Related papers: Second Renormalization of Tensor-Network States
We have discussed the tensor-network representation of classical statistical or interacting quantum lattice models, and given a comprehensive introduction to the numerical methods we recently proposed for studying the tensor-network…
The higher-order tensor renormalization group is a tensor-network method providing estimates for the partition function and thermodynamical observables of classical and quantum systems in thermal equilibrium. At every step of the iterative…
We discuss in detail algorithms for implementing tensor network renormalization (TNR) for the study of classical statistical and quantum many-body systems. Firstly, we recall established techniques for how the partition function of a 2D…
We introduce a tensor renormalization group scheme for coarse-graining a two-dimensional tensor network that can be successfully applied to both classical and quantum systems on and off criticality. The key innovation in our scheme is to…
Exact many-body quantum problems are known to be computationally hard due to the exponential scaling of the numerical resources required. Since the advent of the Density Matrix Renormalization Group, it became clear that a successful…
Techniques for approximately contracting tensor networks are limited in how efficiently they can make use of parallel computing resources. In this work we demonstrate and characterize a Monte Carlo approach to the tensor network…
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…
The tensor-entanglement renormalization group approach is applied to Hamiltonians that realize a class of topologically ordered states -- string-net condensed states. We analyze phase transitions between phases with and without string-net…
We propose a new tensor network renormalization group (TNR) scheme based on global optimization and introduce a new method for constructing the finite-temperature density matrix of two-dimensional quantum systems. Combining these two into a…
We present a new strategy for contracting tensor networks in arbitrary geometries. This method is designed to follow as strictly as possible the renormalization group philosophy, by first contracting tensors in an exact way and, then,…
We investigate tree tensor network states for quantum chemistry. Tree tensor network states represent one of the simplest generalizations of matrix product states and the density matrix renormalization group. While matrix product states…
We propose a real-space renormalization group algorithm for accurately coarse-graining two-dimensional tensor networks. The central innovation of our method lies in utilizing variational boundary tensors as a globally optimized environment…
We describe a simple real space renormalization group technique for two dimensional classical lattice models. The approach is similar in spirit to block spin methods, but at the same time it is fundamentally based on the theory of quantum…
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…
We introduce a coarse-graining transformation for tensor networks that can be applied to study both the partition function of a classical statistical system and the Euclidean path integral of a quantum many-body system. The scheme is based…
We present applications of the renormalization algorithm with graph enhancement (RAGE). This analysis extends the algorithms and applications given for approaches based on matrix product states introduced in [Phys. Rev. A 79, 022317 (2009)]…
We review recent developments in tensor network approaches, focusing on renormalization group methods. Since they are free from the negative sign and complex action problems, there is growing interest in their application to lattice field…
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 discuss a renormalization procedure for random tensor networks, and show that the corresponding renormalization-group flow is given by the Hamiltonian vector flow of the canonical tensor model, which is a discretized model of quantum…
We propose a hybrid quantum-classical algorithm for approximating the ground state of two-dimensional quantum systems using an isometric tensor network ansatz, which maps naturally to quantum circuits. Inspired by the density matrix…