Bosonic Spinons Research Articles

Spin density wave, Fermi liquid, and fractionalized phases in a theory of antiferromagnetic metals using paramagnons and bosonic spinons

Spin density wave, Fermi liquid, and fractionalized phases in a theory of antiferromagnetic metals using paramagnons and bosonic spinons

Anderson localization of emergent quasiparticles: Spinon and vison interplay at finite temperature in a Z2 gauge theory in three dimensions

Fractional statistics of quasiparticle excitations often plays an important role in the detection and characterization of topological systems. In this paper, we investigate the case of a three-dimensional (3D) Z2 gauge theory, where the excitations take the form of bosonic spinon quasiparticle and vison flux tubes, with mutual semionic statistics. We focus on an experimentally relevant intermediate temperature regime, where sparse spinons hop coherently on a dense quasistatic and stochastic vison background. The effective Hamiltonian reduces to a random-sign bimodal tight-binding model, where both the particles and the disorder are borne out of the same underlying quantum spin liquid (QSL) degrees of freedom, and the coupling between the two is purely driven by the mutual fractional statistics. We study the localization properties and observe a mobility edge located close to the band edge, whose transition belongs to the 3D Anderson model universality class. Spinons allowed to propagate through the quasistatic vison background appear to display quantum diffusive behavior. When the visons are allowed to relax, in response to the presence of spinons in equilibrium, we observe the formation of vison depletion regions slave to the support of the spinon wavefunction. We discuss how this behavior can give rise to measurable effects in the relaxation, response and transport properties of the system and how these may be used as signatures of the mutual semionic statistics and as precursors of the QSL phase arising in the system at lower temperatures.

SU(2) gauge theory of the pseudogap phase in the two-dimensional Hubbard model

We present a SU(2) gauge theory of fluctuating magnetic order in the two-dimensional Hubbard model. The theory is based on a fractionalization of electrons in fermionic chargons and bosonic spinons. The chargons undergo N\'eel or spiral magnetic order below a density-dependent transition temperature ${T}^{*}$. Fluctuations of the spin orientation are described by a nonlinear sigma model obtained from a gradient expansion of the spinon action. The spin stiffnesses are computed from a renormalization group improved random phase approximation. Our approximations are designed for moderate, not for strong, Hubbard interactions. The stiffnesses are strongly doping dependent with discontinuities at half-filling and a pronounced electron-hole asymmetry. The spinon fluctuations prevent magnetic long-range order of the electrons at any finite temperature. The phase with magnetic chargon order shares characteristic features with the pseudogap regime in high-${T}_{c}$ cuprates: a strong reduction of charge carrier density, a spin gap, and Fermi arcs. A substantial fraction of the pseudogap regime exhibits electronic nematicity.

Spin liquid to spin glass crossover in the random quantum Heisenberg magnet

We study quantum SU($M$) spins with all-to-all and random Heisenberg exchange interactions of root-mean-square strength $J$. The $M \rightarrow \infty$ model has a spin liquid ground state with the spinons obeying the equations of the Sachdev-Ye-Kitaev (SYK) model. Numerical studies of the SU(2) model with $S=1/2$ spins show spin glass order in the ground state, but also display SYK spin liquid behavior in the intermediate frequency spin spectrum. We employ a $1/M$ expansion to describe the crossover from fractionalized fermionic spinons to a confining spin glass state with weak spin glass order $q_{EA}$. The SYK spin liquid behavior persists down to a frequency $\omega_\ast \sim J q_{EA}$, and for $\omega < \omega_\ast$, the spectral density is linear in $\omega$, thus quenching the extensive zero temperature entropy of the spin liquid. The linear $\omega$ spectrum is qualitatively similar to that obtained earlier using bosonic spinons for large $q_{EA}$. We argue that the extensive SYK spin liquid entropy is transformed as $T \rightarrow 0$ to an extensive complexity of the spin glass state.

