We study the real-time dynamics of a highly excited charge carrier coupled to quantum phonons via a Holstein-type electron-phonon coupling. This is a prototypical example for the nonequilibrium dynamics in an interacting many-body system where excess energy is transferred from electronic to phononic degrees of freedom. We use diagonalization in a limited functional space (LFS) to study the nonequilibrium dynamics on a finite one-dimensional chain. This method agrees with exact diagonalization and the time-evolving block-decimation method, in both the relaxation regime and the long-time stationary state, and among these three methods it is the most efficient and versatile one for this problem. We perform a comprehensive analysis of the time evolution by calculating the electron, phonon and electron-phonon coupling energies, and the electronic momentum distribution function. The numerical results are compared to analytical solutions for short times, for a small hopping amplitude and for a weak electron-phonon coupling. In the latter case, the relaxation dynamics obtained from the Boltzmann equation agrees very well with the LFS data. We also study the time dependence of the eigenstates of the single-site reduced density matrix, which defines the so-called optimal phonon modes. We discuss their structure in nonequilibrium and the distribution of their weights. Our analysis shows that the structure of optimal phonon modes contains very useful information for the interpretation of the numerical data.
We present a method for simulating the time evolution of one-dimensional correlated electronphonon systems which combines the time-evolving block decimation algorithm with a dynamical optimization of the local basis. This approach can reduce the computational cost by orders of magnitude when boson fluctuations are large. The method is demonstrated on the nonequilibrium Holstein polaron by comparison with exact simulations in a limited functional space and on the scattering of an electronic wave packet by local phonon modes. Our study of the scattering problem reveals a rich physics including transient self-trapping and dissipation.
We study the Holstein model of spinless fermions, which at half filling exhibits a quantum phase transition from a metallic Tomonaga-Luttinger liquid phase to an insulating charge-density-wave (CDW) phase at a critical electron-phonon coupling strength. In our work, we focus on the realtime evolution starting from two different types of initial states that are CDW ordered: (i) ideal CDW states with and without additional phonons in the system and (ii) correlated ground states in the CDW phase. We identify the mechanism for CDW melting in the ensuing real-time dynamics and show that it strongly depends on the type of initial state. We focus on the far-from-equilibrium regime and emphasize the role of electron-phonon coupling rather than dominant electronic correlations, thus complementing a previous study of photo induced CDW melting [H. Hashimoto and S. Ishihara, Phys. Rev. B 96, 035154 (2017)]. The numerical simulations are performed by means of matrix-product-state based methods with a local basis optimization (LBO). Within these techniques, one rotates the local (bosonic) Hilbert spaces adaptively into an optimized basis that can then be truncated while still maintaining a high precision. In this work, we extend the time-evolving block decimation (TEBD) algorithm with LBO, previously applied to single-polaron dynamics, to a half-filled system. We demonstrate that in some parameter regimes, a conventional TEBD method without LBO would fail. Furthermore, we introduce and use a ground-state densitymatrix renormalization group method for electron-phonon systems using local basis optimization.In our examples, we account for up to M ph = 40 bare phonons per site by working with O(10) optimal phonon modes.
Motivated by recent experiments with ultracold quantum gases in optical lattices we study the decay of the staggered moment in the one-dimensional Fermi-Hubbard model starting from a perfect Néel state using exact diagonalization and the infinite-system-size time-evolving-block-decimation method. This extends previous work in which the same problem has been addressed for pure spin Hamiltonians. As a main result, we show that the relaxation dynamics of the double occupancy and of the staggered moment are different. The former is controlled by the nearest-neighbor tunneling rate while the latter is much slower and strongly dependent on the interaction strength, indicating that spin excitations are important. This difference in characteristic energy scales for the fast charge dynamics and the much slower spin dynamics is also reflected in the real-time evolution of nearest-neighbor density and spin correlations. A very interesting time dependence emerges in the von Neumann entropy, which at short times increases linearly with a slope proportional to the tunneling matrix element while the long-time growth of entanglement is controlled by spin excitations. Our predictions for the different relaxation dynamics of the staggered moment and the double occupancy should be observable in state-of-the-art optical lattice experiments. We further compare time averages of the double occupancy to the expectation values in both the canonical and diagonal ensembles, which quantitatively disagree with each other on finite systems. We relate the question of thermalization to the eigenstate thermalization hypothesis.PHYSICAL REVIEW A 91, 053628 (2015)
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