Related papers: Unified tensor network theory for frustrated class…
The strongly correlated fermions play a vital role in modern physics. For a given fermionic Hamiltonian system, the most widely used approach to explore the underlying physics is to study the wave function that incorporates Fermi-Dirac…
Diagrammatic summation is a common bottleneck in modern applications of projected entangled-pair states, especially in computing low-energy excitations of a two-dimensional quantum many-body system. To solve this problem, here we extend the…
We propose a novel algorithm with a modified Tucker decomposition for tensor network that allows for efficiently and precisely calculating the ground state and thermodynamic properties of two-dimensional (2D) quantum spin lattice systems,…
An efficient algorithm is constructed for contracting two-dimensional tensor networks under periodic boundary conditions. The central ingredient is a novel renormalization step that scales linearly with system size, i.e. from $L \to L+1$.…
We investigate the finite-temperature phase diagram of the classical $J_1$-$J_2$ XY model on a square lattice using a tensor network approach designed for frustrated spin systems. This model, characterized by competing nearest-neighbor and…
We show that ground states of unfrustrated quantum spin-1/2 systems on general lattices satisfy an entanglement area law, provided that the Hamiltonian can be decomposed into nearest-neighbor interaction terms which have entangled excited…
We show how to efficiently simulate a quantum many-body system with tree structure when its entanglement is bounded for any bipartite split along an edge of the tree. This is achieved by expanding the {\em time-evolving block decimation}…
Geometric frustration emerges when local interaction energies in an ordered lattice structure cannot be simultaneously minimized, resulting in a large number of degenerate states. The numerous degenerate configurations may lead to practical…
The dynamics of disordered two-dimensional systems is much less understood than the dynamics of disordered chains, mainly due to the lack of appropriate numerical methods. We demonstrate that a single-trajectory version of the fermionic…
Recently, there has been significant progress in solving quantum many-particle problem via machine learning based on the restricted Boltzmann machine. However, it is still highly challenging to solve frustrated models via machine learning,…
We investigate the computational power of the recently introduced class of isometric tensor network states (isoTNSs), which generalizes the isometric conditions of the canonical form of one-dimensional matrix-product states to tensor…
Tensor network algorithms provide a suitable route for tackling real-time dependent problems in lattice gauge theories, enabling the investigation of out-of-equilibrium dynamics. We analyze a U(1) lattice gauge theory in (1+1) dimensions in…
The optimal use of quantum and classical computational techniques together is important to address problems that cannot be easily solved by quantum computations alone. This is the case of the ground state problem for quantum many-body…
Quantum antiferromagnets have proven to be some of the cleanest realizations available for theoretical, numerical, and experimental studies of quantum fluctuation effects. At finite temperatures, however, the additional effects of thermal…
We analyze the universal features of the critical behaviour of frustrated spin systems with noncollinear order. By means of the field theoretical renormalization group approach, we study the 3d model of a frustrated magnet and obtain…
Density functional theory underlies the most successful and widely used numerical methods for electronic structure prediction of solids. However, it has the fundamental shortcoming that the universal density functional is unknown. In…
Tensor networks capture large classes of ground states of phases of quantum matter faithfully and efficiently. Their manipulation and contraction has remained a challenge over the years, however. For most of the history, ground state…
Tensor network theory and quantum simulation are respectively the key classical and quantum computing methods in understanding quantum many-body physics. Here, we introduce the framework of hybrid tensor networks with building blocks…
In this review article, we discuss connections between the physics of disordered systems, phase transitions in inference problems, and computational hardness. We introduce two models representing the behavior of glassy systems, the spiked…
We investigate the disordered spin-$\frac12$Heisenberg model in two dimensions and employ tree tensor networks (TTNs) with a physics-informed structural optimization of the tree layout, to simulate dynamics in the many-body localization…