Bosonic spinons in anisotropic triangular antiferromagnets

Anisotropic triangular antiferromagnets can host two primary spin excitations, namely, spinons and triplons. Here, we utilize polarization-resolved Raman spectroscopy to assess the statistics and dynamics of spinons in Ca3ReO5Cl2. We observe a magnetic Raman continuum consisting of one- and two-pair spinon-antispinon excitations as well as triplon excitations. The twofold rotational symmetry of the spinon and triplon excitations are distinct from magnons. The strong thermal evolution of spinon scattering is compatible with the bosonic spinon scenario. The quasilinear spinon hardening with decreasing temperature is envisaged as the ordering of one-dimensional topological defects. This discovery will enable a fundamental understanding of novel phenomena induced by lowering spatial dimensionality in quantum spin systems.

Competing orders in pyrochlore magnets from a Z2 spin liquid perspective

The pyrochlore materials have long been predicted to harbor a quantum spin liquid, an intrinsic long-range-entangled state supporting fractionalized excitations. Existing pyrochlore experiments, on the other hand, have discovered several weakly ordered states and a tendency of close competition amongst them. Motivated by these facts, we give a complete classification of spin-orbit-coupled ${\mathbb{Z}}_{2}$ spin-liquid states on the pyrochlore lattice by using the projective symmetry group (PSG) approach for bosonic spinons. For each spin liquid, we construct a mean-field Hamiltonian that can be used to describe phase transitions out of the spin liquid via spinon condensation. Studying these phase transitions, we establish phase diagrams for our mean-field Hamiltonians that link magnetic orders to specific spin liquids. In general, we find that seemingly unrelated magnetic orders are intertwined with each other and that the conventional spin orders seen in the experiments are accompanied by more exotic hidden orders. Our critical theories are categorized into $z=1$ and $z=2$ types, based on their spinon dispersion and Hamiltonian diagonalizability, and are shown to give distinct signatures in the heat capacity and the spin structure factor. This study provides a clear map of pyrochlore phases for future experiments and variational Monte Carlo studies in pyrochlore materials.

Magnetic Monopole Supercurrent through a Quantum Spin Ice Tunnel Junction

Magnetic monopoles are hypothetical particles that may exist as quantized sources and sinks of the magnetic field. In materials, they may appear in an emergent quantum electrodynamics described by a U(1) lattice gauge theory. Particularly, quantum spin ice hosts monopoles as bosonic spinons coupled to emergent gauge fields in a U(1) quantum spin liquid, namely, a deconfined Coulomb phase. When monopoles are condensed to form a long-range order, monopoles and gauge fields are screened and confined. Here we show, however, that monopole supercurrent flows across a junction of two ferromagnets that are weakly linked through and placed on top of the U(1) QSL, when a gauge-invariant phase difference of spinons across the junction is generated by quenching or an applied electric voltage parallel to the junction. This novel phenomenon paves the way to a new paradigm of spinonics for a dissipationless control of magnetism.

First-Principles Design of the Spinel Iridate Ir_{2}O_{4} for High-Temperature Quantum Spin Ice.

Insulating magnetic rare-earth pyrochlores related to spin ice host emergent bosonic monopolar spinons, which obey a magnetic analogue of quantum electrodynamics and may open a route to spinonics. However, the energy scales of the interactions among rare-earth moments are so low (∼ 1K) that the possible quantum coherence can be achieved at a sub-Kelvin scale. Here, we design high-temperature quantum spin ice materials from first principles. It is shown that the A-site deintercalated spinel iridate Ir_{2}O_{4}, which has been experimentally grown as epitaxial thin films, is a promising candidate for quantum spin ice with a spin-ice-rule interaction of a few tens of meV. Controlling electronic structures of Ir_{2}O_{4} through substrates, it is possible to tune magnetic interactions so that a magnetic Coulomb liquid persists at high temperatures.

Orbital currents in insulating and doped antiferromagnets

We describe square lattice spin liquids which break time-reversal symmetry, while preserving translational symmetry. The states are distinguished by the manner in which they transform under mirror symmetries. All the states have non-zero scalar spin chirality, which implies the appearance of spontaneous orbital charge currents in the bulk (even in the insulator); but in some cases, orbital currents are non-zero only in a formulation with three orbitals per unit cell. The states are formulated using both the bosonic and fermionic spinon approaches. We describe states with $\mathbb{Z}_2$ and U(1) bulk topological order, and the chiral spin liquid with semionic excitations. The chiral spin liquid has no orbital currents in the one-band formulation, but does have orbital currents in the three-band formulation. We discuss application to the cuprate superconductors, after postulating that the broken time-reversal and mirror symmetries persist into confining phases which may also break other symmetries. In particular, the broken symmetries of the chiral spin liquid could persist into the N\'eel state.

