We consider Mott insulators driven by periodic coherent laser radiation, using both single orbital and multi-orbital models, noting that the latter is of more interest in solid state systems. We derive general expressions for the resulting periodically driven spin models and spin-orbital models using time-dependent perturbation theory. First, we show that the effective exchange interactions of the Floquet Hamiltonians are highly tunable by the frequency, amplitude, and polarization of the laser. Second, we take the effect of finite bandwidth of excitations into account and study possible heating effects. Using the same formalism with a slight modification we also consider the small frequency regime and study the dielectric breakdown of Mott insulators.
The dynamics of holon-doublon pairs is studied in Hubbard two-leg ladders using the time-dependent Density Matrix Renormalization Group method. We find that the geometry of the two-leg ladder, that is qualitatively different from a one-dimensional chain due to the presence of a spin-gap, strongly affects the propagation of a doublon-holon pair. Two distinct regimes are identified. For weak inter-leg coupling, the results are qualitatively similar to the case of the propagation previously reported in Hubbard chains, with only a renormalization of parameters. More interesting is the case of stro…
An analytical solution of the Mott transition is obtained for the Hubbard model on the Bethe lattice in the large coordination number ($z$) limit. The excitonic binding of doublons (doubly occupied sites) and holons (empty sites) is shown to be the origin of a continuous Mott transition between a metal and an emergent quantum spin liquid insulator. The doublon-holon binding theory enables a different large-$z$ limit and a different phase structure than the dynamical meanfield theory by allowing intersite spinon correlations to lift the $2^N$-fold degeneracy of the local moments in the insulati…
We argue that the binding between doubly occupied (doublon) and empty (holon) sites governs the incoherent excitations and plays a key role in the Mott transition in strongly correlated Mott-Hubbard systems. We construct a new saddle point solution with doublon-holon binding in the Kotliar-Ruckenstein slave-boson functional integral formulation of the Hubbard model. On the half-filled honeycomb lattice and square lattice, the ground state is found to exhibit a continuous transition from the paramagnetic semimetal/metal to an antiferromagnetic ordered Slater insulator with coherent quasiparticl…
We study the binding of a holon to a doublon in a half-filled Hubbard model as the mechanism of the zero-temperature metal-insulator transition. In a spin polarized system and a non-bipartite lattice a single holon-doublon (HD) pair exhibits a binding transition (e.g., on a face-centred cubic lattice), or a sharp crossover (e.g., on a triangular lattice) corresponding well to the standard Mott transition in unpolarized systems. We extend the HD-pair study towards non-polarized systems by considering more general spin background and by treating the finite HD density within a BCS-type approximat…
The arguments presented in PRL. vol. 102, 056404 (2009) are discussed in the context of the vast literature on spectral weight transfer in doped Mott insulators. We show that the conclusions regarding spectral weight transfer in PRL. vol. 102, 056404 (2009) are, where novel, internally inconsistent and where correct, have been reached at least 18 years ago.
Multiorbital interactions have the capacity to produce an interesting kind of doublon-holon bound state that consists of a single-hole state in one band and a doubly-occupied state in another band. Interband doublon-holon pair excitations in the two-orbital Hubbard model are studied by using dynamical mean-field theory with the Lanczos method as the impurity solver. We find that the interband bound states may provide several in-gap quasiparticle peaks in the density of states of the narrow band in the orbital-selective Mott phase with a small Hund's rule coupling ($J$). There exists a correspo…
A mechanism of Mott transitions in a Bose Hubbard model on a square lattice is studied, using a variational Monte Carlo method. Besides an onsite correlation factor, we introduce a four-body doublon-holon factor into the trial state, which considerably improves the variational energy and can appropriately describe a superfluid-insulator transition. Its essense consists in binding (and unbinding) of a doublon to a holon in a finite short range, identical with the cases of fermions. The features of this transition are qualitatively different from those of Brinkman-Rice-type transitions.
