Holon Excitations Research Articles

Z2 metallic spin liquid on a frustrated Kondo lattice

Metallic spin liquid has been reported in several correlated metals, but a satisfactory theoretical description is not yet available. Here we propose a potential route to realize the metallic spin liquid and construct an effective $\mathbb{Z}_2$ gauge theory with charged fractionalized excitations on the triangular Kondo lattice. This leads to a $\mathbb{Z}_2$ metallic spin liquid featured with long-lived, heavy holon excitations of spin 0 and charge $+e$ and a partially enlarged electron Fermi surface. It differs from the weak-coupling FL$^*$ state proposed earlier and may be viewed as a fractionalized heavy fermion liquid. Our theory provides a general framework to describe the metallic spin liquid in frustrated Kondo lattice systems.

Spectroscopic signatures of next-nearest-neighbor hopping in the charge and spin dynamics of doped one-dimensional antiferromagnets

We study the impact of next-nearest-neighbor (NNN) hopping on the low-energy collective excitations of strongly correlated doped antiferromagnetic cuprate spin chains. Specifically, we use exact diagonalization and the density matrix renormalization group method to study the single-particle spectral function, the dynamical spin and charge structure factors, and the Cu $L$-edge resonant inelastic x-ray scattering (RIXS) intensity of the doped $t\text{\ensuremath{-}}t\ensuremath{'}\text{\ensuremath{-}}J$ model for a set of $t\ensuremath{'}$ values. We find evidence that the spin and charge degrees of freedom of the doped holes are not strictly separated anymore as $|t\ensuremath{'}|$ increases and identify the consequences of this in the dynamical response functions. The inclusion of NNN hopping couples the spinon and holon excitations, resulting in the formation of a spin polaron, where a ferromagnetic spin-polarization cloud dresses the doped carrier. The spin polaron manifests itself as additional spectral weight in the dynamical correlation functions, which appear simultaneously in the spin- and charge-sensitive channels. We also demonstrate that RIXS can provide a unique view of the spin polaron, due to its sensitivity to both the spin and charge degrees of freedom.

Angle resolved photoemission spectroscopy reveals spin charge separation in metallic MoSe2 grain boundary

Material line defects are one-dimensional structures but the search and proof of electron behaviour consistent with the reduced dimension of such defects has been so far unsuccessful. Here we show using angle resolved photoemission spectroscopy that twin-grain boundaries in the layered semiconductor MoSe2 exhibit parabolic metallic bands. The one-dimensional nature is evident from a charge density wave transition, whose periodicity is given by kF/π, consistent with scanning tunnelling microscopy and angle resolved photoemission measurements. Most importantly, we provide evidence for spin- and charge-separation, the hallmark of one-dimensional quantum liquids. Our studies show that the spectral line splits into distinctive spinon and holon excitations whose dispersions exactly follow the energy-momentum dependence calculated by a Hubbard model with suitable finite-range interactions. Our results also imply that quantum wires and junctions can be isolated in line defects of other transition metal dichalcogenides, which may enable quantum transport measurements and devices.

Non-Abelian Statistics in a Quantum Antiferromagnet

We propose a novel spin liquid state for a spin S = 1 antiferromagnet in two dimensions. The ground state violates P and T, is a spin-singlet, and is fully invariant under the lattice symmetries. The spinon and holon excitations are deconfined and obey non-Abelian statistics. We present preliminary numerical evidence that the universality class of this topological liquid can be stabilized by a local Hamiltonian involving three-spin interactions.

Spinon-holon interactions in an anisotropict−Jchain: A comprehensive study

We consider a generalization of the one-dimensional t-J model with anisotropic spin-spin interactions. We show that the anisotropy leads to an effective attractive interaction between the spinon and holon excitations, resulting in a localized bound state. Detailed quantitative analytic predictions for the dependence of the binding energy on the anisotropy are presented and are verified by precise numerical simulations. The binding energy is found to interpolate smoothly between a finite value in the t- Jz limit and zero in the isotropic limit, going to zero exponentially in the vicinity of the latter. We identify changes in spinon dispersion as the primary factor for this nontrivial behavior. © 2007 The American Physical Society.