Quantum spin superfluid from Bose-Einstein condensation of spinons in pyrochlore spin ice

Quantum spin ice in pyrochlore lattice exemplifies three-dimensional frustrated spin systems. In existing studies, Bose-Einstein condensation of bosonic spinons gives rise to magnetically ordered ground state. A truly liquid quantum spin superfluid state that manifests a deconfined Higgs condensate of spinons is demonstrated. This state is shown to occur in the fully antiferromagnetic case of the non-Kramers quantum spin ice with a fluctuation-induced first-order quantum phase transition from the U(1) spin liquid to the spin superfluid. The spin superfluid density jump is obtained analytically.

Fermionic Spinon Theory of Square Lattice Spin Liquids near the Néel State

Quantum fluctuations of the N\'eel state of the square lattice antiferromagnet are usually described by a $\mathbb{CP}^1$ theory of bosonic spinons coupled to a U(1) gauge field, and with a global SU(2) spin rotation symmetry. Such a theory also has a confining phase with valence bond solid (VBS) order, and upon including spin-singlet charge 2 Higgs fields, deconfined phases with $\mathbb{Z}_2$ topological order possibly intertwined with discrete broken global symmetries. We present dual theories of the same phases starting from a mean-field theory of fermionic spinons moving in $\pi$-flux in each square lattice plaquette. Fluctuations about this $\pi$-flux state are described by 2+1 dimensional quantum chromodynamics (QCD$_3$) with a SU(2) gauge group and $N_f=2$ flavors of massless Dirac fermions. It has recently been argued by Wang et al. (arXiv:1703.02426) that this QCD$_3$ theory describes the N\'eel-VBS quantum phase transition. We introduce adjoint Higgs fields in QCD$_3$, and obtain fermionic dual descriptions of the phases with $\mathbb{Z}_2$ topological order obtained earlier using the bosonic $\mathbb{CP}^1$ theory. We also present a fermionic spinon derivation of the monopole Berry phases in the U(1) gauge theory of the VBS state. The global phase diagram of these phases contains multi-critical points, and our results imply new boson-fermion dualities between critical gauge theories of these points.

Quantum spin liquid and magnetic order in a two-dimensional nonsymmorphic lattice: Considering the distorted kagome lattice of volborthite

The Kagome-lattice-based material, Volborthite, $\mathrm{Cu_3 V_2 O_7 (OH)_2 \cdot 2 H_2 O}$, has been considered as a promising platform for discovery of unusual quantum ground states due to the frustrated nature of spin interactions. Here we explore possible quantum spin liquid and magnetically ordered phases in a two-dimensional non-symmorphic lattice described by $p2gg$ layer space group, which is consistent with the spatial anisotropy of the spin model derived from density functional theory (DFT) for Volborthite. Using the projective symmetry group (PSG) analysis and Schwinger boson mean field theory, we classify possible spin liquid phases with bosonic spinons and investigate magnetically ordered phases connected to such states. It is shown, in general, that only translationally invariant mean field states are allowed in two-dimensional non-symmorphic lattices, which simplifies the classification considerably. The mean field phase diagram of the DFT-derived spin model is studied and it is found that possible quantum spin liquid phases are connected to two types of magnetically ordered phases, a coplanar incommensurate $(q,0)$ spiral order as the ground state and a closely competing coplanar commensurate $(\pi,\pi)$ spin density wave order. In addition, periodicity enhancement of the two-spinon continuum, a signature of symmetry fractionalization, is found in the spin liquid phases connected to the $(\pi,\pi)$ spin density wave order. We discuss relevance of these results to recent and future experiments on Volborthite.

Realization of the Haldane-Kane-Mele Model in a System of Localized Spins.