Dynamical mean-field theory (DMFT) studies frequently observe a fine structure in the local spectral function of the SU(2) Fermi-Hubbard model at half filling: In the metallic phase close to the Mott transition, subpeaks emerge at the inner edges of the Hubbard bands. Here we demonstrate that these subpeaks originate from the low-energy effective interaction of doublon-holon pairs, by investigating how the correlation functions of doublon and holon operators contribute to the subpeaks. A mean-field analysis of the low-energy effective Hamiltonian provides results consistent with our DMFT calcu…
Sub-cycle doublon-holon dynamics in one-dimensional Mott insulators revealed by two-color high-harmonic spectroscopy
Purdue University（普渡大学）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Colorado State University（科罗拉多州立大学）；Brookhaven National Laboratory（布鲁克海文国家实验室）；Joint Attosecond Science Laboratory (JASLab), National Research Council of Canada and University of Ottawa（联合阿秒科学实验室（JASLab），加拿大国家研究委员会和渥太华大学）
Using the one-dimensional Hubbard model, which is commonly used for describing, e.g., high-$T_c$ superconducting cuprates, we study high-harmonic generation (HHG) from doped, correlated materials. Doping is modeled by changing the number of electrons in the lattice from the conventional half-filling case. For relatively small Hubbard $U$, i.e., small electron-electron correlation, we find little to no effect of doping on the dynamics and the HHG spectra. For increasing $U$ the degree of doping has a marked effect on the dynamics and spectra. We explain these findings through the quasiparticle-…
The Mott metal-insulator transition in the Hubbard model is studied by constructing a dynamical slave-boson mean-field theory in the limit of large lattice coordination number $z$ that incorporates the binding between doubly occupied (doublon) and empty (holon) sites. On the Mott insulating side where all doublons and holons bond in real space into excitonic pairs leading to the charge gap, the theory simplifies considerably to leading order in $1/\sqrt{z}$, and becomes exact on the infinite-$z$ Bethe lattice. An asymptotic solution is obtained for a continuous Mott transition associated with …
We study the real-time evolution of a charge-excited state in a one-dimensional $e_{\rm g}$-orbital degenerate Hubbard model, by a time-dependent density-matrix renormalization group method. Considering a chain along the $z$ direction, electrons hop between adjacent $3z^2-r^2$ orbitals, while $x^2-y^2$ 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 $3z^2-r^2$ orbital in a doublon site. As the time evolves, the holon motion…
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 notabl…
We investigate the effect of nonlocal interactions on the photo-doped Mott insulating state of the two-dimensional Hubbard model using a nonequilibrium generalization of the dynamical cluster approximation. In particular, we compare the situation where the excitonic states are lying within the continuum of doublon-holon excitations to a set-up where the excitons appear within the Mott gap. In the first case, the creation of nearest-neighbor doublon-holon pairs by excitations across the Mott gap results in enhanced excitonic correlations, but these excitons quickly decay into uncorrelated doubl…
Photoemission Signatures of Photoinduced Carriers and Excitons in One-Dimensional Mott Insulators
The University of Tokyo（东京大学）；Institute for Materials Research, Tohoku University（东北大学物质材料研究机构）；RIKEN Center for Emergent Matter Science (CEMS)（理化学研究所新兴物质科学中心）；Trans-Scale Quantum Science Institute, University of Tokyo（东京大学跨尺度量子科学研究所）
Using Floquet dynamical mean-field theory, we study the high-harmonic generation in the time-periodic steady states of wide-gap Mott insulators under AC driving. In the strong-field regime, the harmonic intensity exhibits multiple plateaus, whose cutoff energies $ε_{\rm cut} = U + mE_0$ scale with the Coulomb interaction $U$ and the maximum field strength $E_0$. In this regime, the created doublons and holons are localized because of the strong field and the $m$-th plateau originates from the recombination of $m$-th nearest-neighbor doublon-holon pairs. In the weak-field regime, there is only …
To understand the mechanism of Mott transitions in case of no magnetic influence, superfluid-insulator (Mott) transitions in the S=0 Bose Hubbard model at unit filling are studied on the square and triangular lattices, using a variational Monte Carlo method. In trial many-body wave functions, we introduce various types of attractive correlation factors between a doubly-occupied site (doublon, D) and an empty site (holon, H), which play a central role for Mott transitions, in addition to the onsite repulsive (Gutzwiller) factor. By optimizing distance-dependent parameters, we study various prop…
