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 the picosecond range, can be explained even quantitatively with the multimagnon 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 consequently large exciton-magnon coupling.
Weak perturbations can drive an interacting many-particle system far from its initial equilibrium state if one is able to pump into degrees of freedom approximately protected by conservation laws. This concept has for example been used to realize Bose–Einstein condensates of photons, magnons and excitons. Integrable quantum systems, like the one-dimensional Heisenberg model, are characterized by an infinite set of conservation laws. Here, we develop a theory of weakly driven integrable systems and show that pumping can induce large spin or heat currents even in the presence of integrability breaking perturbations, since it activates local and quasi-local approximate conserved quantities. The resulting steady state is qualitatively captured by a truncated generalized Gibbs ensemble with Lagrange parameters that depend on the structure but not on the overall amplitude of perturbations nor the initial state. We suggest to use spin-chain materials driven by terahertz radiation to realize integrability-based spin and heat pumps.
Generalized Gibbs ensembles have been used as powerful tools to describe the steady state of integrable many-particle quantum systems after a sudden change of the Hamiltonian. Here we demonstrate numerically, that they can be used for a much broader class of problems. We consider integrable systems in the presence of weak perturbations which both break integrability and drive the system to a state far from equilibrium. Under these conditions, we show that the steady state and the time-evolution on long time-scales can be accurately described by a (truncated) generalized Gibbs ensemble with time-dependent Lagrange parameters, determined from simple rate equations. We compare the numerically exact time evolutions of density matrices for small systems with a theory based on block-diagonal density matrices (diagonal ensemble) and a time-dependent generalized Gibbs ensemble containing only small number of approximately conserved quantities, using the onedimensional Heisenberg model with perturbations described by Lindblad operators as an example.
We present a linear-response formalism for a system of correlated electrons out of equilibrium, as relevant for the probe optical absorption in pump-probe experiments. We consider the time dependent optical conductivity σ(ω, t) and its nonequilibrium properties. As an application we numerically study a single highly excited charged particle in the spin background, as described within the two-dimensional t-J model. Our results show that the optical sum rule approaches the equilibrium-like one very fast, however, the time evolution and the final asymptotic behavior of the absorption spectra in the finite systems considered still reveal dependence on the type of initial pump perturbation. This is observed in the evolution of its main features: the mid-infrared peak and the Drude weight.
We develop a Liouville perturbation theory for weakly driven and weakly open quantum systems in situations when the unperturbed system has a number of conservations laws. If the perturbation violates the conservation laws, it drives the system to a new steady state which can be approximately but efficiently described by a (generalized) Gibbs ensemble characterized by one Lagrange parameter for each conservation law. The value of those has to be determined from rate equations for conserved quantities. Remarkably, even weak perturbations can lead to large responses of conserved quantities. We present a perturbative expansion of the steady state density matrix; first we give the condition that fixes the zeroth order expression (Lagrange parameters) and then determine the higher order corrections via projections of the Liouvillian. The formalism can be applied to a wide range of problems including two-temperature models for electron-phonon systems, Bose condensates of excitons or photons or weakly perturbed integrable models. We test our formalism by studying interacting fermions coupled to non-thermal reservoirs, approximately described by a Boltzmann equation. In equilibrium many particle systems can be efficiently described by Gibbs ensembles, characterized by one Lagrange parameter (inverse temperature, chemical potential) for each exactly conserved quantity (energy, particle number). Such a simple but powerful description is, in general, absent for driven non-equilibrium systems. As long as weak perturbations, which drive the system out of equilibrium, have small effects one can resort to perturbation theory. Kubo formulas, for example, describe the response to time-dependent Hamiltonian perturbations. Also for open systems described by Lindblad operators similar formulations of perturbation theory can be developed [1-9]. If the density matrix of the unperturbed system is not unique (as is the case for all Hamiltonian systems) one has to use degenerate Liouville perturbation theory [1,7].There are many situations where even weak perturbations of interacting many-particle systems can have large effects. A famous example is the Bose-Einstein condensation of excitons and polaritons [10][11][12]: irradiation by light creates more and more excitons which equilibrate approximately and form a Bose-Einstein condensate. Importantly, the exciton number is approximately conserved thus even weak pumping can compensate for exciton losses and leads to large densities of these excitations. Similarly, condensations of photons or magnons have been observed [13][14][15][16][17]. This is a general phenomenon: whenever approximate conservation laws exist, small perturbations which weakly break those conservation laws can drive the system out of equilibrium, to a steady state completely different from the initial one. In the example given above, the approximately conserved quantity is the exciton number. Other examples use the approximate conservation of spin to induce large nuclear spin polarization [18] for medical applications o...
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