Related papers: Tensor network formulation of the massless Schwing…
We study fermionic matrix product operator algebras and identify the associated algebraic data. Using this algebraic data we construct fermionic tensor network states in two dimensions that have non-trivial symmetry-protected or intrinsic…
A general framework is proposed to solve the two-dimensional fully frustrated XY model for the Josephson junction arrays in a perpendicular magnetic field. The essential idea is to encode the ground-state local rules induced by frustrations…
Tensor networks provide a natural language for non-invertible symmetries in general Hamiltonian lattice models. We use ZX-diagrams, which are tensor network presentations of quantum circuits, to define a non-invertible operator implementing…
Tensor network (TN) methods are well established for computing partition functions in statistical mechanics, though this use has traditionally been limited to lattice models. We extend the scope of TN methodology to interacting particle…
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…
The tensor renormalization group attracts great attention as a new numerical method that is free of the sign problem. In addition to this striking feature, it also has an attractive aspect as a coarse-graining of space-time; the…
Tensor network states are powerful variational ans\"atze for many-body ground states of quantum lattice models. The use of Monte Carlo sampling techniques in tensor network approaches significantly reduces the cost of tensor contractions,…
Tensor networks are a powerful tool to simulate a variety of different physical models, including those that suffer from the sign problem in Monte Carlo simulations. The Hubbard model on the honeycomb lattice with non-zero chemical…
We present a new tensor network algorithm for calculating the partition function of interacting quantum field theories in 2 dimensions. It is based on the Tensor Renormalization Group (TRG) protocol, adapted to operate entirely at the level…
We apply the higher-order tensor renormalization group to the lattice CP($N-1$) model in two dimensions. A tensor network representation of the CP($N-1$) model in the presence of the $\theta$ term is derived. We confirm that the numerical…
We apply a series of projection techniques on top of tensor networks to compute energies of ground state wave functions with higher accuracy than tensor networks alone with minimal additional cost. We consider both matrix product states as…
Tensor Network States are ans\"atze for the efficient description of quantum many-body systems. Their success for one dimensional problems, together with the fact that they do not suffer from the sign problem and can address the simulation…
We study the XXZ Heisenberg model in a staggered magnetic field using the HOTRG tensor renormalization method. Built into the tensor representation of the XXZ model is the U(1) symmetry, which is systematically maintained at each…
We compute the $\theta$-dependent mass spectrum of the 2-flavor Schwingr model using the tensor network (DMRG) in the Hamiltonian formalism. The pion and the sigma meson are identified as stable particles of the model for nonzero $\theta$…
We discuss how to formulate lattice gauge theories in the Tensor Network language. In this way we obtain both a consistent truncation scheme of the Kogut-Susskind lattice gauge theories and a Tensor Network variational ansatz for gauge…
The evaluation of partition functions is a central problem in statistical physics. For lattice systems and other discrete models the partition function may be expressed as the contraction of a tensor network. Unfortunately computing such…
We determine the mass gap of a two-dimensional $O(3)$ nonlinear sigma model augmented with a topological $\theta$-term using tensor network and digital quantum algorithms. As proof of principle, we consider the example $\theta = \pi$ and…
We investigate the phase transition of the four-dimensional Ising model with two types of tensor network scheme, one is the higher-order tensor renormalization group and the other is the anisotropic tensor renormalization group. The results…
We introduce a novel tensor network structure augmenting the well-established Tree Tensor Network representation of a quantum many-body wave function. The new structure satisfies the area law in high dimensions remaining efficiently…
We derive a general formula of the tensor network representation for $d$-dimensional lattice fermions with ultra-local interactions, including Wilson fermions, staggered fermions, and domain-wall fermions. The Grassmann tensor is concretely…