We study a spin Hamiltonian for spin-orbit-coupled ferromagnets on the honeycomb lattice. At sufficiently low temperatures supporting the ordered phase, the effective Hamiltonian for magnons, the quanta of spin-wave excitations, is shown to be equivalent to the Haldane model for electrons, which indicates the nontrivial topology of the band and the existence of the associated edge state. At high temperatures comparable to the ferromagnetic-exchange strength, we take the Schwinger-boson representation of spins, in which the mean-field spinon band forms a bosonic counterpart of the Kane-Mele model. The nontrivial geometry of the spinon band can be inferred by detecting the spin Nernst effect. A feasible experimental realization of the spin Hamiltonian is proposed.

Superconductivity from a confinement transition out of a fractionalized Fermi liquid withZ2topological and Ising-nematic orders

The Schwinger-boson theory of the frustrated square lattice antiferromagnet yields a stable, gapped $\mathbb{Z}_2$ spin liquid ground state with time-reversal symmetry, incommensurate spin correlations and long-range Ising-nematic order. We obtain an equivalent description of this state using fermionic spinons (the fermionic spinons can be considered to be bound states of the bosonic spinons and the visons). Upon doping, the $\mathbb{Z}_2$ spin liquid can lead to a fractionalized Fermi liquid (FL*) with small Fermi pockets of electron-like quasiparticles, while preserving the $\mathbb{Z}_2$ topological and Ising-nematic orders. We describe a Higgs transition out of this deconfined metallic state into a confining superconducting state which is usually of the Fulde-Ferrell-Larkin-Ovchinnikov type, with spatial modulation of the superconducting order.

Kagome Chiral Spin Liquid as a Gauged U(1) Symmetry Protected Topological Phase.

While the existence of a chiral spin liquid (CSL) on a class of spin-1/2 kagome antiferromagnets is by now well established numerically, a controlled theoretical path from the lattice model leading to a low-energy topological field theory is still lacking. This we provide via an explicit construction starting from reformulating a microscopic model for a CSL as a lattice gauge theory and deriving the low-energy form of its continuum limit. A crucial ingredient is the realization that the bosonic spinons of the gauge theory exhibit a U(1) symmetry protected topological (SPT) phase, which upon promoting its U(1) global symmetry to a local gauge structure ("gauging"), yields the CSL. We suggest that such an explicit lattice-based construction involving gauging of a SPT phase can be applied more generally to understand topological spin liquids.

Violation of the spin-statistics theorem and the bose-einstein condensation of particles with half-integer spin.

We consider the Bose condensation of bosonic particles with spin 1/2. The condensation is driven by an external magnetic field. Our work is motivated by ideas of quantum critical deconfinement and bosonic spinons in spin liquid states. We show that both the nature of the novel Bose condensate and the excitation spectrum are fundamentally different from that in the usual integer spin case. We predict two massive ("Higgs") excitations and two massless Goldstone excitations. One of the Goldstone excitations has a linear excitation spectrum and another has a quadratic spectrum. This implies that the Bose condensate does not support superfluidity, the Landau criterion is essentially violated. We formulate a "smoking gun" criterion for searches of the novel Bose condensation.

Stoner Instability Revisited: Emergence of Local Quantum Criticality?

We revisit Stoner instability, an old problem but in a modern point of view. An idea is to extract out dynamics of directional fluctuations of spins explicitly, resorting to the CP$^{1}$ representation and integrating over their amplitude fluctuations. As a result, we derive an effective field theory for ferromagnetic quantum phase transitions in terms of bosonic spinons and fermionic holons. We show that this effective field theory reproduces overdamped spin dynamics in a paramagnetic Fermi liquid and magnon spectrum in a ferromagnetic Fermi liquid. An interesting observation is that the velocity of spinons becomes zero, approaching the ferromagnetic quantum critical point, which implies emergence of local quantum criticality. Based on this scenario, we predict the $\omega/T$ scaling behavior near ferromagnetic quantum criticality beyond the conventional scenario of the weak-coupling approach.

