Spin-charge Separation Research Articles

Spin-charge separation in the quantum boomerang effect

Spin-charge separation in the quantum boomerang effect

Phase diagram and crossover phases of topologically ordered graphene zigzag nanoribbons: role of localization effects

We computed the phase diagram of zigzag graphene nanoribbons as a function of on-site repulsion, doping, and disorder strength. The topologically ordered phase undergoes topological phase transitions into crossover phases, which are new disordered phases with non-universal topological entanglement entropy that exhibits significant variance. We explored the nature of non-local correlations in both the topologically ordered and crossover phases. In the presence of localization effects, strong on-site repulsion and/or doping weaken non-local correlations between the opposite zigzag edges of the topologically ordered phase. In one of the crossover phases, both e−/2 solitonic fractional charges and spin-charge separation were absent; however, charge-transfer correlations between the zigzag edges were possible. Another crossover phase contains solitonic e−/2 fractional charges but lacks charge transfer correlations. We also observed properties of non-topological, strongly disordered, and strongly repulsive phases. Each phase on the phase diagram exhibits a different zigzag-edge structure. Additionally, we investigated the tunneling of solitonic fractional charges under an applied voltage between the zigzag edges of undoped topologically ordered zigzag ribbons, and found that it may lead to a zero-bias tunneling anomaly.

Temperature-driven change in band structure reflecting spin-charge separation of Mott and Kondo insulators

Temperature-driven change in band structure reflecting spin-charge separation of Mott and Kondo insulators

Quasi-fractionalization of edge spin in chirality-assisted cluster-based Haldane state on triangular spin tube

Fractionalization of quantum degrees of freedom holds the key to finding new phenomena in physics, e.g., the quark model in hadron physics and the spin-charge separation in strongly-correlated electron systems. A typical example of the fractionalization in quantum spin systems is the spin-1 Haldane state, whose intriguing characteristics are well described by fractionalized virtual spins, delivering two individual spin-1/2 degrees of freedom as edge states. Here we theoretically propose an exotic extension of the Haldane state to the pseudo spin-1 model consisting of the mixture of real spin and spin chirality, resulting in quasi-fractionalization of spin-1/2 magnetization, i.e., an approximately-1/4 spin. Existence of the edge state is confirmed both analytically and numerically in a triangular spin tube, combining a low-energy perturbation theory and variational matrix-product state method. Our study not only proposes an unconventional quantum spin object but paves a way to chop the elementary quantities further.

Spin-charge separation and quantum spin Hall effect of beta-bismuthene

Multiple works suggest the possibility of classification of quantum spin Hall effect with magnetic flux tubes, which cause separation of spin and charge degrees of freedom and pumping of spin or Kramers-pair. However, the proof of principle demonstration of spin-charge separation is yet to be accomplished for realistic, ab initio band structures of spin-orbit-coupled materials, lacking spin-conservation law. In this work, we perform thought experiments with magnetic flux tubes on beta-bismuthene, and demonstrate spin-charge separation, and quantized pumping of spin for three insulating states, that can be accessed by tuning filling fractions. With a combined analysis of momentum-space topology and real-space response, we identify important role of bands supporting even integer invariants, which cannot be addressed with symmetry-based indicators. Our work sets a new standard for the computational diagnosis of two-dimensional, quantum spin-Hall materials by going beyond the mathbb {Z}_{2} paradigm and providing an avenue for precise determination of the bulk invariant through computation of quantized, real-space response.

Thermal disruption of a Luttinger liquid

The Tomonaga–Luttinger liquid (TLL) theory describes the low-energy excitations of strongly correlated one-dimensional (1D) fermions. In the past years, a number of studies have provided a detailed understanding of this universality class. More recently, theoretical investigations that go beyond the standard low-temperature, linear-response TLL regime have been developed. While these provide a basis for understanding the dynamics of the spin-incoherent Luttinger liquid, there are few experimental investigations in this regime. Here we report the observation of a thermally induced, spin-incoherent Luttinger liquid in a 6Li atomic Fermi gas confined to 1D. We use Bragg spectroscopy to measure the suppression of spin-charge separation and the decay of correlations as the temperature is increased. Our results probe the crossover between the coherent and incoherent regimes of the Luttinger liquid and elucidate the roles of the charge and the spin degrees of freedom in this regime.

