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A modified density matrix renormalization group (DMRG) algorithm is applied to the zigzag spin-1/2 chain with frustrated antiferromagnetic exchange $J_1$, $J_2$ between first and second neighbors. The modified algorithm yields accurate…

The density matrix renormalization group (DMRG) is a numerical method that optimizes a variational state expressed by a tensor product. We show that the ground state is not fully optimized as far as we use the standard finite system…

We study the continuous phase transition and thermodynamic observables in the three-dimensional Euclidean $SU(2)$ principal chiral field model with the triad tensor renormalization group (tTRG) and the anisotropic tensor renormalization…

The widely used density matrix renormalization group (DRMG) method often fails to converge in systems with multiple length scales, such as lattice discretizations of continuum models and dilute or weakly doped lattice models. The local…

A renormalization group (RG) analysis of the superconductive instability of an anisotropic fermionic system is developed at a finite temperature. The method appears a natural generalization of Shankar's approach to interacting fermions and…

Tensor networks have proven to be a valuable tool, for instance, in the classical simulation of (strongly correlated) quantum systems. As the size of the systems increases, contracting larger tensor networks becomes computationally…

In this thesis, we present a novel method combining energy-based finite-size scaling with tensor network renormalization (TNR) to study phase transitions in lattice models. This approach effectively calculates running coupling constants and…

Tensor renormalization group (TRG) constitutes an important methodology for accurate simulations of strongly correlated lattice models. Facilitated by the automatic differentiation technique widely used in deep learning, we propose a…

We develop coarse-graining tensor renormalization group algorithms to compute physical properties of two-dimensional lattice models on finite periodic lattices. Two different coarse-graining strategies, one based on the tensor…

Many recent tensor network algorithms apply unitary operators to parts of a tensor network in order to reduce entanglement. However, many of the previously used iterative algorithms to minimize entanglement can be slow. We introduce an…

We introduce a family of numerical algorithms for the solution of linear system in higher dimensions with the matrix and right hand side given and the solution sought in the tensor train format. The proposed methods are rank--adaptive and…

In this work we apply two different real-space renormalization-group (RSRG) approaches to the anisotropic antiferromagnetic spin-1/2 Heisenberg model on the square lattice. Our calculations allow for an approximate evaluation of the $T$ vs.…

Tensor renormalization group method (TRG) is a real space renormalization group approach. It has been successfully applied to both classical and quantum systems. In this paper, we study a disordered and frustrated system, the…

The renormalization group equations describing a finite 2DXY system with fourfold anisotropy are solved in two steps, in order to study the magnetic transition to paramagnetism in an ultrathin film. First, the equations are linearized near…

We present a method for computing resonant inelastic x-ray scattering (RIXS) spectra in one-dimensional systems using the density matrix renormalization group (DMRG) method. By using DMRG to address the problem, we shift the computational…

Tensor decomposition is a fundamental method used in various areas to deal with high-dimensional data. \emph{Tensor power method} (TPM) is one of the widely-used techniques in the decomposition of tensors. This paper presents a novel tensor…

Tensor rematerialization allows the training of deep neural networks (DNNs) under limited memory budgets by checkpointing the models and recomputing the evicted tensors as needed. However, the existing tensor rematerialization techniques…

Variational tensor network optimization has become a powerful tool for studying classical statistical models in two dimensions. However, its application to three-dimensional systems remains limited, primarily due to the high computational…

We present two new analytic formulations of the Density Matrix Renormalization Group Method. In these formulations we combine the block renormalization group (BRG) procedure with Variational and Fokker-Planck methods. The BRG method is used…

We present an efficient implementation of the Density Matrix Renormalization Group (DMRG) algorithm that includes an optimal ordering of the proton and neutron orbitals and an efficient expansion of the active space utilizing various…