Related papers: Study of multi-particle states with tensor renorma…
A tensor network renormalization algorithm with global optimization based on the corner transfer matrix is proposed. Since the environment is updated by the corner transfer matrix renormalization group method, the forward-backward iteration…
We investigate the metal-insulator transition of the (1+1)-dimensional Hubbard model in the path-integral formalism with the tensor renormalization group method. The critical chemical potential $\mu_{\rm c}$ and the critical exponent $\nu$…
The particle-hole version of the density-matrix renormalization-group method (PH-DMRG) is utilized to calculate the ground-state energy of an interacting two-dimensional quantum dot. We show that a modification of the method, termed…
We perform a quantum simulation of the Ising model with a transverse field using a collection of three trapped atomic ion spins. By adiabatically manipulating the Hamiltonian, we directly probe the ground state for a wide range of fields…
The outcomes of projective measurements on a quantum many-body system in a chosen basis are inherently probabilistic. The Shannon entropy of this probability distribution (the "diagonal entropy") often reveals universal features, such as…
We propose a method to compute the entanglement entropy (EE) using the tensor renormalization group (TRG) method. The reduced density matrix of a $d$-dimensional quantum system is represented as a $(d+1)$-dimensional tensor network. We…
We present a renormalization group (RG) procedure which works naturally on a wide class of interacting one-dimension models based on perturbed (possibly strongly) continuum conformal and integrable models. This procedure integrates Kenneth…
We analyze the Ising model on a random surface with a boundary magnetic field using matrix model techniques. We are able to exactly calculate the disk amplitude, boundary magnetization and bulk magnetization in the presence of a boundary…
We apply both a scalar field theory and a recently developed transfer-matrix method to study the stationary properties of metastability in a two-state model with weak, long-range interactions: the $N$$\times$$\infty$ quasi-one-dimensional…
The transverse-field Ising model on the Sierpi\'nski fractal, which is characterized by the fractal dimension $\log_2^{~} 3 \approx 1.585$, is studied by a tensor-network method, the Higher-Order Tensor Renormalization Group. We analyze the…
A prerequisite to the successful development of quantum computers and simulators is precise understanding of physical processes occurring therein, which can be achieved by measuring the quantum states they produce. However, the resources…
We present our progress on a study of the $O(3)$ model in two-dimensions using the Tensor Renormalization Group method. We first construct the theory in terms of tensors, and show how to construct $n$-point correlation functions. We then…
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…
The two- and three-dimensional transverse-field Ising models with ferromagnetic exchange interactions are analyzed by means of the real-space renormalization group method. The basic strategy is a generalization of a method developed for the…
Tensor network states provide an efficient class of states that faithfully capture strongly correlated quantum models and systems in classical statistical mechanics. While tensor networks can now be seen as becoming standard tools in the…
Diagrammatic summation is a common bottleneck in modern applications of projected entangled-pair states, especially in computing low-energy excitations of a two-dimensional quantum many-body system. To solve this problem, here we extend the…
We study the tomography of multispin quantum states in the context of finite-dimensional Wigner representations. An arbitrary operator can be completely characterized and visualized using multiple shapes assembled from linear combinations…
It has proved difficult to extend the density matrix renormalization group technique to large two-dimensional systems. In this Communication I present a novel approach where the calculation is done directly in two dimensions. This makes it…
Using eigen-functional bosonization method, we study quantum many-particle systems, and show that the quantum many-particle problems end in to solve the differential equation of the phase fields which represent the particle correlation…
We propose a symmetric version of the multi-scale entanglement renormalization Ansatz (MERA) in two spatial dimensions (2D) and use this Ansatz to find an unknown ground state of a 2D quantum system. Results in the simple 2D quantum Ising…