Disorder-induced spin-charge separation in the one-dimensional Hubbard model

Many-body localization is believed to be generically unstable in quantum systems with continuous non-Abelian symmetries, even in the presence of strong disorder. Breaking these symmetries can stabilize the localized phase, leading to the emergence of an extensive number of quasilocally conserved quantities known as local integrals of motion, or $l$ bits. Using a sophisticated nonperturbative technique based on continuous unitary transforms, we investigate the one-dimensional Hubbard model subject to both spin and charge disorder, compute the associated $l$ bits and demonstrate that the disorder gives rise to a novel form of spin-charge separation. We examine the role of symmetries in delocalizing the spin and charge degrees of freedom, and show that while symmetries generally lead to delocalization through multiparticle resonant processes, certain subsets of states appear stable.

Efficient Mott insulator-metal transition by an intense terahertz electric field pulse via quantum tunneling

When a semiconductor is subjected to a strong electric field, carriers are generated via quantum tunneling; this is termed as dielectric breakdown. Thus, using a terahertz pulse to drive the dielectric breakdown in Mott insulators, which exhibit variations in their electronic structures under carrier doping, a filling-controlled transition can be induced in the subpicosecond time scale. However, to generate carriers via quantum tunneling in a material with a band gap in the visible or near-infrared regions, an electric field pulse significantly exceeding $1 \mathrm{MV} {\mathrm{cm}}^{\ensuremath{-}1}$ is necessary. In this paper, using an organic molecular compound, bis(ethylenedithio)tetrathiafulvalene-difluorotetracyanoquinodimethane, which is a typical one-dimensional (1D) Mott insulator with a Mott gap of 0.7 eV, we aimed at realizing carrier generation and metallization via a strong electric field component of a terahertz pulse enhanced with an organic nonlinear optical crystal up to $2.8 \mathrm{MV} {\mathrm{cm}}^{\ensuremath{-}1}$. Even after the terahertz electric field decays, the reflectivity change caused by the terahertz pulse remains; this is different from the case involving the use of weaker electric fields. More importantly, this response indicates a threshold behavior against the electric field amplitude, which is characteristic of carrier generation via the quantum tunneling process. Furthermore, transient reflectivity spectra across the mid-infrared region could be reproduced well by numerical simulations using the Drude model, in which inhomogeneous carrier distributions are considered. The observed Drude response of the doublons and holons was ascribed to the spin-charge separation characteristic of 1D strongly correlated electron systems. We also demonstrate that the energy efficiency of such carrier generation by the terahertz pulse excitation is at least five times greater than that when using photoexcitation beyond the Mott gap. This indicates that excitation with the strong terahertz pulse is more effective for carrier doping in solids; thus, the proposed method is expected to be widely applicable for the electronic-state control of various correlated electron materials in which chemical carrier doping is currently difficult.

Topology of three-dimensional Dirac semimetals and quantum spin Hall systems without gapless edge modes

A theoretical framework is outlined for calculating the spin-Chern number of topological Dirac semimetals and quantum spin Hall insulators lacking spin-conservation law and gapless edge modes. Spin-charge separation and quantized spin-pumping are probed by inserting a magnetic flux tube.

Continuous transition from a Landau quasiparticle to a neutral spinon

We examine a wavefunction ansatz in which a doped hole can experience a quantum transition from a charge $+e$ Landau quasiparticle to a neutral spinon as a function of the underlying spin-spin correlation. As shown variationally, such a wavefunction accurately captures all the essential features revealed by exact diagonalization and density matrix renormalization group simulations in a two-leg $t$-$J$ ladder. Hence its analytic form can provide an explicit understanding of the mechanism for the unconventional ground state. The transition in the phase diagram is accompanied by a change of the hole composite from a tight charge-spin binding to a loosely-bound hole-spin pair. In the latter, the hole carries a \emph{finite} spin current but with vanishing charge current in the degenerate ground states. We show that the charge of the hole composite here is dynamically diminished due to an internal relative hole-spin motion, which is fundamentally distinct from a simple charge-spin separation in a one-dimensional case. We further show that the same effect is also responsible for a strong pairing between two doped holes in such a non-Landau quasiparticle regime.

Phase diagram of mixed-dimensional anisotropic t−J models

We study the phase diagram of two different mixed-dimensional $t-J_z-J_{\perp}$-models on the square lattice, in which the hopping amplitude $t$ is only nonzero along the $x$-direction. In the first, bosonic, model, the spin exchange amplitude $J_{\perp}$ is negative and isotropic along the $x$ and $y$ directions of the lattice, and $J_z$ is isotropic and positive. The low-energy physics is characterized by spin-charge separation: the holes hop as free fermions in an easy-plane ferromagnetic background. In the second model, $J_{\perp}$ is restricted to the $x$-axis while $J_z$ remains isotropic and positive. The model is agnostic to particle statistics, and shows stripe patterns with anti-ferromagnetic N{\'e}el order at low temperature and high hole concentrations, in resemblance of the mixed-dimensional $t-J_z$ and $t-J$ models. At lower hole concentration, a very strong first order transition and hysteresis loop is seen extending to a remarkably high 14(1)% hole doping.

