Related papers: Tensor Networks Can Resolve Fermi Surfaces

We show that two different tensors defining the same translational invariant injective Projected Entangled Pair State (PEPS) in a square lattice must be the same up to a trivial gauge freedom. This allows us to characterize the existence of…

Matrix product states (MPS) illustrate the suitability of tensor networks for the description of interacting many-body systems: ground states of gapped $1$-D systems are approximable by MPS as shown by Hastings [J. Stat. Mech. Theor. Exp.,…

Here we show how the Minimally Entangled States (MES) of a 2d system with topological order can be identified using the geometric measure of entanglement. We show this by minimizing this measure for the doubled semion, doubled Fibonacci and…

Determination and characterization of criticality in two-dimensional (2D) quantum many-body systems belong to the most important challenges and problems of quantum physics. In this paper we propose an efficient scheme to solve this problem…

We study the nature of the ground state of the frustrated J1-J2 model and the J1-J3 model using a variational algorithm based on projected entangled-pair states (PEPS). By investigating spin-spin correlation functions, we observe a…

We present an approach to identify topological order based on unbiased infinite projected entangled-pair states (iPEPS) simulations, i.e. where we do not impose a virtual symmetry on the tensors during the optimization of the tensor network…

We describe our implementation of fermionic tensor network contraction on arbitrary lattices within both a globally ordered and locally ordered formalism. We provide a pedagogical description of these two conventions as implemented for the…

We propose a flexible numerical framework for extracting the energy spectra and photon transfer dynamics of a unit kagome cell with disordered cavity-cavity couplings under realistic experimental conditions. A projected-entangled pair state…

Projected entangled pair states (PEPS) provide a natural ansatz for the ground states of gapped, local Hamiltonians in which global characteristics of a quantum state are encoded in properties of local tensors. We develop a framework to…

Extending corresponding results for matrix product states [Verstraete and Cirac, PRB 73, 094423 (2006); Schuch et al. PRL 100, 030504 (2008)], it is shown how the approximation error of tree tensor network states (TTNS) can be bounded using…

We provide a generalisation of the matrix product operator (MPO) formalism for string-net projected entangled pair states (PEPS) to include non-unitary solutions of the pentagon equation. These states provide the explicit lattice…

We investigate quantum random tensor network states where the bond dimensions scale polynomially with the system size, $N$. Specifically, we examine the delocalization properties of random Matrix Product States (RMPS) in the computational…

We construct a family of simple fermionic projected entangled pair states (fPEPS) on the square lattice with bond dimension $D=3$ which are exactly hole-doped resonating valence bond (RVB) wavefunctions with short-range singlet bonds. Under…

We present a 2D bosonization duality using the language of tensor networks. Specifically, we construct a tensor network operator (TNO) that implements an exact 2D bosonization duality. The primary benefit of the TNO is that it allows for…

We study the realization of anyon-permuting symmetries of topological phases on the lattice using tensor networks. Working on the virtual level of a projected entangled pair state, we find matrix product operators (MPOs) that realize all…

Projected wave functions offer a means for incorporating local correlation effects in gapless electronic phases of matter like metals. Although such wave functions can be readily specified formally, it is challenging to compute their…

Properties of confined mesoscopic systems have been extensively studied numerically over recent years. We discuss an analytical approach to the study of finite rotating fermionic systems in two dimension. We first construct the energy…

We propose an improved approach to carry out the imaginary time evolution of infinite projected entangled-pair states (iPEPS), especially for systems with criticality. A cyclic optimal truncation is introduced to update the tensors along a…

These are lecture notes from the 44th IFF Spring School "Quantum Information Processing" in Juelich, discussing applications of entanglement theory in condensed matter. The focus of the notes is on tensor network states, in particular…

Using correlated photons from parametric downconversion, we extend the boundaries of experimentally accessible two-qubit Hilbert space. Specifically, we have created and characterized maximally entangled mixed states (MEMS) that lie above…