相关论文: Projected Entangled Pair States at Finite Temperat…
A variety of generative neural networks recently adopted from machine learning have provided promising strategies for studying quantum matter. In particular, the success of autoregressive models in natural language processing has motivated…
This thesis contributes to the understanding of symmetry-enriched topological phases focusing on their descriptions in terms of tensor network states. The Projected Entangled Pair State (PEPS) formalism allows us to locally encode the main…
An extended ensemble Monte Carlo algorithm is proposed by introducing a violation of the detailed balance condition to the update scheme of the inverse temperature in simulated tempering. Our method, irreversible simulated tempering, is…
A Gibbs operator $e^{-\beta H}$ for a 2D lattice system with a Hamiltonian $H$ can be represented by a 3D tensor network, the third dimension being the imaginary time (inverse temperature) $\beta$. Coarse-graining the network along $\beta$…
Tensor networks, a model that originated from quantum physics, has been gradually generalized as efficient models in machine learning in recent years. However, in order to achieve exact contraction, only tree-like tensor networks such as…
Entanglement renormalization is a method for coarse-graining a quantum state in real space, with the multi-scale entanglement renormalization ansatz (MERA) as a notable example. We obtain an entanglement renormalization scheme for…
We investigate the topological character of lattice chiral Gaussian fermionic states in two dimensions possessing the simplest descriptions in terms of projected entangled-pair states (PEPS). They are ground states of two different kinds of…
We propose an environment recycling scheme to speed up a class of tensor network algorithms that produce an approximation to the ground state of a local Hamiltonian by simulating an evolution in imaginary time. Specifically, we consider the…
Representing the time-evolution operator as a tensor network constitutes a key ingredient in several algorithms for studying quantum lattice systems at finite temperature or in a non-equilibrium setting. For a Hamiltonian composed of…
We use Projected Entangled Pair States (PEPS) to study topological quantum phase transitions. The local description of topological order in the PEPS formalism allows us to set up order parameters which measure condensation and deconfinement…
We investigate the thermal properties of the 1/3 plateau in the Shastry-Sutherland model with infinite projected entangled-pair states (iPEPS) by performing the imaginary time evolution of the infinite temperature density matrix. We show…
We propose and test a scheme for entanglement renormalization capable of addressing large two-dimensional quantum lattice systems. In a translationally invariant system, the cost of simulations grows only as the logarithm of the lattice…
Systems with quenched disorder possess complex energy landscapes that are challenging to explore under the conventional Monte Carlo method. In this work, we implement an efficient entropy sampling scheme for accurate computation of the…
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…
Projected Entangled Pair States (PEPS) are used in practice as an efficient parametrization of the set of ground states of quantum many body systems. The aim of this paper is to present, for a broad mathematical audience, some mathematical…
By using a different quantum-to-classical mapping from the Trotter-Suzuki decomposition, we identify the entanglement structure of the maximal eigenvectors for the associated quantum transfer matrix. This observation provides a deeper…
We present a continuous tensor-network construction for the states of quantum fields called cPEPS (continuous projected entangled pair state), which enjoys the same spatial and global symmetries of ground-states of relativistic field…
We study the $q$-state Potts models on a cubic lattice in the thermodynamic limit using tensor renormalization group transformations with the triad approximation. By computing the thermodynamic potentials, we locate the first-order phase…
The 1-form symmetry, manifesting as loop-like symmetries, has gained prominence in the study of quantum phases, deepening our understanding of symmetry. However, the role of 1-form symmetries in Projected Entangled-Pair States (PEPS),…
We introduce a class of states, called minimally entangled typical thermal states (METTS), designed to resemble a typical state of a quantum system at finite temperature with a bias towards classical (minimally entangled) properties. These…