Related papers: Unified tensor network theory for frustrated class…
Using a {\it collective} Monte Carlo algorithm we study the low-temperature and long-distance properties of two systems of two-dimensional classical tops. Both systems have the same spin-wave dynamics (low-temperature behavior) as a large…
We predict and observed novel highly anisotropic magnetic patterns obtained in the model of frustrated planar interacting magnetic moments (the classical $X-Y$ model) on the regular kagome lattice. The frustration is provided by the…
This work aims at the goal whether the artificial intelligence can recognize phase transition without the prior human knowledge. If this becomes successful, it can be applied to, for instance, analyze data from quantum simulation of…
For the signed graph associated to a deep neural network, one can compute the frustration level, i.e., test how close or distant the graph is to structural balance. For all the pretrained deep convolutional neural networks we consider, we…
Frustrated systems are ubiquitous and interesting because their behavior is difficult to predict. Magnetism offers extreme examples in the form of spin lattices where all interactions between spins cannot be simultaneously satisfied. Such…
Tensor network methods are powerful tools for studying quantum many-body systems. In this paper, we investigate the emergent statistical properties of random high-dimensional tensor-network states and the trainability of variational tensor…
The simulation of lattice gauge theories with tensor network (TN) methods is becoming increasingly fruitful. The vision is that such methods will, eventually, be used to simulate theories in $(3+1)$ dimensions in regimes difficult for other…
Accurate contraction of tensor networks beyond one dimension is essential in various fields including quantum many-body physics. Existing approaches typically rely on approximate contraction schemes and do not provide certified error bars.…
We present a comprehensive study on the frustrated $J_1$-$J_2$ classical $q$-state clock model with even $q>4$ on a two-dimensional square lattice, revealing a rich ensemble of phases driven by competing interactions. In the unfrustrated…
A novel algorithm based on the optimized decimation of tensor networks with super-orthogonalization (ODTNS) that can be applied to simulate efficiently and accurately not only the thermodynamic but also the ground state properties of…
The study of frustrated spin systems often requires time-consuming numerical simulations. As the simplest approach, the classical Ising model is often used to investigate the thermodynamic behavior of such systems. Exploiting the small…
We introduce the concept of concatenated tensor networks to efficiently describe quantum states. We show that the corresponding concatenated tensor network states can efficiently describe time evolution and possess arbitrary block-wise…
We investigate the behavior of genuine multipartite entanglement of paradigmatic frustrated quantum spin systems. We consider six different spin models, whose frustration ranges from being very high to very low. We find that the highly…
We have discussed the tensor-network representation of classical statistical or interacting quantum lattice models, and given a comprehensive introduction to the numerical methods we recently proposed for studying the tensor-network…
The frustrated Ising model on a two-dimensional lattice with open boundary conditions is revisited. A hidden Z2 gauge symmetry relates models with different frustrations which, however, share the same partition function. By means of a…
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 present a compendium of numerical simulation techniques, based on tensor network methods, aiming to address problems of many-body quantum mechanics on a classical computer. The core setting of this anthology are lattice problems in low…
Understanding quantum magnetism in two-dimensional systems represents a lively branch in modern condensed-matter physics. In the presence of competing super-exchange couplings, magnetic order is frustrated and can be suppressed down to zero…
The recognition that large classes of quantum many-body systems have limited entanglement in the ground and low-lying excited states led to dramatic advances in their numerical simulation via so-called tensor networks. However, global…
Tensor network methods are powerful and efficient tools to study the properties and dynamics of statistical and quantum systems, in particular in one and two dimensions. In recent years, these methods were applied to lattice gauge theories,…