Related papers: Efficient tensor network algorithm for layered sys…
An infinite projected entangled pair state (iPEPS) is a tensor network ansatz to represent a quantum state on an infinite 2D lattice whose accuracy is controlled by the bond dimension $D$. Its real, Lindbladian or imaginary time evolution…
We propose the entanglement bipartitioning approach to design an optimal network structure of the tree-tensor-network (TTN) for quantum many-body systems. Given an exact ground-state wavefunction, we perform sequential bipartitioning of…
We describe a practical and efficient approach to represent physically realistic long-range interactions in two-dimensional tensor network algorithms via projected entangled-pair operators (PEPOs). We express the long-range interaction as a…
Extracting momentum-resolved excitation spectra in strongly correlated quantum systems remains a major challenge, especially beyond one spatial dimension. We present an efficient tensor-network approach to compute dispersion relations via…
In this study, we introduce a novel family of tensor networks, termed constrained matrix product states (MPS), designed to incorporate exactly arbitrary discrete linear constraints, including inequalities, into sparse block structures.…
In this article we present analytical results on the exact tensor network representations and correlation functions of the first examples of 2D ground states with quantum phase transitions between area law and extensive entanglement…
In this paper we propose a special type of a tree tensor network that has the geometry of a comb---a 1D backbone with finite 1D teeth projecting out from it. This tensor network is designed to provide an effective description of higher…
This thesis is divided into two mainly independent parts: In the first part, we derive a criterion to determine when a translationally invariant Matrix Product State (MPS) has long range localizable entanglement, which indicates that the…
Tensor network states (TNS) are a promising but numerically challenging tool for simulating two-dimensional (2D) quantum many-body problems. We introduce an isometric restriction of the TNS ansatz that allows for highly efficient…
Two dimensional tensor networks such as projected entangled pairs states (PEPS) are generally hard to contract. This is arguably the main reason why variational tensor network methods in 2D are still not as successful as in 1D. However,…
We implement and benchmark tensor network algorithms with $SU(2)$ symmetry for systems in two spatial dimensions and in the thermodynamic limit. Specifically, we implement $SU(2)$-invariant versions of the infinite Projected Entangled Pair…
We introduce a tensor network algorithm for the solution of $p$-spin models. We show that bond compression through rank-revealing decompositions performed during the tensor network contraction resolves logical redundancies in the system…
Compressive lensless imagers enable novel applications in an extremely compact device, requiring only a phase or amplitude mask placed close to the sensor. They have been demonstrated for 2D and 3D microscopy, single-shot video, and…
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…
Originating in quantum physics, tensor networks (TNs) have been widely adopted as exponential machines and parameter decomposers for recognition tasks. Typical TN models, such as Matrix Product States (MPS), have not yet achieved successful…
This work introduces SpinGlassPEPS$.$jl, a software package implemented in Julia, designed to find low-energy configurations of generalized Potts models, including Ising and QUBO problems, utilizing heuristic tensor network contraction…
Matrix product states (MPS) and matrix product operators (MPOs) are one dimensional tensor networks that underlie the modern density matrix renormalization group (DMRG) algorithm. The use of MPOs accounts for the high level of generality…
In this paper we explore the practical use of the corner transfer matrix and its higher-dimensional generalization, the corner tensor, to develop tensor network algorithms for the classical simulation of quantum lattice systems of infinite…
The tensor network algorithm, a family of prevalent numerical methods for quantum many-body problems, aptly captures the entanglement properties intrinsic to quantum systems, enabling precise representation of quantum states. However, its…
This brief review introduces the reader to tensor network methods, a powerful theoretical and numerical paradigm spawning from condensed matter physics and quantum information science and increasingly exploited in different fields of…