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arXiv:2212.06263 · Physical Review Letters

Spin, Charge, and η -Spin Separation in One-Dimensional Photodoped Mott Insulators

Yuta Murakami, Shintaro Takayoshi, Tatsuya Kaneko, Andreas Martin Läuchli, Philipp Werner

Published Mar 10, 2023• 21 citations
arXivHTMLPDF

Abstract

We show that effectively cold metastable states in one-dimensional photodoped Mott insulators described by the extended Hubbard model exhibit spin, charge, and η-spin separation. Their wave functions in the large on-site Coulomb interaction limit can be expressed as |Ψ⟩=|Ψ_{charge}⟩|Ψ_{spin}⟩|Ψ_{η-spin}⟩, which is analogous to the Ogata-Shiba states of the doped Hubbard model in equilibrium. Here, the η-spin represents the type of photo-generated pseudoparticles (doublon or holon). |Ψ_{charge}⟩ is determined by spinless free fermions, |Ψ_{spin}⟩ by the isotropic Heisenberg model in the squeezed spin space, and |Ψ_{η-spin}⟩ by the XXZ model in the squeezed η-spin space. In particular, the metastable η-pairing and charge-density-wave (CDW) states correspond to the gapless and gapful states of the XXZ model. The specific form of the wave function allows us to accurately determine the exponents of correlation functions. The form also suggests that the central charge of the η-pairing state is 3 and that of the CDW phase is 2, which we numerically confirm. Our study provides analytic and intuitive insights into the correlations between active degrees of freedom in photodoped strongly correlated systems.

