phase. Parton mean-field theory was used to propose fermionic QSLs that will be called quantum spin-orbital liquids (QSOLs) due their dependence with s and τ. On ODPs, I studied a chiral QSOL with Majorana fermion excitations and a gapless spectrum characterized by nodal lines along the edges of the Brillouin zone. These nodal lines are topological defects of a non-Abelian Berry connection and the system exhibits dispersing surface states. Several experimental responses of the chiral QSOL within the mean-field approximation are compared with the experimental data available for the spin liquid candidate Ba2YMoO6. Moreover, based on a symmetry analysis, I discuss the operators involved in resonant inelastic X-ray scattering (RIXS) amplitudes for 4/5d1 Mott insulators and show that the RIXS cross sections allow one to selectively probe pseudospin and pseudo-orbital degrees of freedom. For the chiral spin-orbital liquid in particular, these cross sections provide information about the spectrum for different flavors of Majorana fermions. The model for materials isostructural to the Kitaev materials has an emergent SU(4) symmetry that is made explicit by means of a Klein transformation on pseudospin degrees of freedom. The model is known to stabilize a QSOL on the honeycomb lattice and instigated the investigation of QSOLs on a generalization of this lattice to three dimensions. Parton mean-field theory was used once again to propose the liquid states, and a variational Monte Carlo (VMC) method was used to compute the energies of the projected wave functions. The numerical results show that the lowest-energy QSOL corresponds to a zero-flux state with a Fermi surface of four-color fermionic partons. Further VMC computations also revealed that this state is stable against formation of plaquette ordering (tetramerization). The energy of this QSOL is highly competitive even when Hund\'s coupling induced perturbations are included, as shown by comparison with simple ordered states. Extensions and perspectives for future work are discussed in the end of this thesis.
We show that the nonlinear transport of bosonic excitations in a two-dimensional honeycomb lattice of spin-orbit-coupled Rydberg atoms gives rise to disordered quantum phases which are topological and may be candidates for quantum spin liquids. As recently demonstrated by Lienhard et al. [Phys. Rev. X 10, 021031 (2020)] the spin-orbit coupling breaks time-reversal and chiral symmetries and leads to a tunable density-dependent complex hopping of spin excitations which behave as hard-core bosons. Using exact diagonalization (ED), we numerically investigate the phase diagram resulting from the competition between density-dependent and direct transport terms as well as density-density interactions. In mean-field approximation there is a phase transition from a condensate to a ${120}^{\ensuremath{\circ}}$ phase when the amplitude of the complex hopping exceeds that of the direct one. In the full model a new phase emerges close to the mean-field critical point as a result of quantum correlations induced by the density dependence of the complex hopping. We show that without density-density interactions this phase is a genuine disordered one, has large spin chirality, and is characterized by a nontrivial many-body Chern number. The Chern number is found to be robust to disorder. ED simulations of small lattices with up to 30 lattice sites give indications for a nondegenerate ground state with finite spin and collective gaps and thus for a bosonic integer quantum Hall phase, protected by U(1)\mathrm{U}(1)U(1) symmetry. On the other hand, while staying finite, the many-body gap varies substantially when different twisted boundary conditions are applied, which points to a gapless phase. For very strong negative nonlinear hopping amplitudes we find another disordered regime with vanishing spin gap. This phase also has a large spin chirality and could be a gapless spin liquid but lies outside the parameter regime experimentally accessible in the Rydberg system.
We study an exactly solvable quantum spin model of Kitaev type on the kagome lattice. We find a rich phase diagram which includes a topological (gapped) chiral spin liquid with gapless chiral edge states, and a gapless chiral spin liquid phase with a spin Fermi surface. The ground state of the current model contains an odd number of electrons per unit cell, which qualitatively distinguishes it from previously studied exactly solvable models with a spin Fermi surface. Moreover, we show that the spin Fermi surface is stable against weak perturbations.