We study interaction-driven ultrafast dynamics in finite graphene flakes following an optical pump quench in an interacting tight-binding model. By comparing exact real-time evolution with simulations restricted to particle-hole excitation subspaces, we assess when relaxation can be captured by low-order many-body processes and when this is not sufficient. The single-particle orbital entropy provides a compact diagnostic for dynamic correlation growth. For the systems studied here, periodic graphene flakes are well described by low-order excitations, whereas confined geometries require substantial higher-order contributions even for relatively small interaction strengths. The quench protocol combines simple initial-state preparation with strongly correlated dynamics, identifying a promising benchmark problem for future quantum-computing simulations.
We study interaction-driven ultrafast dynamics in finite graphene flakes following an optical pump quench in an interacting tight-binding model. By comparing exact real-time evolution with simulations restricted to particle-hole excitation subspaces, we assess when relaxation can be captured by low-order many-body processes and when this is not sufficient. The single-particle orbital entropy provides a compact diagnostic for dynamic correlation growth. For the systems studied here, periodic graphene flakes are well described by low-order excitations, whereas confined geometries require substantial higher-order contributions even for relatively small interaction strengths. The quench protocol combines simple initial-state preparation with strongly correlated dynamics, identifying a promising benchmark problem for future quantum-computing simulations.
The dynamics of out-of-time order correlators is studied in strongly correlated electron systems. This certain type of correlation function is a measure for the process of quantum information scrambling which is linked to the fundamental processes of entanglement growth and thermalization in quantum systems. Particularly interesting are quantum chaotic systems where the scrambling rate specifies the exponential growth of out-of-time order correlators. Whereas the scrambling rate is well defined theoretically, its interpretation in a physical context is still under debate. Furthermore, its role for physical effects and quantities which can be measured in experiments is little understood and deserves further investigation. In the first part of this work, scrambling rates are determined analytically and are analyzed for interacting electrons in graphene and electrons in a disordered metal coupled to a dissipative bath of phonons. A resemblance between the scrambling rate and the single-particle scattering rates is observed. In addition, a proposed link between quantum chaotic dynamics of out-of-time order correlators and the dynamics of fluctuations of observables is investigated. This principle could be used to determine scrambling rates in experiments. Subsequently, possible electron orders are investigated in the system of small-angle twisted-bilayer graphene in the second part of this work. Here, the interplay between the moiré interference pattern and the interlayer hybridization due to a finite interlayer tunneling of electrons causes the bandwidth of the so-called moiré bands to depend on the twist-angle. For twist-angles in the vicinity of the magic-angle, interaction effects are strongly enhanced and a series of strong correlation effects is expected. A minimal low-energy model of interacting electrons is derived where relevant electron-electron interaction processes are identified. This model is analyzed with respect to possible electronic ground states as a function of the twist-angle. A tendency towards a formation of nematic states is observed in a weak-coupling regime, whereas various Mott-insulating states are found for strong couplings.
We investigate the quantum Mpemba effect in a graphene nanotorus qubit and show that its strength depends strongly on how the initial state is prepared. We compare two protocols that share the same final Hamiltonian, thermal bath, and Markovian Liouvillian: bare Gibbs preparation, in which the coherent drive is switched on only at the final quench, and driven steady-state preparation, in which the initial states are stationary states of the driven dynamics. Using the distance to the final stationary state and an integrated Mpemba parameter, we find broad regions of strong anomalous relaxation for bare Gibbs preparation, with MB approaching unity, whereas the driven steady-state protocol almost completely suppresses the effect. A Liouvillian-mode analysis reveals the mechanism: the bare Gibbs protocol typically yields a smaller hot-state weight in the slow active sector than the cold state, Rs<1, while the driven steady-state protocol predominantly gives Rs>1. Since the final Liouvillian spectrum is identical for both protocols at corresponding parameter points, the contrast originates from preparation-dependent modal weights rather than from changes in the decay-rate hierarchy. These results identify state preparation as a control parameter for anomalous quantum relaxation in a curved graphene qubit.