Temperature dependence of spinon and holon excitations in one-dimensional Mott insulators

Motivated by the recent angle-resolved photoemission spectroscopy (ARPES) measurements on one-dimensional Mott insulators, SrCuO${}_{2}$ and Na${}_{0.96}$V${}_{2}$O${}_{5}$, we examine the single-particle spectral weight of the one-dimensional (1D) Hubbard model at half-filling. We are particularly interested in the temperature dependence of the spinon and holon excitations. For this reason, we have performed the dynamical density matrix renormalization group and determinantal quantum Monte Carlo (QMC) calculations for the single-particle spectral weight of the 1D Hubbard model. In the QMC data, the spinon and holon branches become observable at temperatures where the short-range antiferromagnetic correlations develop. At these temperatures, the spinon branch grows rapidly. In the light of the numerical results, we discuss the spinon and holon branches observed by the ARPES experiments on SrCuO${}_{2}$. These numerical results are also in agreement with the temperature dependence of the ARPES results on Na${}_{0.96}$V${}_{2}$O${}_{5}$.

Z2 gauge theory of electron fractionalization in the t,t' - J model with uniaxial anisotropy

We consider a strongly correlated spin model with a positive uniaxial anisotropy. We show that in2+1 dimensions this model is equivalent to spinon and holon excitations coupled to aZ2 Ising gaugefield. The Z2 gauge field represents the vortex monopole excitations of the X–Y model. As a function ofthe hole concentration the X–Y model has two phases: a spin wave phase and afree vortex monopole phase. In the spin wave phase the spinons and the holonsare weakly interacting, giving rise to a spin–charge separated phase which atzero temperature is superconducting. When the hole concentration increases theZ2 excitations (the monopole currents) become free, giving rise to holon–spinon binding. Thedestruction of superconductivity at zero temperature coincides with the appearance of thefree monopole currents.

Quasiparticles as composite objects in the resonating valence bond superconductor

We study the nature of the superconducting state, the origin of d-wave pairing, and elementary excitations of a resonating valence bond (RVB) superconductor. We show that the phase string formulation of the t-J model leads to confinement of bare spinon and holon excitations in the superconducting state, though the vacuum is described by the RVB state. Nodal quasiparticles are obtained as composite excitations of spinon and holon excitations. The d-wave pairing symmetry is shown to arise from short range antiferromagnetic correlations.

Fictitious flux confinement: Magnetic pairing in coupled spin chains or planes

The spinon and holon excitations of two-leg Heisenberg or lightly doped $t\ensuremath{-}J$ ladders are shown to be bound in pairs by string confinement forces given approximately by the antiferromagnetic exchange energy across the rungs, ${F=J}_{\ensuremath{\perp}}〈{\mathbf{S}}_{i}{\mathbf{S}}_{j}{〉}_{\ensuremath{\perp}}/b.$ These forces originate from fictitious flux tubes associated with the half-Fermi statistics of the excitations. It is conjectured that similar confinement forces, determined by the antiferromagnetic exchange energy across the layers, are partially responsible for the spin gap and the pairing of charge carriers in multilayer CuO superconductors.

S=1 Spin Liquids: Broken Discrete Symmetries Restored

We introduce a novel kind of spin liquid, the spin 1 chirality liquid, whichprovides a generic paradigm for a disordered spin 1 antiferromagnet in twodimensions. It supports spinon and holon excitations, which carry a chiralityquantum number. These excitations obey half-fermi statistics. The sign ofthe statistical parameter is determined by the chirality. The spin 1 chiralityliquid is the first example of a two dimensional quantum state which supportsexcitations with fractional statistics but does not violate P or T.

Nature of spin-charge separation in thet−Jmodel

Quasiparticle properties are explored in an effective theory of the $t-J$ model which includes two important components: spin-charge separation and unrenormalizable phase shift. We show that the phase shift effect indeed causes the system to be a non-Fermi liquid as conjectured by Anderson on a general ground. But this phase shift also drastically changes a conventional perception of quasiparticles in a spin-charge separation state: an injected hole will remain {\em stable} due to the confinement of spinon and holon by the phase shift field despite the background is a spinon-holon sea. True {\em deconfinement} only happens in the {\em zero-doping} limit where a bare hole will lose its integrity and decay into holon and spinon elementary excitations. The Fermi surface structure is completely different in these two cases, from a large band-structure-like one to four Fermi points in one-hole case, and we argue that the so-called underdoped regime actually corresponds to a situation in between, where the ``gap-like'' effect is amplified further by a microscopic phase separation at low temperature. Unique properties of the single-electron propagator in both normal and superconducting states are studied by using the equation of motion method. We also comment on some of influential ideas proposed in literature related to the Mott-Hubbard insulator and offer a unified view based on the present consistent theory.

