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.

The momentum, electronic density, spin density, and interaction dependences of the exponents that control the (k, ω)-plane singular features of the σ =↑, ↓ one-electron spectral functions of the 1D Hubbard model at finite magnetic field are studied. The usual half-filling concepts of one-electron lower Hubbard band and upper Hubbard band are defined for all electronic density and spin density values and the whole finite repulsion range in terms of the rotated electrons associated with the model Bethe-ansatz solution. Such rotated electrons are the link of the non-perturbative relation between the electrons and the pseudofermions. Our results further clarify the microscopic processes through which the pseudofermion dynamical theory accounts for the σ one-electron matrix elements between the ground state and excited energy eigenstates.Here C α are normalization constants and α = η, s. The model in its full Hilbert space can be described either directly within the BA solution [35,52] or by application onto the Bethe states of the η-spin and spin SU (2) symmetry algebras off-diagonal generators, as given in Eq. (3).Relying on the model symmetries, for simplicity and without loss in generality the studies of this paper refer to electronic densities and spin densities in the ranges n e ∈ [0, 1[ and m ∈ [0, n e ], respectively. For such electronic densities and spin densities the model ground states are LWSs of both the η-spin and spin SU (2) symmetry algebras so that in the studies of this paper we use the LWS formulation of 1D Hubbard model BA solution.The PDT is used in it to clarify one of the unresolved questions concerning the physics of the 1D Hubbard model at finite magnetic field, Eq. (1), by deriving the momentum, repulsive interaction u = U/4t, electron-density n e , and spindensity m dependences of the exponents that control the singularities at the σ one-electron spectral functions. These exponents control the line shape near the singularities of the following σ one-electron spectral function B σ,γ (k, ω) such that γ = −1 (and γ = +1) for one-electron removal (and addition),Here c k,σ and c † k,σ are electron annihilation and creation operators, respectively, of momentum k and |GS denotes the initial N σ -electron ground state of energy E Nσ GS . The ν − and ν + summations run over the N σ − 1 and N σ + 1-electron excited energy eigenstates, respectively, and E Nσ−1 ν − and E Nσ+1 ν + are the corresponding energies. The remainder of the paper is organized as follows. In Section II the σ one-electron lower-Hubbard band (LHB) and upper-Hubbard band (UHB) are defined for u > 0 and all densities in terms of quantum numbers associated with the σ rotated-electron energy eigenstates occupancies. Moreover, the relation of the β pseudoparticle representation to such σ rotated electrons, which are uniquely defined in terms of the matrix elements of the electron -rotated-electron unitary operator between all model 4 L energy and momentum eigenstates, is an issue also addressed in that section. The PDT suitable for the...