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We use our recently developed functional renormalization group (FRG) approach for quantum spin systems to investigate the phase diagram of the frustrated $J_{1}J_{2}J_{3}$ quantum Heisenberg model on a cubic lattice. From a simple…
We introduce a method that ensures efficient computation of one-dimensional quantum systems with long-range interactions across all temperatures. Our algorithm operates within a quasi-polynomial runtime for inverse temperatures up to…
We develop high temperature series expansions for $\ln{Z}$ and the uniform structure factor of the spin-half Heisenberg model on the hyperkagome lattice to order $\beta^{16}$. These expansions are used to calculate the uniform…
We develop a numerical method based on matrix product states for simulating quantum many-body systems at finite temperatures without importance sampling and evaluate its performance in spin 1/2 systems. Our method is an extension of the…
We present results of numerical simulations performed on one-dimensional spin chains in order to extract the so-called relaxation rate $1/T_1$ accessible through NMR experiments. Building on numerical tensor network methods using the Matrix…
We present a hybrid numerical approach to simulate quantum many body problems on two spatial dimensional quantum lattice models via the non-Abelian ab initio version of the density matrix renormalization group method on state-of-the-art…
We discuss a few simple modifications to time-dependent density matrix renormalization group (DMRG) algorithms which allow to access larger time scales. We specifically aim at beginners and present practical aspects of how to implement…
Tensor-network methods are used to perform a comparative study of the two-dimensional classical Heisenberg and $\mathrm{RP}^2$ models. We demonstrate that uniform matrix product states (MPS) with explicit $\mathrm{SO}(3)$ symmetry can probe…
Accessing the thermodynamic-limit properties of strongly correlated quantum matter requires simulations on very large lattices, a regime that remains challenging for numerical methods, especially in frustrated two-dimensional systems. We…
We formulate a real-space renormalization group (RG) approach for efficient numerical analysis of the low-temperature hopping dynamics in energy-disordered lattices. The approach explicitly relies on the time-scale separation of the…
As inverter-based resources (IBRs) penetrate power systems, the dynamics become more complex, exhibiting multiple timescales, including electromagnetic transient (EMT) dynamics of power electronic controllers and electromechanical dynamics…
We perform quantum simulation on classical and quantum computers and set up a machine learning framework in which we can map out phase diagrams of known and unknown quantum many-body systems in an unsupervised fashion. The classical…
Google's Tensor Processing Units (TPUs) are integrated circuits specifically built to accelerate and scale up machine learning workloads. They can perform fast distributed matrix multiplications and therefore be repurposed for other…
This thesis develops advanced Tensor Network (TN) methods to address Hamiltonian Lattice Gauge Theories (LGTs), overcoming limitations in real-time dynamics and finite-density regimes. A novel dressed-site formalism is introduced, enabling…
We investigate the application of tensor-train (TT) algorithms to multigroup thermal radiation transport (i.e., photon radiation transport). The TT framework enables simulations at discretizations that might otherwise be computationally…
We introduce a novel tensor network structure augmenting the well-established Tree Tensor Network representation of a quantum many-body wave function. The new structure satisfies the area law in high dimensions remaining efficiently…
We develop an alternative time-dependent numerical renormalization group (TDNRG) formalism for multiple quenches and implement it to study the response of a quantum impurity system to a general pulse. Within this approach, we reduce the…
Constructing quantum Hamiltonians for simulating and controlling the exotic physics of many-body systems belongs to the most important topics of condensed matter physics and quantum technologies. The main challenge that hinders the future…
We consider quantum Heisenberg ferro- and antiferromagnets on the square lattice with exchange anisotropy of easy-plane or easy-axis type. The thermodynamics and the critical behaviour of the models are studied by the pure-quantum…
Thermodynamic properties of the one-dimensional Kondo lattice model at half-filling are studied by the density matrix renormalization group method applied to the quantum transfer matrix. Spin susceptibility, charge susceptibility, and…