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arXiv:2311.13933 · Physical Review Letters

Numerically Exact Simulation of Photodoped Mott Insulators

Fabian Künzel, André Erpenbeck, Daniel Werner, Enrico Arrigoni, Emanuel Gull, Guy Cohen, Martin Eckstein

Published Apr 23, 2024• 18 citations
arXivHTMLPDF

Abstract

A description of long-lived photodoped states in Mott insulators is challenging, as it needs to address exponentially separated timescales. We demonstrate how properties of such states can be computed using numerically exact steady state techniques, in particular, the quantum Monte Carlo algorithm, by using a time-local ansatz for the distribution function with separate Fermi functions for the electron and hole quasiparticles. The simulations show that the Mott gap remains robust to large photodoping, and the photodoped state has hole and electron quasiparticles with strongly renormalized properties.

DOI
10.1103/physrevlett.132.176501

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A description of long-lived photodoped states in Mott insulators is challenging, as it needs to address exponentially separated timescales. We demonstrate how properties of such states can be computed using numerically exact steady state techniques, in particular, the quantum Monte Carlo algorithm, by using a time-local ansatz for the distribution function with separate Fermi functions for the electron and hole quasiparticles. The simulations show that the Mott gap remains robust to large photodoping, and the photodoped state has hole and electron quasiparticles with strongly renormalized properties.
Photodoped states are widely observed in laser-excited Mott insulators, in which charge excitations are quickly created and can exist beyond the duration of the external driving. Despite the fruitful experimental explorations, theoretical studies on the microscopic models face the challenge to simultaneously deal with exponentially separated time scales, especially in multiband systems, where the longtime behaviors are often well beyond the reach of state-of-the-art numerical tools. Here, we address this difficulty by introducing a steady-state description of photodoped Mott insulators using an open-system setup, where the photodoped system is stabilized as a nonequilibrium steady state by a weak external driving. Taking advantage of the stationarity, we implement and discuss the details of an efficient numerical tool using the steady-state dynamical mean-field theory combined with the noncrossing approximation. We demonstrate that these stationary photodoped states exhibit the same properties of their transient counterparts, while being solvable with reasonable computational efforts. Furthermore, they can be parametrized by just a few physical quantities, including the effective temperature and the density of charge excitations, which confirms the universal nature of photodoped states indeed independent of the excitation protocols. As a first application, we consider the stationary photodoped states in a two-band Hubbard model with intertwined spin-and-orbital ordering and find a family of hidden phases unknown from the previous studies, implying an apparently unexplored time regime of the relaxation of the intertwined orders.
Photodoping of Mott insulators or correlated metals can create an unusual metallic state which simultaneously hosts holelike and electronlike particles. We study the dynamics of this state up to long times, as it passes its kinetic energy to the environment. When the system cools down, it crosses over from a bad metal into a resilient quasiparticle regime, in which quasiparticle bands are formed with separate Fermi levels for electrons and holes, but quasiparticles do not yet satisfy the Fermi-liquid paradigm. Subsequently, the transfer of energy to the environment slows down significantly, and the system does not reach the Fermi-liquid state even on the timescale of picoseconds. The transient photodoped strange metal exhibits unusual properties of relevance for ultrafast charge and heat transport: In particular, there can be an asymmetry in the properties of electrons and holes, and strong correlations between electrons and holes, as seen in the spectral properties.
We investigate the properties of the metallic state obtained by photodoping carriers into a Mott insulator. In a strongly interacting system, these carriers have a long lifetime, so that they can dissipate their kinetic energy to a phonon bath. In the relaxed state, the scattering rate saturates at a nonzero temperature-independent value, and the momentum-resolved spectral function features broad bands which differ from the well-defined quasiparticle bands of a chemically doped system. Our results indicate that a photodoped Mott insulator behaves as a bad metal, in which strong scattering between doublons and holes inhibits Fermi-liquid behavior down to low temperature.
We study the nature of electronic states induced by the non-magnetic impurities in a hole-doped Mott insulator. We further examine the consequences of doping on the transport and spectral properties. By employing exact diagonalizaton + Monte-Carlo simulation based on the many-body computational techniques, which allows for the thermal and spatial fluctuations besides a fine resolution in the momentum-space spectral function, the current investigation unravels the degree of localization of the electronic states induced by the impurity atoms as a function of temperature. The major consequences of doping impurity, which introduces holes in the systems, include the appearance of impurity states just above the Fermi level and only in the vicinity of momenta where the gap opens along the normal state Fermi surface in the insulating state. The electronic state at the impurity site is split because of the antiferromagnetic background. The pseudogap-like behavior of the density of states is weakened as reflected by the enhanced charge fluctuations even away from the impurity site at an elevated temperature. Our study also reflects on the degree of improvement in conductivity as well as particle-hole asymmetry introduced in the momentum-resolved spectral function, which maximizes towards the high-symmetry points like ([Formula: see text].
Using the standard quantum Monte Carlo technique for the Hubbard model, I present here a numerical investigation of the hole propagation in a quantum antiferromagnet. The calculation is very well stabilized, using selected-size systems and a special choice of the trial wave function that satisfies the ``closed-shell condition'' in the presence of an arbitrarily weak Zeeman magnetic field. First it is shown that the presence of this magnetic field does not affect the thermodynamic properties of the half-filled system. Then I use the same selected sizes for the one-hole ground state. I investigate the question of vanishing or nonvanishing quasiparticle weight, in order to clarify whether the Mott insulator behaves as a conventional insulator with an upper and lower Hubbard band. By comparing the present finite-size scaling with several techniques that predict a finite quasiparticle weight, the data seem more consistent with a vanishing quasiparticle weight, i.e., the Mott-Hubbard insulator should be characterized by nontrivial excitations that cannot be interpreted in a simple picture. However, one cannot exclude, based only on numerical grounds, a very small but nonvanishing quasiparticle weight. In the last part I give some theoretical arguments to explain the results of the Monte Carlo simulation.
We study a ground-state ansatz for the single-hole-doped $t\text{\ensuremath{-}}J$ model in two dimensions via a variational Monte Carlo method. Such a single-hole wave function possesses finite angular momenta generated by hidden spin currents, which give rise to a novel ground-state degeneracy in agreement with recent exact diagonalization (ED) and density matrix renormalization group (DMRG) results. We further show that the wave function can be decomposed into a quasiparticle component and an incoherent momentum distribution in excellent agreement with the DMRG results up to an $8\ifmmode\times\else\texttimes\fi{}8$ lattice. Such a two-component structure indicates the breakdown of Landau's one-to-one correspondence principle, and in particular, the quasiparticle spectral weight vanishes by a power law in the large sample size limit. By contrast, turning off the phase string induced by the hole hopping in the so-called $\ensuremath{\sigma}\ifmmode\cdot\else\textperiodcentered\fi{}t\text{\ensuremath{-}}J$ model, a conventional Bloch-wave wave function with a finite quasiparticle spectral weight can be recovered, also in agreement with the ED and DMRG results. The present study shows that a singular effect already takes place in the single-hole-doped Mott insulator, by which the bare hole is turned into a non-Landau quasiparticle with translational-symmetry breaking. Generalizations to pairing and finite doping are briefly discussed.