Universal description of dissipative Tomonaga-Luttinger liquids with SU(N) spin symmetry: Exact spectrum and critical exponents

Universal scaling relations for dissipative Tomonaga-Luttinger (TL) liquids with SU($N$) spin symmetry are obtained for both fermions and bosons, by using asymptotic Bethe-ansatz solutions and conformal field theory (CFT) in one-dimensional non-Hermitian quantum many-body systems with SU($N$) symmetry. We uncover that the spectrum of dissipative TL liquids with SU($N$) spin symmetry is described by the sum of one charge mode characterized by a complex generalization of $c=1$ U(1) Gaussian CFT, and $N-1$ spin modes characterized by level-$1$ SU($N$) Kac-Moody algebra with the conformal anomaly $c=N-1$, and thereby dissipation only affects the charge mode as a result of spin-charge separation in one-dimensional non-Hermitian quantum systems. The derivation is based on a complex generalization of Haldane's ideal-gas description, which is implemented by the SU($N$) Calogero-Sutherland model with inverse-square long-range interactions.

Dynamical theory for one-dimensional fermions with strong two-body losses: Universal non-Hermitian Zeno physics and spin-charge separation

We study an interacting one-dimensional gas of spin-1/2 fermions with two-body losses. The dynamical phase diagram that characterises the approach to the stationary state displays a wide quantum-Zeno region, identified by a peculiar behaviour of the lowest eigenvalues of the associated non-Hermitian Hamiltonian. We characterise the universal dynamics of this Zeno regime using an approximation scheme based on a effective decoupling of charge and spin degrees of freedom, where the latter effectively evolve in a non-Markovian way according to a non-Hermitian Heisenberg Hamiltonian. We present detailed results for the time evolution from initial states with one particle per site with either incoherent and antiferromagnetic spin order, showing how the two non-equilibrium evolutions build up drastically different charge correlations.

Generalized hydrodynamics of the repulsive spin- 12 Fermi gas

We study non-homogeneous quantum quenches in a one-dimensional gas of repulsive spin-$1/2$ fermions, as described by the integrable Yang-Gaudin model. By means of generalized hydrodynamics (GHD), we analyze in detail the real-time evolution following a sudden change of the confining potential. We consider in particular release protocols and trap quenches, including a version of the quantum Newton's cradle. At zero temperature, we employ a simplified phase-space hydrodynamic picture to characterize the dynamics of the particle- and spin-density profiles. Away from zero temperatures, we perform a thorough numerical study of the GHD equations, and provide quantitative predictions for different values of the temperature, external magnetic field, and chemical potential. We highlight the qualitative features arising due to the multi-component nature of the elementary excitations, discussing in particular effects of spin-charge separation and dynamical polarization.

Spin-charge separation in two dimensions: Spinon-chargon gauge theories from duality

Strong interactions between electrons in two dimensions can realize phases where their spins and charges separate. We capture this phenomenon within a dual formulation. Focusing on square lattices, we analyze the long-wavelength structure of vortices when the microscopic particles -- electrons or spinful bosons -- are near half-filling. These conditions lead to a compact gauge theory of spinons and chargons, which arise as the fundamental topological defects of the low-energy vortices. The gauge theory formulation is particularly suitable for studying numerous exotic phases and transitions. We support the general analysis by an exact implementation of the duality of a coupled-wire array. Finally, we demonstrate how the latter can be exploited to construct parent Hamiltonians for fractional phases and their transitions.

Perturbative Quantum Simulation.

Approximation based on perturbation theory is the foundation for most of the quantitative predictions of quantum mechanics, whether in quantum many-body physics, chemistry, quantum field theory, or other domains. Quantum computing provides an alternative to the perturbation paradigm, yet state-of-the-art quantum processors with tens of noisy qubits are of limited practical utility. Here, we introduce perturbative quantum simulation, which combines the complementary strengths of the two approaches, enabling the solution of large practical quantum problems using limited noisy intermediate-scale quantum hardware. The use of a quantum processor eliminates the need to identify a solvable unperturbed Hamiltonian, while the introduction of perturbative coupling permits the quantum processor to simulate systems larger than the available number of physical qubits. We present an explicit perturbative expansion that mimics the Dyson series expansion and involves only local unitary operations, and show its optimality over other expansions under certain conditions. We numerically benchmark the method for interacting bosons, fermions, and quantum spins in different topologies, and study different physical phenomena, such as information propagation, charge-spin separation, and magnetism, on systems of up to 48 qubits only using an 8+1 qubit quantum hardware. We demonstrate our scheme on the IBM quantum cloud, verifying its noise robustness and illustrating its potential for benchmarking large quantum processors with smaller ones.