We demonstrate the existence of long-lived prethermalized states in the Mott insulating Hubbard model driven by periodic electric fields. These states, which also exist in the resonantly driven case with a large density of photo-induced doublons and holons, are characterized by a nonzero current and an effective temperature of the doublons and holons which depends sensitively on the driving condition. Focusing on the specific case of resonantly driven models whose effective time-independent Hamiltonian in the high-frequency driving limit corresponds to noninteracting fermions, we show that the…
Excitation by light pulses enables the manipulation of phases of quantum condensed matter. Here, we photoexcite high-energy holon-doublon pairs as a way to alter the magnetic free energy landscape of the Kitaev-Heisenberg magnet $α$-RuCl$_3$, with the aim to dynamically stabilize a proximate spin liquid phase. The holon-doublon pair recombination through multimagnon emission is tracked through the time-evolution of the magnetic linear dichroism originating from the competing zigzag spin ordered ground state. A small holon-doublon density suffices to reach a spin disordered state. The phase tra…
Employing time-resolved photoelectron spectroscopy we analyze the relaxation dynamics of hot electrons in the charge density wave / Mott material 1T-TaS_2. At 1.2 eV above the Fermi level we observe a hot electron lifetime of 12 +- 5 fs in the metallic state and of 60 +- 10 fs in the broken symmetry ground state - a direct consequence of the reduced phase space for electron-electron scattering determined by the Mott gap. Boltzmann equation calculations which account for the interaction of hot electrons in a Bloch band with a doublon-holon excitation in the Mott state provide insight into the u…
We study high-harmonic generation (HHG) in the one-dimensional Hubbard model in order to understand its relation to elementary excitations as well as the similarities and differences to semiconductors. The simulations are based on the infinite time-evolving block decimation (iTEBD) method and exact diagonalization. We clarify that the HHG originates from the doublon-holon recombination, and the scaling of the cutoff frequency is consistent with a linear dependence on the external field. We demonstrate that the subcycle features of the HHG can be reasonably described by a phenomenological three…
We give a self-contained derivation of the low-energy effective interactions of the SU($N$) Hubbard model, a multiflavor generalization of the one-band Hubbard model, by using a generalized Schrieffer-Wolff transformation (SWT). The effective interaction of doublons and holons, which has been largely ignored in previous SWT studies (e.g., the $t$-$J$ model), leads to distinct peaks in the local density of states. As shown by Lee et al. [Phys. Rev. Lett. 119, 236402 (2017)], this underlying effective doublon-holon interaction explains the numerical observation of the subpeaks at the inner edges…
The Mott insulator is the quintessential strongly correlated electronic state. We obtain complete insight into the physics of the two-dimensional Mott insulator by extending the slave-fermion (holon-doublon) description to finite temperatures. We first benchmark its predictions against state-of-the-art quantum Monte Carlo simulations, demonstrating quantitative agreement. Qualitatively, the short-ranged spin fluctuations both induce holon-doublon bound states and renormalize the charge sector to form the Hubbard bands. The Mott gap is understood as the charge gap renormalized downwards by thes…
We define, compute and analyze the nonequilibrium differential optical conductivity of the one-dimensional extended Hubbard model at half-filling after applying a pump pulse, using the time-dependent density matrix renormalization group method. The melting of the Mott insulator is accompanied by a suppression of the local magnetic moment and ensuing photogeneration of doublon-holon pairs. The differential optical conductivity reveals $(i)$ mid-gap states related to parity-forbidden optical states, and $(ii)$ strong renormalization and hybridization of the excitonic resonance and the absorption…
We theoretically investigate pump-probe optical responses in the two-dimensional extended Hubbard model describing cuprates by using a time-dependent Lanczos method. At half filling, pumping generates photoinduced absorptions inside the Mott gap. A part of low-energy absorptions is attributed to the independent propagation of photoinduced holons and doublons. The spectral weight just below the Mott gap increases with decreasing the on-site Coulomb interaction $U$. We find that the next-nearest-neighbor Coulomb interaction $V_1$ enhances this $U$ dependence, indicating the presence of biexciton…
We study the double occupancy in a fermionic Mott insulator at half-filling generated via a dynamical periodic modulation of the hopping amplitude. Tuning the modulation amplitude, we describe a crossover in the nature of doublon-holon excitations from a Fermi Golden Rule regime to damped Rabi oscillations. The decay time of excited states diverges at a critical modulation strength, signaling the transition to a dynamically bound non-equilibrium state of doublon-holon pairs. A setup using a fermionic quantum gas should allow to study the critical exponents.
