37 research outputs found
Time-dependent variational principle in matrix-product state manifolds: pitfalls and potential
We study the applicability of the time-dependent variational principle in
matrix product state manifolds for the long time description of quantum
interacting systems. By studying integrable and nonintegrable systems for which
the long time dynamics are known we demonstrate that convergence of long time
observables is subtle and needs to be examined carefully. Remarkably, for the
disordered nonintegrable system we consider the long time dynamics are in good
agreement with the rigorously obtained short time behavior and with previous
obtained numerically exact results, suggesting that at least in this case the
apparent convergence of this approach is reliable. Our study indicates that
while great care must be exercised in establishing the convergence of the
method, it may still be asymptotically accurate for a class of disordered
nonintegrable quantum systems.Comment: We trade the discussion of a diffusive integrable system in favor of
a discussion of diffusive nonintegrable system, which better highlights the
outcome of our wor
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Numerically exact quantum dynamics of low-dimensional lattice systems
In this thesis I present contributions to the development, analysis and application of tensor network state methods for numerically exact quantum dynamics in one and two-dimensional lattice systems. The setting of numerically exact quantum dynamics is introduced in Chapter 2. This includes a discussion of exact diagonalization approaches and massively parallel implementations thereof as well as a brief introduction of tensor network states.
In Chapter 3, I perform a detailed analysis of the performance of n-ary tree tensor network states for simulating the dynamics of two-dimensional lattices. This constitutes the first application of this class of tensor network to dynamics in two spatial dimensions, a long-standing challenge, and the method is found to perform on par with existing state-of-the-art approaches.
Chapter 4 showcases the efficacy of a novel tensor network format I developed, tailored to electron-phonon coupled problems in their single-electron sector, through an application to the Holstein model. The applicability of the approach to a broad range of parameters of the model allows to reveal the strong influence of the spread of the electron distribution on the initial state of the phonons at the site where the electron is introduced, for which a simple physical picture is offered. I depart from method development in Chapter 5 and analyse the prospects of using tensor network states evolved using the time-dependent variational principle as an approximate approach to determine asymptotic transport properties with a finite, moderate computational effort. The method is shown to not yield the correct asymptotics in a clean, non-integrable system and can thus not be expected to work in generic systems, outside of finely tuned parameter regimes of certain models.
Chapters 6 and 7 are concerned with studies of spin transport in long-range interacting systems using tensor network state methods. For the clean case, discussed in Chapter 6, we find that for sufficiently short-ranged interactions, the spreading of the bulk of the excitation is diffusive and thus dominated by the local part of the interaction, while the tail of the excitation decays with a powerlaw that is twice as large as the powerlaw of the interaction. Similarly, in the disordered case, analysed in Chapter 7, we find subdiffusive transport of spin and sub-linear growth of entanglement entropy. This behaviour is in agreement with the behaviour of systems with local interactions at intermediate disorder strength, but provides evidence against the phenomelogical Griffith picture of rare, strongly disordered insulating regions. We generalize the latter to long-ranged interactions and show that it predicts to diffusion, in contrast to the local case where it results in subdiffusive behaviour
Fragmented superconductivity in the Hubbard model as solitons in Ginzburg-Landau theory
The phenomena of superconductivity and charge density waves are observed in
close vicinity in many strongly correlated materials. Increasing evidence from
experiments and numerical simulations suggests both phenomena can also occur in
an intertwined manner, where the superconducting order parameter is coupled to
the electronic density. Employing density matrix renormalization group
simulations, we investigate the nature of such an intertwined state of matter
stabilized in the phase diagram of the elementary -- Hubbard
model in the strong coupling regime. Remarkably, the condensate of Cooper pairs
is shown to be fragmented in the presence of a charge density wave where more
than one pairing wave function is macroscopically occupied. Moreover, we
provide conclusive evidence that the macroscopic wave functions of the
superconducting fragments are well-described by soliton solutions of a
Ginzburg-Landau equation in a periodic potential constituted by the charge
density wave. In the presence of an orbital magnetic field, the order
parameters are gauge invariant, and superconducting vortices are pinned between
the stripes. This intertwined Ginzburg-Landau theory is proposed as an
effective low-energy description of the stripe fragmented superconductor.Comment: 12 pages, 9 figure
Phonon-induced disorder in dynamics of optically pumped metals from non-linear electron-phonon coupling
The non-equilibrium dynamics of matter excited by light may produce
electronic phases that do not exist in equilibrium, such as laser-induced
high- superconductivity. Here we simulate the dynamics of a metal driven
at by a pump that excites dipole-active vibrational modes that couple
quadratically to electrons, and study the evolution of its electronic and
vibrational observables. We provide evidence for enhancement of local
electronic correlations, including double occupancy, accompanied by rapid loss
of long-range spatial phase coherence. Concurrently, the onsite vibrational
reduced density matrix evolves from its initial coherent state to one with a
predominantly diagonal structure whose distribution qualitatively resembles the
coherent state Poisson character. This rapid loss of coherence controls the
electronic dynamics as the system evolves towards a correlated electron-phonon
long-time state. We show that a simple model based on an effective disorder
potential generated by the oscillator dephasing dynamics for the electrons
provides an explanation for the flattening in momentum of electronic
correlations. Our results provide a basis within which to understand
correlation dynamics of vibrationally coupled electrons in pump-probe
experiments.Comment: 7 pages main text + 3 pages appendices, 5 figures main text + 2
figures appendice
Non-equilibrium correlation dynamics in the one-dimensional Fermi-Hubbard model: A testbed for the two-particle reduced density matrix theory
We explore the non-equilibrium dynamics of a one-dimensional Fermi-Hubbard
system as a sensitive testbed for the capabilities of the time-dependent
two-particle reduced density matrix (TD2RDM) theory to accurately describe
time-dependent correlated systems. We follow the time evolution of the
out-of-equilibrium finite-size Fermi-Hubbard model initialized by a quench over
extended periods of time. By comparison with exact calculations for small
systems and with matrix product state (MPS) calculations for larger systems but
limited to short times, we demonstrate that the TD2RDM theory can accurately
account for the non-equilibrium dynamics in the regime from weak to moderately
strong inter-particle correlations. We find that the quality of the approximate
reconstruction of the three-particle cumulant (or correlation) required for the
closure of the equations of motion for the reduced density matrix is key to the
accuracy of the numerical TD2RDM results. We identify the size of the
dynamically induced three-particle correlations and the amplitude of cross
correlations between the two- and three-particle cumulants as critical
parameters that control the accuracy of the TD2RDM theory when current
state-of-the art reconstruction functionals are employed.Comment: 18 pages, 13 figure