相关论文: Tensor renormalization group analysis of ${\rm CP}…
We investigate the two-dimensional lattice U(1) gauge-Higgs model with a topological term, employing L\"uscher's admissibility condition. The standard Monte Carlo simulation for this model is hindered not only by the complex action problem…
A $\theta$ term, which couples to topological charge, is added to the lattice $CP^{N-1}$ model. The strong-coupling character expansion is developed. The series for the free energy and mass gap are respectively computed to tenth order and…
We perform a tensor renormalization group simulation of non-Abelian gauge theory in three dimensions using a formulation based on the `armillary sphere.' In this formulation, matrix indices are completely traced out, eliminating the…
The tensor renormalization group method is a promising approach to lattice field theories, which is free from the sign problem unlike standard Monte Carlo methods. One of the remaining issues is the application to gauge theories, which is…
Tensor renormalization group, originally devised as a numerical technique, is emerging as a rigorous analytical framework for studying lattice models in statistical physics. Here we introduce a new renormalization map - the 2x1 map - which…
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 tensor-network renormalization group (TNRG) is an accurate numerical real-space renormalization group method for studying phase transitions in both quantum and classical systems. Continuous phase transitions, as an important class of…
We perform a tensor network simulation of the (1+1)-dimensional $O(3)$ nonlinear $\sigma$-model with $\theta=\pi$ term. Within the Hamiltonian formulation, this field theory emerges as the finite-temperature partition function of a modified…
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…
We study the recovery of the underlying graphs or permutations for tensors in the tensor ring or tensor train format. Our proposed algorithms compare the matricization ranks after down-sampling, whose complexity is $O(d\log d)$ for $d$-th…
We study the ultraviolet properties of the supersymmetric CP^{N-1} sigma model in three dimensions to next-to-leading order in the 1/N expansion. We calculate the \beta-function to this order and verify that it has no next-to-leading order…
We develop a new methodology to contract tensor networks within the corner transfer matrix renormalization group approach for a wide range of two-dimensional lattice geometries. We discuss contraction algorithms on the example of…
We present a real-space renormalization group transformation with continuous scale change to calculate the continuous renormalization group $\beta$ function in non-perturbative lattice simulations. Our method is motivated by the connection…
We study fixed points of the easy-plane $\mathbb{CP}^{N-1}$ field theory by combining quantum Monte Carlo simulations of lattice models of easy-plane SU($N$) superfluids with field theoretic renormalization group calculations, by using…
A Gibbs operator $e^{-\beta H}$ for a 2D lattice system with a Hamiltonian $H$ can be represented by a 3D tensor network, the third dimension being the imaginary time (inverse temperature) $\beta$. Coarse-graining the network along $\beta$…
We present a tree-tensor-network-based method to study strongly correlated systems with nonlocal interactions in higher dimensions. Although the momentum-space and quantum-chemistry versions of the density matrix renormalization group…
The renormalization of the topological term in the two-dimensional nonlinear O(3) model is studied by means of the Functional Renormalization Group. By considering the topological charge as a limit of a more general operator, it is shown…
We investigate the $\theta$-dependence of 2-dimensional $CP^{N-1}$ models in the large-$N$ limit by lattice simulations. Thanks to a recent algorithm proposed by M. Hasenbusch to improve the critical slowing down of topological modes,…
We investigate the phase structure of the (1+1)-dimensional U(1) gauge-Higgs model with a $\theta$ term, where the U(1) gauge action is constructed with L\"uscher's admissibility condition. Using the tensor renormalization group, both the…
We prove that the rank 3 analogue of the tensor model defined in [arXiv:1111.4997 [hep-th]] is renormalizable at all orders of perturbation. The proof is given in the momentum space. The one-loop $\gamma$- and $\beta$-functions of the model…