Exotic continuous quantum phase transition betweenZ2topological spin liquid and Néel order

Recent numerical simulations with different techniques have all suggested the existence of a continuous quantum phase transition between the ${\mathbb{Z}}_{2}$ topological spin-liquid phase and a conventional N\'eel order. Motivated by this numerical progress, we propose a candidate theory for such ${\mathbb{Z}}_{2}$-N\'eel transition. We first argue on general grounds that, for a SU(2)-invariant system, this transition can not be interpreted as the condensation of spinons in the ${\mathbb{Z}}_{2}$ spin-liquid phase. Then, we propose that such ${\mathbb{Z}}_{2}$-N\'eel transition is driven by proliferating the bound state of the bosonic spinon and vison excitation of the ${\mathbb{Z}}_{2}$ spin liquid, i.e., the so-called $(e,m)$-type excitation. Universal critical exponents associated with this exotic transition are computed using $1/N$ expansion. This theory predicts that at the ${\mathbb{Z}}_{2}$-N\'eel transition, there is an emergent quasi-long-range power-law correlation of columnar valence bond solid order parameter.

Generic quantum spin ice

We consider possible exotic ground states of quantum spin ice as realized in rare earth pyrochlores. Prior work [Savary and Balents, Phys. Rev. Lett. 108, 037202 (2012).] introduced a gauge mean-field theory (gMFT) to treat spin or pseudospin Hamiltonians for such systems, reformulated as a problem of bosonic spinons coupled to a $U(1)$ gauge field. We extend gMFT to treat the most general nearest-neighbor exchange Hamiltonian, which contains a further exchange interaction. This term leads to interactions between spinons and requires a significant extension of gMFT, which we provide. As an application, we focus especially on the non-Kramers materials Pr${}_{2}T{M}_{2}$O${}_{7}$ ($TM=$ Sn, Zr, Hf, and Ir), for which the additional term is especially important, but for which an Ising-planar exchange coupling discussed previously is forbidden by time-reversal symmetry. In this case, when the planar $\mathit{XY}$ exchange is unfrustrated, we perform a full analysis and find three quantum ground states: a $U(1)$ quantum spin liquid (QSL), an antiferroquadrupolar ordered state and a noncoplanar ferroquadrupolar ordered one. We also consider the case of frustrated $\mathit{XY}$ exchange, and find that it favors a $\ensuremath{\pi}$-flux QSL, with an emergent line degeneracy of low-energy spinon excitations. This feature greatly enhances the stability of the QSL with respect to classical ordering.

Hole pairing from attraction of opposite-chirality spin vortices: Non-BCS superconductivity in underdoped cuprates

Within a gauge approach to the t-J model, we propose a new, non-BCS mechanism of superconductivity for underdoped cuprates. We implement the no-double occupancy constraint with a (semionic) slave-particle formalism. The dopant generates a vortex-like quantum distortion of the AF background centered on the empty sites, with opposite chirality for cores on the two N\'eel sublattices. Empty sites are described in terms of spinless fermionic holons and the long-range attraction between spin vortices on two opposite N\'eel sublattices is the holon pairing force, leading eventually to SC. The spin fluctuations are described by bosonic spinons with a gap generated by scattering on spin vortices. Due to the occupation constraint, there is a gauge attraction between holon and spinon, binding them into a physical hole. Through gauge interaction the spin vortex attraction induces the formation of spin-singlet RVB pairs reducing the spinon gap. Lowering T, there are two crossovers as precursors of the SC transition: at the higher one a gas of holon pairs appears, reducing the hole spectral weight, while at the lower one a gas of spinon pairs also appears, giving rise to a gas of incoherent preformed hole pairs with magnetic vortices in the plasma phase, supporting a Nernst signal. At an even lower T the hole pairs become coherent and SC appears beyond a critical doping. The proposed SC mechanism is not of the BCS-type, because it involves a gain in kinetic energy (lowering of spinon gap) and it is "almost" of the classical 3D XY-type. Since both the spinon gap and the holon pairing originate from the same term in the slave-particle representation of the t-J model, this approach incorporates a strong interplay between AF and SC, giving rise to a universal relation between Tc and the energy of the resonance mode, as observed in neutron scattering experiments.