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Emergent nonequilibrium phases in the photo-doped one-dimensional Mott insulator

Yuta Murakami, Shintaro Takayoshi, Tatsuya Kaneko, Zhiyuan Sun, Denis Golež, Andrew J. Millis, Philipp Werner

Published May 28, 2021• 0 citations
OpenAlex

Abstract

We study the nonequilibrium phase diagram of long-lived photo-doped states in the one-dimensional $U$-$V$ Hubbard model, where $\eta$-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 ($\eta$-paring) and gapped (CDW) features in the nonequilibrium spectra. For small $V$, the $\eta$-pairing correlations dominate over a wide doping range even when the SU$_c(2)$ symmetry that protects $\eta$-pairing in the pure Hubbard model is absent. With increasing $V$, 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.

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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.
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.
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.
The study of nonequilibrium phenomena in interacting lattice systems can provide new perspectives on correlation effects, and information on metastable states of matter. Mott insulators are a promising class of systems for nonequilibrium studies, since they exhibit exotic phenomena and complex phase diagrams upon doping, and because a large Mott gap provides protection against fast thermalization and heating after photo-excitations. We can thus expect the emergence of interesting transient states and photo-induced phases in Mott systems. This review presents the current understanding of the mechanisms which control the time evolution of photo-doped charge carriers and the properties of photo-induced metastable states. We focus on recent theoretical progress, identify the relevant underlying concepts, and link them to experimental observations. The review starts with a general discussion of field-induced nonequilibrium setups and an overview of key experiments which revealed characteristic properties of photo-excited Mott states, proceeds with a compact overview of the theoretical tools which have been developed to investigate these strongly correlated nonequilibrium states, and then analyzes Mott insulators driven out of equilibrium by static electric fields, periodic fields, and short laser pulses. We also discuss the appearance of nonthermal electronic orders in photo-excited Mott systems, including nonthermal spin and orbital orders, ηηη pairing states, and novel types of excitonic orders.
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.
By utilizing time-dependent tensor-network algorithms in the infinite matrix-product-state representation, we theoretically investigate the pump-probe spectroscopy of the one-dimensional extended Hubbard model at half filling. Our focus lies on nonequilibrium optical conductivity and single-particle excitation spectra. In the spin-density-wave (SDW) phase, we identify an in-gap state in the nonequilibrium optical conductivity due to the formation of excitons (or doublon-holon pairs), generated by the pulse through nonlocal interactions. In the strong-coupling regime, we discern additional multiple in-gap and out-of-gap states. In the charge-density-wave (CDW) phase, we detect not only an in-gap state but also a finite Drude weight, which results from the dissolution of charge order by photoexcitation. Analyzing time-dependent single-particle excitation spectra directly in the thermodynamic limit confirms the origin of these new states in the SDW and CDW phases as the excitation of newly emerged dispersions. We illustrate that the pump-probe spectroscopy simulations in the thermodynamic limit furnish unambiguous spectral structures that allow for direct comparison with experimental results, and the integration of nonequilibrium optical conductivity and time- and angle-resolved photoemission spectroscopy provides comprehensive insights into nonequilibrium states.
We determine the spin and charge orders in the ground state of the doped two-dimensional (2D) Hubbard model in its simplest form, namely with only nearest-neighbor hopping and on-site repulsion. At half-filling, the ground state is known to be an antiferromagnetic Mott insulator. Doping Mott insulators is believed to be relevant to the superconductivity observed in cuprates. A variety of candidates have been proposed for the ground state of the doped 2D Hubbard model. A recent work employing a combination of several state-of-the-art numerical many-body methods established the stripe order as the ground state near 1/81/81/8 doping at strong interactions. In this paper, we apply one of these methods, the cutting-edge constrained-path auxiliary field quantum Monte Carlo (AFQMC) method with self-consistently optimized gauge constraints, to systematically study the model as a function of doping and interaction strength. With careful finite size scaling based on large-scale computations, we map out the ground state phase diagram in terms of its spin and charge order. We find that modulated antiferromagnetic order persists from near half-filling to about 1/51/51/5 doping. At lower interaction strengths or larger doping, these ordered states are best described as spin-density waves, with essentially delocalized holes and modest oscillations in charge correlations. When the charge correlations are stronger (large interaction or small doping), they are best described as stripe states, with the holes more localized near the node in the antiferromagnetic spin order. In both cases, we find that the wavelength in the charge correlations is consistent with so-called filled stripes.