Related papers: Unified tensor network theory for frustrated class…
We have developed a tensor network approach to the two-dimensional fully frustrated classical XY spin model on the kagome lattice, and clarified the nature of the possible phase transitions of various topological excitations.We find that…
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 network states provide an efficient class of states that faithfully capture strongly correlated quantum models and systems in classical statistical mechanics. While tensor networks can now be seen as becoming standard tools in the…
After a short introduction on frustrated spin systems, we study in this chapter several two-dimensional frustrated Ising spin systems which can be exactly solved by using vertex models. We show that these systems contain most of the…
In 1977, G\'erard Toulouse has proposed a new concept termed as "frustration" in spin systems. Using this definition, several frustrated models have been created and studied, among them we can mention the Villain's model, the fully…
Machine-learning techniques have proved successful in identifying ordered phases of matter. However, it remains an open question how far they can contribute to the understanding of phases without broken symmetry, such as spin liquids. Here…
Motivated by the recent success of tensor networks to calculate the residual entropy of spin ice and kagome Ising models, we develop a general framework to study frustrated Ising models in terms of infinite tensor networks %, i.e. tensor…
By means of the recently developed algorithm based on the tensor product states, the magnetization process of frustrated spin-1/2 spin-dimer models on a square lattice is investigated. Various field-induced quantum phases are discovered. In…
The use of artificial neural networks to represent quantum wave-functions has recently attracted interest as a way to solve complex many-body problems. The potential of these variational parameterizations has been supported by analytical…
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…
Tensor network techniques are becoming increasingly popular tools to solve partial differential equations within the so-called quantics representation. Their popularity stems from the fact that their spatial resolution depends only…
We develop a tensor network technique that can solve universal reversible classical computational problems, formulated as vertex models on a square lattice [Nat. Commun. 8, 15303 (2017)]. By encoding the truth table of each vertex…
We introduce a U(1) lattice gauge theory which incorporates explicit frustration in $d>2$. We show, by identifying an appropiate order parameter and through computer simulations, the existence of a frustrated region in the phase diagram of…
The classical Heisenberg model in two spatial dimensions constitutes one of the most paradigmatic spin models, taking an important role in statistical and condensed matter physics to understand magnetism. Still, despite its paradigmatic…
Tensor network methods have progressed from variational techniques based on matrix-product states able to compute properties of one-dimensional condensed-matter lattice models into methods rooted in more elaborate states such as projected…
We develop a technique for calculating three-dimensional classical partition functions using projected entangled-pair states (PEPS). Our method is based on variational PEPS optimization algorithms for two-dimensional quantum spin systems,…
Tensor network decompositions offer an efficient description of certain many-body states of a lattice system and are the basis of a wealth of numerical simulation algorithms. We discuss how to incorporate a global symmetry, given by a…
Tensor network (TN), a young mathematical tool of high vitality and great potential, has been undergoing extremely rapid developments in the last two decades, gaining tremendous success in condensed matter physics, atomic physics, quantum…
We consider a quantum two-dimensional O(N)xO(2)/O(N-2)xO(2) nonlinear sigma model for frustrated spin systems and formulate its 1/N-expansion which involves fluctuating scalar and vector fields describing kinematic and dynamic interactions,…
One of the challenging problems in the condensed matter physics is to understand the quantum many-body systems, especially, their physical mechanisms behind. Since there are only a few complete analytical solutions of these systems, several…