We consider the dynamics of an impurity atom immersed in an ideal Fermi gas at zero temperature. We focus on the coherent quantum evolution of the impurity following a quench to strong impurity-fermion interactions, where the interactions are assumed to be short range like in cold-atom experiments. To approximately model the many-body time evolution, we use a truncated basis method, where at most two particle-hole excitations of the Fermi sea are included. When the system is initially noninteracting, we show that our method exactly captures the short-time dynamics following the quench, and we find that the overlap between initial and final states displays a universal nonanalytic dependence on time in this limit. We further demonstrate how our method can be used to compute the impurity spectral function, as well as describe many-body phenomena involving coupled impurity spin states, such as Rabi oscillations in a medium or highly engineered quantum quenches.
Correlated real-time dynamics in large, spatially inhomogeneous quantum systems remain difficult to access with nonequilibrium many-body methods. Two-time nonequilibrium Green functions (NEGF) retain dynamical correlations but their computational runtime grows cubically with the number of time steps Nt. This scaling bottleneck could recently be overcome by introducing the G1--G2 scheme that is linear in Nt, but requires propagation of a two-particle correlation function and may suffer from numerical instabilities. This has restricted simulations to small systems with Nb∼102 basis states. Here we introduce a quantum-fluctuation formulation of nonequilibrium Green functions, denoted δNEGF, that represents dynamical two-particle correlations through fluctuations of field-operator products, δG^. This guarantees stable dynamics by preserving the positivity of the reduced density matrices, avoids the explicit storage of the two-particle Green function, and reduces the propagation to a finite ensemble of Hartree-Fock-like trajectories. Combined with a stochastic low-rank decomposition of the correlation functions, the method retains time-linear scaling while extending dynamical GW and particle-particle and particle-hole T-matrix simulations to basis sizes of order Nb∼104. We benchmark δNEGF against exact and HF-GKBA results for lattice systems, finding stable correlated dynamics also at strong coupling. We further demonstrate large-scale simulations of diffusion in two-dimensional Hubbard lattices and ultrafast relaxation in graphene nanoribbon heterostructures with long-range Coulomb interactions. These results establish δNEGF as a scalable route to dynamical self-energy simulations of large, spatially inhomogeneous correlated quantum systems beyond the reach of existing NEGF implementations.
We investigate the nonequilibrium relaxation dynamics of the one-dimensional (1D) Fermi-Hubbard model subjected to abrupt, global interaction quenches. Specifically, we benchmark the convergence properties, structural accuracy, and algorithmic breakdown of the Magnus expansion against numerically exact results obtained via full Exact Diagonalization (ED) on small, periodic lattice clusters. By tracking the real-time evolution of local observables, double occupancy (doublon density), and many-body state fidelity metrics, we map out the validity bounds of the low-order Magnus series across weak, moderate, and strong interaction regimes. Our findings demonstrate that while the Magnus expansion provides an exceptionally accurate description of short-time coherent dynamics, rapid phase matching, and initial prethermalization tendencies, its convergence is fundamentally bottlenecked at longer timescales. This breakdown is driven by the rapid growth of multi-particle entanglement, non-local operator spreading via nested commutators, and the emergence of severe state-space fragmentation inherent to dense, strongly interacting many-body spectra.
Simulating quantum many-body systems is essential for understanding complex phenomena in condensed matter, chemistry, and materials science. Quantum computing offers a way to overcome the limitations of classical methods by operating directly in exponentially large Hilbert spaces. In particular, classical methods often fail to capture the dynamics of strongly correlated systems, which makes quantum algorithms a promising alternative for exploring these challenging regimes. This thesis uses quantum dynamics simulations to probe the behaviour of many-body systems. We first introduce a spectroscopy-based protocol to extract excitation spectra from the time evolution of observables and analyse its performance on near-term quantum devices. We show that the protocol requires only short evolution times and is resilient to errors, facilitating its implementation on real hardware. Building on this, we simulate fermionic excitation spectra using current quantum devices, introducing resource optimisations - including an approximate free-fermion initial state, a unitary quench without ancillae, and reduced Trotter steps - that significantly lower circuit depth. These improvements enable simulations at system sizes competitive with the state of the art, yielding results that match classical benchmarks. While most studies focus on unitary dynamics of isolated systems, open quantum dynamics is increasingly relevant for describing non-equilibrium processes across biology, materials science, and quantum control. We extend our scope to systems coupled to an environment and governed by Lindbladian evolution. By studying simulation complexity through physically meaningful quantities - such as correlation length and mixing time - we explore whether open-system dynamics can be as tractable as their unitary counterparts. These findings provide insights into the computational complexity landscape of open-system simulation and highlight regimes where quantum methods offer a clear advantage.