Mechanisms of Mott transitions and dx2-y2-wave superconductivity (SC) are studied in the half-filled-band Hubbard model on square lattices with a diagonal hopping term (t'), using an optimization (or correlated) variational Monte Carlo method. In the trial wave functions, a doublon-holon binding effect is introduced in addition to the onsite Gutzwiller projection. We mainly treat a d-wave singlet state and a projected Fermi sea. In both wave functions, first-order Mott transitions without direct relevance to magnetic orders take place at U=Uc approximately of the bandwidth for arbitrary t'/t. …
We study the high harmonic generation (HHG) in Mott insulators using Floquet dynamical mean-field theory (DMFT). We show that the main origin of the HHG in Mott insulators is the doublon-holon recombination, and that the character of the HHG spectrum differs depending on the field strength. In the weaker-field regime, the HHG spectrum shows a single plateau as in the HHG from gases, and its cut-off energy $ε_{\rm cut}$ scales linearly with the field strength $E_0$ as $ε_{\rm cut}=Δ_{\rm gap} + αE_0$, where $Δ_{\rm gap}$ is the Mott gap. On the other hand, in the stronger-field regime, multiple…
We show that backflow correlations in the variational wave function for the Hubbard model greatly improve the previous results given by the Slater-Jastrow state, usually considered in this context. We provide evidence that, within this approach, it is possible to have a satisfactory connection with the strong-coupling regime. Moreover, we show that, for the Hubbard model on the lattice, backflow correlations are essentially short range, inducing an effective attraction between empty (holons) and doubly occupied sites (doublons). In presence of frustration, we report the evidence that the metal…
Mott transition plays a key role in strongly correlated physics but its nature is not yet fully understood. Motivated by recent development of Schwinger boson approach for the Kondo lattice, we propose in this work a novel slave fermion algorithm to study the Mott transition. Upon local approximation, our method yields a phase diagram with a zero-temperature continuous (Mott) metal-insulator transition at finite Coulomb interaction $U$ for the half-filled one-band Hubbard model on a square lattice, and the resistivity exhibits a critical scaling around the quantum Widom line. We argue that the…
We study the real-time dynamics of a pair hole/doubly-occupied-site, namely a holon and a doublon, in a 1D Hubbard insulator with on-site and nearest-neighbor Coulomb repulsion. Our analysis shows that the pair is long-lived and the expected decay mechanism to underlying spin excitations is actually inefficient. For a nonzero inter-site Coulomb repulsion, we observe that part of the wave-function remains in a bound state. Our study also provides insight on the holon-doublon propagation in real space. Due to the one-dimensional nature of the problem, these particles move in opposite directions …
Charge excitations in Mott insulators (MIs) are distinct from their band-insulator counterparts and they can provide a mechanism for energy harvesting in solar cells based on strongly correlated electronic materials. In this paper, we study the real-time dynamics of holon-doublon pairs in a MI connected to metallic leads using the time-dependent density matrix renormalization group method. The transfer of charge across the MI-metal interface is controlled by both the electron-electron interaction strength within the MI and the voltage difference between the leads. We find an overall enhancemen…
Conventional wisdom suggests that the long time behavior of isolated interacting periodically driven (Floquet) systems is a featureless maximal entropy state characterized by an infinite temperature. Efforts to thwart this uninteresting fixed point include adding sufficient disorder to realize a Floquet many-body localized phase or working in a narrow region of drive frequencies to achieve glassy non-thermal behavior at long time. Here we show that in clean systems the Floquet eigenstates can exhibit non-thermal behavior due to finite system size. We consider a one-dimensional system of spinle…
We present a theory for the recombination of (charged) holons and doublons in one-dimensional organic Mott insulators, which is responsible for the decay of a photoexcited metallic state. Due to the charge-spin separation, the dominant mechanism for recombination at low density of charges involves a multi-phonon emission. We show that a reasonable coupling to phonons is sufficient to explain the fast recombination observed by pump-probe experiments in ET-F$_2$TCNQ, whereby we can also account for the measured pressure dependence of the recombination rate.
