Motivated by experimental developments introducing the concept of spin-orbit separation, we study the real-space real-time evolution of an excitonic wave packet using a two-orbital Hubbard model in a chain. The exciton is created by exciting an electron from a lower-energy half-filled orbital to a higher-energy empty orbital. We carry out the real-time dynamics of the resulting excitonic wave packet using the time-dependent density matrix renormalization group. We find clear evidence of charge-spin and spin-orbit separation in real space, by tracking the time evolution of local observables. We show that the velocity of the orbiton can be tuned varying the interorbital interactions. We also present a comparative study of the dynamics of a hole in one-orbital and two-orbital Hubbard models. Moreover, we analyze the dynamics of an exciton with spin-flip excitation, where we observe fractionalized spinons induced by Hund's interaction.
Motivated by experimental developments introducing the concept of spin-orbit separation, we study the real-space real-time evolution of an excitonic wave packet using a two-orbital Hubbard model in a chain. The exciton is created by exciting an electron from a lower-energy half-filled orbital to a higher-energy empty orbital. We carry out the real-time dynamics of the resulting excitonic wave packet using the time-dependent density matrix renormalization group. We find clear evidence of charge-spin and spin-orbit separation in real space, by tracking the time evolution of local observables. We show that the velocity of the orbiton can be tuned varying the interorbital interactions. We also present a comparative study of the dynamics of a hole in one-orbital and two-orbital Hubbard models. Moreover, we analyze the dynamics of an exciton with spin-flip excitation, where we observe fractionalized spinons induced by Hund's interaction.
Using the time-dependent density-matrix renormalization group, we study the time evolution of electronic wave packets in the one-dimensional extended Hubbard model with on-site and nearest-neighbor repulsion, U and V, respectively. As expected, the wave packets separate into spin-only and charge-only excitations (spin-charge separation). Charge and spin velocities exhibit nonmonotonic dependence on V. For small and intermediate values of V, both velocities increase with V. However, the charge velocity exhibits a stronger dependence than that of the spin, leading to a more pronounced spin-charge separation. Charge fractionalization, on the other hand, is weakly affected by V. The results are explained in terms of Luttinger liquid theory in the weak-coupling limit and an effective model in the strong-coupling regime.
We study the real-time evolution of a charge-excited state in a one-dimensional eg-orbital degenerate Hubbard model, by a time-dependent density-matrix renormalization group method. Considering a chain along the z direction, electrons hop between adjacent 3z2−r2 orbitals, while x2−y2 orbitals are localized. For the charge-excited state, a holon-doublon pair is introduced into the ground state at quarter filling. At initial time, there is no electron in a holon site, while a pair of electrons occupies 3z2−r2 orbital in a doublon site. As the time evolves, the holon motion is governed by the nearest-neighbor hopping, but the electron pair can transfer between 3z2−r2 orbital and x2−y2 orbital through the pair hopping in addition to the nearest-neighbor hopping. Thus holon and doublon propagate at different speed due to the pair hopping that is characteristic of multi-orbital systems.
We study the photoinduced breakdown of a two-orbital Mott insulator and resulting metallic state. Using time-dependent density matrix renormalization group, we scrutinize the real-time dynamics of the half-filled two-orbital Hubbard model interacting with a resonant radiation field pulse. The breakdown, caused by production of doublon-holon pairs, is enhanced by Hund's exchange, which dynamically activates large orbital fluctuations. The melting of the Mott insulator is accompanied by a high to low spin transition with a concomitant reduction of antiferromagnetic spin fluctuations. Most notably, the overall time response is driven by the photogeneration of excitons with orbital character that are stabilized by Hund's coupling. These unconventional ``Hund excitons'' correspond to bound spin-singlet orbital-triplet doublon-holon pairs. We study exciton properties such as bandwidth, binding potential, and size within a semiclassical approach. The photometallic state results from a coexistence of Hund excitons and doublon-holon plasma.
Using the adaptive time-dependent density-matrix renormalization group method for the 1D Hubbard model, the splitting of local perturbations into separate wave packets carrying charge and spin is observed in real time. We show the robustness of this separation beyond the low-energy Luttinger liquid theory by studying the time evolution of single particle excitations and density wave packets. A striking signature of spin-charge separation is found in 1D cold Fermi gases in a harmonic trap at the boundary between liquid and Mott-insulating phases. We give quantitative estimates for an experimental observation of spin-charge separation in an array of atomic wires.
We present a comprehensive study of a one-dimensional two-orbital model at and below quarter filling that realizes a number of unconventional phases. In particular, we find an excitonic density wave in which excitons quasicondense with finite center-of-mass momentum and an order parameter that changes phase with wave vector Q. In this phase, excitons behave as hard-core bosons without charge order. In addition, excitons can pair to form biexcitons in a state that is close to a charge- density-wave instability. When pairing dominates over the interorbital repulsion, we encounter a regime in which one orbital is metallic, while the other forms a spin-gapped superconductor, a genuine orbital-selective paired state. All these results are supported by both analytical and numerical calculations. By assuming a quasiclassical approximation, we solve the three-body hole-electron-spinon problem and show that excitons are held together by forming a bound state with spinons. In order to preserve the antiferromagnetic background, excitons acquire a dispersion that has a minimum away from k=0. The full characterization of the different phases is obtained by means of extensive density-matrix renormalization-group calculations.
Uniform spin-orbit coupling in an open single-band Hubbard chain is an exactly removable SU(2) gauge field at the Hamiltonian level, but not at the level of laboratory-frame spin correlations. We study this separation using density matrix renormalization group calculations for the repulsive one-dimensional Rashba-Hubbard chain. For open boundary conditions, a site-dependent spin rotation maps the model with hopping t and Rashba spin-orbit strength λ onto the ordinary Hubbard chain with renormalized hopping tλ=t2+λ2. Consequently, charge and energy diagnostics are affected only through the bandwidth renormalization, which is quadratic in weak λ/t. Spin correlations, however, respond already at linear order because the same transformation rotates the local spin basis by the wave vector kso=2arctan(λ/t). We use DMRG to verify this observable consequence across the filling diagram of finite open chains. The filling structure follows the gauge-equivalent Hubbard model, whereas the spin structure factor shows the predicted spin-orbit sidebands. A dominant Hubbard-chain magnetic wave vector k0 is transformed into components at k0±kso, folded into the open-chain Brillouin zone. At half filling, where k0=π, the two sidebands fold onto a single, in-plane, spin spiral wave with k=π−kso<π. Away from half filling, the incommensurate Hubbard spin response splits into two distinct spin-orbit-shifted components, producing a real-space beating pattern. Our results provide a filling-resolved tensor-network benchmark for the exactly removable limit of one-dimensional spin-orbit coupling, and establish a controlled reference point for ladders, multiorbital chains, rings, proximitized wires, and higher-dimensional Hubbard systems where spin-orbit coupling can no longer be gauged away.