DOI
10.1103/physrevlett.130.106501

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We show that effectively cold metastable states in one-dimensional photodoped Mott insulators described by the extended Hubbard model exhibit spin, charge, and η-spin separation. Their wave functions in the large on-site Coulomb interaction limit can be expressed as |Ψ⟩=|Ψ_{charge}⟩|Ψ_{spin}⟩|Ψ_{η-spin}⟩, which is analogous to the Ogata-Shiba states of the doped Hubbard model in equilibrium. Here, the η-spin represents the type of photo-generated pseudoparticles (doublon or holon). |Ψ_{charge}⟩ is determined by spinless free fermions, |Ψ_{spin}⟩ by the isotropic Heisenberg model in the squeezed spin space, and |Ψ_{η-spin}⟩ by the XXZ model in the squeezed η-spin space. In particular, the metastable η-pairing and charge-density-wave (CDW) states correspond to the gapless and gapful states of the XXZ model. The specific form of the wave function allows us to accurately determine the exponents of correlation functions. The form also suggests that the central charge of the η-pairing state is 3 and that of the CDW phase is 2, which we numerically confirm. Our study provides analytic and intuitive insights into the correlations between active degrees of freedom in photodoped strongly correlated systems.
We study the nonequilibrium phase diagram of long-lived photo-doped states in the one-dimensional UUU-VVV Hubbard model, where η\etaη-pairing, spin density wave and charge density wave (CDW) phases are found. The photo-doped states are studied using an effective model obtained by a Schrieffer-Wolff transformation combined with separate chemical potentials for the approximately conserved pseudoparticle excitations, leading to a generalized Gibbs ensemble type description. These photo-doped states are characterized by gapless (η\etaη-paring) and gapped (CDW) features in the nonequilibrium spectra. For small VVV, the η\etaη-pairing correlations dominate over a wide doping range even when the SUc(2)_c(2)c​(2) symmetry that protects η\etaη-pairing in the pure Hubbard model is absent. With increasing VVV, the CDW correlations take over in a wide doping range and are strong relative to the chemically doped case. We attribute the strong CDW correlations to the competition between intra- and inter-species repulsion and the one-dimensional configuration. Our results show that photo-doped strongly correlated systems exhibit different phases than conventional semiconductors.
We demonstrate the existence of an unconventional pairing state in photodoped Mott insulators on ladder and quasi-two-dimensional geometries, characterized by quasi-long-range doublon-holon correlations that signal Mott exciton condensation. The doublon-holon pairing exhibits correlations of ddd-wave-like symmetry, reminiscent of superconducting pairing in chemically doped Mott insulators. By constructing the phase diagram, using density matrix renormalization group, we reveal that the doublon-holon pairing state in the photodoped ladder emerges between the spin-singlet, charge-density-wave, and ηηη-pairing phases. Our study suggests that the interplay of charge, spin, and ηηη-spin degrees of freedom can give rise to exotic quantum many-body states in photodoped Mott insulators.
Although charge-spin separation has important consequences for the properties of one-dimensional (1D) Mott-Hubbard insulators, matrix elements in some of its dynamical correlation functions involve the coupling of spin and charge degrees of freedom. The corresponding interplay of the 1D Mott-Hubbard insulator's charge and spin degrees of freedom is an issue of both fundamental and technological interest, for instance, concerning their dynamics at subpicosecond timescales. On the other hand, the up- and down-spin one-particle spectral functions are the simplest dynamical correlation functions that involve excitation of both the charge and spin degrees of freedom. They are thus suitable to extract basic useful physical information on the above interplay at finite magnetic fields. Here the line shape of such functions at and in the $(k,\ensuremath{\omega})$ plane's vicinity of their cusp singularities is studied for the Mott-Hubbard insulator described by the 1D Hubbard model with one fermion per site at zero and finite magnetic fields. At zero field, they can be accessed in terms of electrons by photoemission experiments. At finite field, such functions and corresponding interplay of correlations and magnetic-field effects refer to an involved nonperturbative many-particle problem that is poorly understood. The Mott-Hubbard gap that separates the addition and removal spectral functions is calculated for all spin densities and interaction values. The qualitative differences in the one-particle properties of the Mott-Hubbard insulator and corresponding doped insulator are also investigated. The relation of our theoretical results and predictions to both condensed-matter and ultracold spin-1/21/21/2 atom systems is discussed.
We introduce a slave-fermion formulation in which to study the charge dynamics of the half-filled Hubbard model on the square lattice. In this description, the charge degrees of freedom are represented by fermionic holons and doublons and the Mott-insulating characteristics of the ground state are the consequence of holon–doublon bound-state formation. The bosonic spin degrees of freedom are described by the antiferromagnetic Heisenberg model, yielding long-ranged (Néel) magnetic order at zero temperature. Within this framework and in the self-consistent Born approximation, we perform systematic calculations of the average double occupancy, the electronic density of states, the spectral function and the optical conductivity. Qualitatively, our method reproduces the lower and upper Hubbard bands, the spectral-weight transfer into a coherent quasiparticle band at their lower edges and the renormalisation of the Mott gap, which is associated with holon–doublon binding, due to the interactions of both quasiparticle species with the magnons. The zeros of the Green function at the chemical potential give the Luttinger volume, the poles of the self-energy reflect the underlying quasiparticle dispersion with a spin-renormalised hopping parameter and the optical gap is directly related to the Mott gap. Quantitatively, the square-lattice Hubbard model is one of the best-characterised problems in correlated condensed matter and many numerical calculations, all with different strengths and weaknesses, exist with which to benchmark our approach. From the semi-quantitative accuracy of our results for all but the weakest interaction strengths, we conclude that a self-consistent treatment of the spin-fluctuation effects on the charge degrees of freedom captures all the essential physics of the antiferromagnetic Mott–Hubbard insulator. We remark in addition that an analytical approximation with these properties serves a vital function in developing a full understanding of the fundamental physics of the Mott state, both in the antiferromagnetic insulator and at finite temperatures and dopings.
With the hierarchical Green’s function approach, we study a doped Mott insulator described with the Hubbard model by analytically solving the equations of motion of an one-particle Green’s function and related multiple-point correlation functions, and find that the separation of the spin and charge degrees of freedom of the electrons is an intrinsic character of the doped Mott insulator. For enough of large on-site repulsive Coulomb interaction, we show that the spectral weight of the one-particle Green’s function is proportional to the hole doping concentration that is mainly produced by the charge fluctuation of electrons, while the excitation spectrum of the electrons is composed of two parts: One is contributed by the spin fluctuation of the electrons, which is proportional to the hole doping concentration, and another one is coming from the coupling between the charge and spin fluctuations of the electrons that takes the maximum at undoping. All of these low energy/temperature physical properties originate from the strong on-site Coulomb interaction. The present results are consistent with the spectroscopy observations of the cuprate superconductors and the numerical calculations in normal state above the pseudogap regime.
Abstract Many experiments show that strong excitations of correlated quantum materials can cause non-thermal phases without equilibrium analogues. Understanding the origin and properties of these nonequilibrium states has been challenging due to the limitations of theoretical methods for nonequilibrium strongly correlated systems. In this work, we introduce a generalized Gibbs ensemble description that enables a systematic analysis of the long-time behavior of photo-doped states in Mott insulators based on equilibrium methods. We demonstrate the power of the method by mapping out the nonequilibrium phase diagram of the one-dimensional extended Hubbard model, which features η-pairing and charge density wave phases in a wide photo-doping range. We furthermore clarify that the peculiar kinematics of photo-doped carriers, and the interaction between them, play an essential role in the formation of these non-thermal phases. Our results establish a new path for the systematic analysis of nonequilibrium strongly correlated systems.