Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSecond Renormalization of Tensor-Network States
177
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We propose a second renormalization group method to handle the tensor-network states or models. This method reduces dramatically the truncation error of the tensor renormalization group. It allows physical quantities of classical tensor-network models or tensor-network ground states of quantum systems to be accurately and efficiently determined.
rate research
Read More
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 renormalization group and the other based on the higher-order tensor renormalization group, are introduced. In order to optimize the tensor-network model globally, a sweeping scheme is proposed to account for the renormalization effect from the environment tensors under the framework of second renormalization group. We demonstrate the algorithms by the classical Ising model on the square lattice and the Kitaev model on the honeycomb lattice, and show that the finite-size algorithms achieve substantially more accurate results than the corresponding infinite-size ones.
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 renormalization group method which can be used straightforwardly on modern computing architectures. We demonstrate the efficiency of the technique and show that Monte Carlo tensor network renormalization provides an attractive path to improving the accuracy of a wide class of challenging computations while also providing useful estimates of uncertainty and a statistical guarantee of unbiased results.
We have proposed a novel numerical method to calculate accurately the physical quantities of the ground state with the tensor-network wave function in two dimensions. We determine the tensor network wavefunction by a projection approach which applies iteratively the Trotter-Suzuki decomposition of the projection operator and the singular value decomposition of matrix. The norm of the wavefunction and the expectation value of a physical observable are evaluated by a coarse grain renormalization group approach. Our method allows a tensor-network wavefunction with a high bond degree of freedom (such as D=8) to be handled accurately and efficiently in the thermodynamic limit. For the Heisenberg model on a honeycomb lattice, our results for the ground state energy and the staggered magnetization agree well with those obtained by the quantum Monte Carlo and other approaches.
We show that the formalism of tensor-network states, such as the matrix product states (MPS), can be used as a basis for variational quantum Monte Carlo simulations. Using a stochastic optimization method, we demonstrate the potential of this approach by explicit MPS calculations for the transverse Ising chain with up to N=256 spins at criticality, using periodic boundary conditions and D*D matrices with D up to 48. The computational cost of our scheme formally scales as ND^3, whereas standard MPS approaches and the related density matrix renromalization group method scale as ND^5 and ND^6, respectively, for periodic systems.
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 classical many-body system or the Euclidean path integral of a 1D quantum system can be represented as a network of tensors, before describing how TNR can be implemented to efficiently contract the network via a sequence of coarse-graining transformations. The efficacy of the TNR approach is then benchmarked for the 2D classical statistical and 1D quantum Ising models; in particular the ability of TNR to maintain a high level of accuracy over sustained coarse-graining transformations, even at a critical point, is demonstrated.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