We investigate a model for a Mott insulator in presence of a time-periodic modulated interaction and a coupling to a thermal reservoir. The combination of drive and dissipation leads to non-equilibrium steady states with a large number of doublon excitations, well above the maximum thermal-equilibrium value. We interpret this effect as an enhancement of local pairing correlations, providing analytical arguments based on a Floquet Hamiltonian. Remarkably, this Hamiltonian shows a tendency to develop long-range staggered superconducting correlations. This suggests the possibility of realizing th…
The mechanism of Mott transition in the Hubbard model on the square lattice is studied without explicit introduction of magnetic and superconducting correlations, using a variational Monte Carlo method. In the trial wave functions, we consider various types of binding factors between a doubly-occupied site (doublon, D) and an empty site (holon, H), like a long-range type as well as a conventional nearest-neighbor type, and add independent long-range D-D (H-H) factors. It is found that a wide choice of D-H binding factor leads to Mott transitions at critical values near the band width. We renew…
Mott insulators sometimes show dramatic changes in their electronic states after photoirradiation, as indicated by photoinduced Mott-insulator-to-metal transition. In the photoexcited states of Mott insulators, electron wavefunctions are more delocalized than in the ground state, and long-range Coulomb interactions play important roles in charge dynamics. However, their effects are difficult to discriminate experimentally. Here, we show that in a one-dimensional Mott insulator, bis(ethylenedithio)tetrathiafulvalene-difluorotetracyanoquinodimethane (ET-F2TCNQ), long-range Coulomb interactions s…
Nonlinear response of a Mott insulator to external electric field, corresponding to dielectric breakdown phenomenon, is studied within of a one-dimensional half-filled Hubbard model. It is shown that in the limit of nearly spin polarized insulator the decay rate of the ground state into excited holon-doublon pairs can be evaluated numerically as well to high accuracy analytically. Results show that the threshold field depends on the charge gap as $F_{th} \propto Δ^{3/2}$. Numerical results on small systems indicate on the persistence of a similar mechanism for the breakdown for decreasing magn…
We present a calculation of the recombination rate of the excited holon-doublon pairs based on the two-dimensional model relevant for undoped cuprates which shows that fast processes, observed in pump-probe experiments on Mott-Hubbard insulators in picosecond range, can be explained even quantitatively with the multi-magnon emission. The precondition is the existence of the Mott-Hubbard bound exciton of the s-type. We find that its decay is exponentially dependent on the Mott-Hubbard gap and on the magnon energy, with a small prefactor which can be traced back to strong correlations and conseq…
We use a three-pulse ultrafast optical spectroscopy to study the relaxation processes in a frustrated Mott insulator Na$_2$IrO$_3$. By being able to independently produce the out-of-equilibrium bound states (excitons) of doublons and holons with the first pulse and suppress the underlying antiferromagnetic order with the second one, we were able to elucidate the relaxation mechanism of quasiparticles in this system. By observing the difference in the exciton dynamics in the magnetically ordered and disordered phases we found that the mass of this quasiparticle is mostly determined by its inter…
To study excitonic effects on high-harmonic generation (HHG) in Mott insulators, we investigate pumped nonequilibrium dynamics in the one-dimensional extended Hubbard model. By employing time-dependent calculations based on the exact diagonalization and infinite time-evolving block decimation methods, we find the strong enhancement of the HHG intensity around the exciton energy. The subcycle analysis in the sub-Mott-gap regime shows that the intensity region of the time-resolved spectrum around the exciton energy splits into two levels and oscillates following the driving electric field. This …
We study evolution of metals from Mott insulators in the carrier-doped 2D Hubbard model using a cluster extension of the dynamical mean-field theory. While the conventional metal is simply characterized by the Fermi surface (pole of the Green function G), interference of the zero surfaces of G with the pole surfaces becomes crucial in the doped Mott insulators. Mutually interfering pole and zero surfaces are dramatically transferred over the Mott gap, when lightly doped holes synergetically loosen the doublon-holon binding. The heart of the Mott physics such as the pseudogap, hole pockets, Fer…
The two-orbital Hubbard model on a square lattice at quarter filling (electron number per site $n=1$) is investigated by the variational Monte Carlo method. For the variational wave function, we include short-range doublon-holon binding factors. We find that the energy of this wave function is lower than that of the density-density Jastrow wave function partially including long-range correlations used in a previous study. We introduce frustration to the model by the next-nearest-neighbor hopping $t'$ in addition to the nearest-neighbor hopping $t$. For $t'=0$, a ferromagnetic state with stagge…
