Related papers: Tensor Product Variational Formulation for Quantum…
The investigation of the behavior of both classical and quantum systems on non-Euclidean surfaces near the phase transition point represents an interesting research area of modern physics. In the case of classical spin systems, a…
We present for the first time time-dependent density-matrix renormalization-group simulations (t-DMRG) at finite temperatures. It is demonstrated how a combination of finite-temperature t-DMRG and time-series prediction allows for an easy…
Configuration-interaction-type calculations on electronic and vibrational structure are often the method of choice for the reliable approximation of many-particle wave functions and energies. The exponential scaling, however, limits their…
We develop a variational framework for addressing two-dimensional non-integrable quantum field theories through the exact structure of their integrable counterparts. Concentrating on the $\varphi^4$ Landau-Ginzburg model, we use the…
We introduce a unified formulation of variational methods for simulating ground state properties of quantum many-body systems. The key feature is a novel variational method over quantum circuits via infinitesimal unitary transformations,…
The Variational Method is applied within the context of Supersymmetric Quantum Mechanics to provide information about the energy states of a hydrogenic donor in a quantum dot.
This paper provides a study and discussion of earlier as well as novel more efficient schemes for the precise evaluation of finite-temperature response functions of strongly correlated quantum systems in the framework of the time-dependent…
We present a new algorithm to calculate the thermodynamic quantities of three-dimensional (3D) classical statistical systems, based on the ideas of the tensor product state and the density matrix renormalization group. We represent the…
The possibility to simulate the properties of many-body open quantum systems with a large number of degrees of freedom is the premise to the solution of several outstanding problems in quantum science and quantum information. The challenge…
We report a real-space renormalization group (RSRG) algorithm, which is formulated through Baxter's corner transfer matrix (CTM), for two-dimensional (d = 2) classical lattice models. The new method performs the renormalization group…
The density matrix renormalization group method is generalized to one dimensional random systems. Using this method, the energy gap distribution of the spin-1/2 random antiferromagnetic Heisenberg chain is calculated. The results are…
Tensor networks (TNs) have become one of the most essential building blocks for various fields of theoretical physics such as condensed matter theory, statistical mechanics, quantum information, and quantum gravity. This review provides a…
Variational algorithms are promising candidates to be implemented on near-term quantum computers. The variational quantum eigensolver (VQE) is a prominent example, where a parametrized trial state of the quantum mechanical wave function is…
We discuss the variational optimization of a unitary tensor-network circuit with different network structures. The ansatz is performed based on a generalization of well-developed multi-scale entanglement renormalization algorithm and also…
Wilson's numerical renormalization group (NRG) method for solving quantum impurity models yields a set of energy eigenstates that have the form of matrix product states (MPS). White's density matrix renormalization group (DMRG) for treating…
Just as matrix product states represent ground states of one-dimensional quantum spin systems faithfully, continuous matrix product states (cMPS) provide faithful representations of the vacuum of interacting field theories in one spatial…
This thesis gives an extension for the Density Matrix Renormalisation Group (DMRG) to two dimensions and described a newly developed combination of the DMRG and a Green Function Monte Carlo simulation (GFMC). The first two chapters focus on…
Given in the title are two algorithms to compute the extreme eigenstate of a high-dimensional Hermitian matrix using the tensor train (TT) / matrix product states (MPS) representation. Both methods empower the traditional alternating…
The Density Matrix Renormalization Group (DMRG) method scales exponentially in the system width for models in two dimensions, but remains one of the most powerful methods for studying 2D systems with a sign problem. Reviewing past…
Fabrication process variations can significantly influence the performance and yield of nano-scale electronic and photonic circuits. Stochastic spectral methods have achieved great success in quantifying the impact of process variations,…