New disordered anyon phase of doped graphene zigzag nanoribbon

We investigate interacting disordered zigzag nanoribbons at low doping, using the Hubbard model to treat electron interactions within the density matrix renormalization group and Hartree-Fock method. Extra electrons that are inserted into an interacting disordered zigzag nanoribbon divide into anyons. Furthermore, the fractional charges form a new disordered anyon phase with a highly distorted edge spin density wave, containing numerous localized magnetic moments residing on the zigzag edges, thereby displaying spin-charge separation and a strong non-local correlation between the opposite zigzag edges. We make the following new predictions, which can be experimentally tested: (1) In the low doping case and weak disorder regime, the soft gap in the tunneling density of states is replaced by a sharp peak at the midgap energy with two accompanying peaks. The e^-/2 fractional charges that reside on the boundary of the zigzag edges are responsible for these peaks. (2) We find that the midgap peak disappears as the doping concentration increases. The presence of e^-/2 fractional charges will be strongly supported by the detection of these peaks. Doped zigzag ribbons may also exhibit unusual transport, magnetic, and inter-edge tunneling properties.

Spin-charge separation in a one-dimensional Fermi gas with tunable interactions.

Ultracold atoms confined to periodic potentials have proven to be a powerful tool for quantum simulation of complex many-body systems. We confine fermions to one dimension to realize the Tomonaga-Luttinger liquid model, which describes the highly collective nature of their low-energy excitations. We use Bragg spectroscopy to directly excite either the spin or charge waves for various strengths of repulsive interaction. We observe that the velocity of the spin and charge excitations shift in opposite directions with increasing interaction, a hallmark of spin-charge separation. The excitation spectra are in quantitative agreement with the exact solution of the Yang-Gaudin model and the Tomonaga-Luttinger liquid theory. Furthermore, we identify effects of nonlinear corrections to this theory that arise from band curvature and back-scattering.

Observing separate spin and charge Fermi seas in a strongly correlated one-dimensional conductor.

An electron is usually considered to have only one form of kinetic energy, but could it have more, for its spin and charge, by exciting other electrons? In one dimension (1D), the physics of interacting electrons is captured well at low energies by the Tomonaga-Luttinger model, yet little has been observed experimentally beyond this linear regime. Here, we report on measurements of many-body modes in 1D gated wires using tunneling spectroscopy. We observe two parabolic dispersions, indicative of separate Fermi seas at high energies, associated with spin and charge excitations, together with the emergence of two additional 1D “replica” modes that strengthen with decreasing wire length. The interaction strength is varied by changing the amount of 1D intersubband screening by more than 45%. Our findings not only demonstrate the existence of spin-charge separation in the whole energy band outside the low-energy limit of the Tomonaga-Luttinger model but also set a constraint on the validity of the newer nonlinear Tomonaga-Luttinger theory.

Imaging gate-tunable Tomonaga-Luttinger liquids in 1H-MoSe2 mirror twin boundaries.

One-dimensional electron systems exhibit fundamentally different properties than higher-dimensional systems. For example, electron-electron interactions in one-dimensional electron systems have been predicted to induce Tomonaga-Luttinger liquid behaviour. Naturally occurring grain boundaries in single-layer transition metal dichalcogenides exhibit one-dimensional conducting channels that have been proposed to host Tomonaga-Luttinger liquids, but charge density wave physics has also been suggested to explain their behaviour. Clear identification of the electronic ground state of this system has been hampered by an inability to electrostatically gate such boundaries and tune their charge carrier concentration. Here we present a scanning tunnelling microscopy and spectroscopy study of gate-tunable mirror twin boundaries in single-layer 1H-MoSe2 devices. Gating enables scanning tunnelling microscopy and spectroscopy for different mirror twin boundary electron densities, thus allowing precise characterization of electron-electron interaction effects. Visualization of the resulting mirror twin boundary electronic structure allows unambiguous identification of collective density wave excitations having two velocities, in quantitative agreement with the spin-charge separation predicted by finite-length Tomonaga-Luttinger liquid theory.