Spectral functions of half-filled one-dimensional Hubbard rings with varying boundary conditions

We study the effect of varying the boundary condition on the spectral function of a finite one-dimensional Hubbard chain, which we compute using direct (Lanczos) diagonalization of the Hamiltonian. By direct comparison with the two-body response functions and with the exact solution of the Bethe ansatz equations, we can identify both spinon and holon features in the spectra. At half-filling the spectra have the well-known structure of a low-energy holon band and its shadow---which spans the whole Brillouin zone---and a spinon band present for momenta less than the Fermi momentum. Features related to the twisted boundary condition are cusps in the spinon band. We show that the spectral building principle, adapted to account for both the finite system size and the twisted boundary condition, describes the spectra well in terms of single spinon and holon excitations. We argue that these finite-size effects are a signature of spin-charge separation and that their study should help establish the existence and nature of spin-charge separation in finite-size systems.

Finite-temperature transport in finite-size Hubbard rings in the strong-coupling limit

We study the current, the curvature of levels, and the finite temperature charge stiffness, D(T,L), in the strongly correlated limit, U>>t, for Hubbard rings of L sites, with U the on-site Coulomb repulsion and t the hopping integral. Our study is done for finite-size systems and any band filling. Up to order t we derive our results following two independent approaches, namely, using the solution provided by the Bethe ansatz and the solution provided by an algebraic method, where the electronic operators are represented in a slave-fermion picture. We find that, in the U=\infty case, the finite-temperature charge stiffness is finite for electronic densities, n, smaller than one. These results are essencially those of spinless fermions in a lattice of size L, apart from small corrections coming from a statistical flux, due to the spin degrees of freedom. Up to order t, the Mott-Hubbard gap is \Delta_{MH}=U-4t, and we find that D(T) is finite for n<1, but is zero at half-filling. This result comes from the effective flux felt by the holon excitations, which, due to the presence of doubly occupied sites, is renormalized to \Phi^{eff}=\phi(N_h-N_d)/(N_d+N_h), and which is zero at half-filling, with N_d and N_h being the number of doubly occupied and empty lattice sites, respectively. Further, for half-filling, the current transported by any eigenstate of the system is zero and, therefore, D(T) is also zero.

Angle-resolved photoemission study ofSr2CuO3

We report angle-resolved photoemission spectroscopy (ARPES) on a single Cu-O chain compound ${\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}$ with Ne I photons. In contrast with previous ARPES with higher-energy photons, the present result clearly shows two well-separated branches of dispersions near ${E}_{F}$ ascribable to spinon and holon excitations, respectively. This indicates that spin and charge degrees of freedom are separated in one-dimensional Cu-O chains, supporting the theoretical prediction as well as the previous ARPES interpretation. Comparison with previous ARPES results indicates that surface, photoionization cross section, and finite-temperature effects substantially modify ARPES spectra.

Angle resolved photoemission study of the spin-Peierls system α′-NaV2O5

Abstract We have made an X-ray photoemission and angle-resolved photoemission (ARPES) study of NaV 2 O 5 at room temperature, i.e. in the paramagnetic phase well above its spin-Peierls transition temperature. The V 2 p core level spectra well reflect its mixed valence nature. The result of the ARPES spectra clarifies the experimental band structure, reflecting the one-dimensionality of this compound. The lower binding energy side of the V 3 d band shows a momentum-dependent modulation with the periodicity of π, suggesting the existence of antiferromagnetic correlations or holon excitations in the one-dimensional Mott insulator.

Single-Particle Excitations in One-Dimensional Mott-Hubbard InsulatorNaV2O5

We have made an angle-resolved photoemission study of ${\mathrm{NaV}}_{2}{\mathrm{O}}_{5}$ at room temperature, i.e., in the paramagnetic phase well above the spin-Peierls transition temperature. The obtained results reflect the one dimensionality of the electronic structure. The lower binding energy side of the V $3d$ band shows a clear momentum-dependent modulation with the periodicity of $\ensuremath{\pi}$, indicating the existence of antiferromagnetic correlations or holon excitations in the one-dimensional Mott insulator. We compare the results with recent theoretical works on the one-dimensional Hubbard and $t$- $J$ models and discuss consistency between model parameters.

Separation of spin and charge excitations in one-dimensionalSrCuO2

In this paper we expand on our earlier results [Phys. Rev. Lett. 77, 4054 (1996)] on angle-resolved photoemission studies on one-dimensional ${\mathrm{SrCuO}}_{2}$ that reveal a behavior of a hole in Cu-O chain. The results cannot be explained within the conventional band theory, but require a picture in which the spin and charge degrees of freedom for a single electron are separated. Instead of a single branch as predicted in band theory, $E$ versus $k$ relationship can be explained by underlying spinon and holon excitations scaled by hopping energy $t$ and exchange energy $J,$ respectively, indicating separated spin and charge excitations. This is an experimental observation of direct consequence of the spin-charge separation driven by electron correlations that was first predicted thirty years ago. It also shows spinon and holons are real particles with definite energy-momentum dispersions.