Related papers: Virasoro Generators in the Fibonacci Model Tensor …

In this paper, we propose a general implementation of the Virasoro generators and Kac-Moody currents in generic tensor network representations of 2-dimensional critical lattice models. Our proposal works even when a quantum Hamiltonian of…

Tensor networks such as matrix product states (MPS) and projected entangled pair states (PEPS) are commonly used to approximate quantum systems. These networks are optimized in methods such as DMRG or evolved by local operators. We provide…

We use a recently proposed class of tensor-network states to study phase transitions in string-net models. These states encode the genuine features of the string-net condensate such as, e.g., a nontrivial perimeter law for Wilson loops…

It is demonstrated that Monte Carlo sampling can be used to efficiently extract the expectation value of projected entangled pair states with large virtual bond dimension. We use the simple update rule introduced by Xiang et al. to obtain…

The performance of tensor network methods has seen constant improvements over the last few years. We add to this effort by introducing a new algorithm that efficiently applies tree tensor network operators to tree tensor network states…

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…

We benchmark recently proposed tensor network based finite-size scaling analysis in Phys. Rev. B {\bf 107}, 205123 (2023) against two-dimensional classical 3-state clock model. Due to the higher complexity of the model, more complicated…

Tensor networks are used to efficiently approximate states of strongly-correlated quantum many-body systems. More generally, tensor network approximations may allow to reduce the costs for operating on an order-$N$ tensor from exponential…

Tensor networks, which are originally developed for characterizing complex quantum many-body systems, have recently emerged as a powerful framework for capturing high-dimensional probability distributions with strong physical…

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.…

Data in the form of images or higher-order tensors is ubiquitous in modern deep learning applications. Owing to their inherent high dimensionality, the need for subquadratic layers processing such data is even more pressing than for…

Tensor networks establish an adaptable framework for the emulation of quantum circuits. By partitioning exponentially large registers and gates into smaller tensors, this unlocks fast transformations through tensor algebra, and grants fine…

We propose an efficient numerical method, which combines the advantages of recently developed tensor-network based methods and standard trial wave functions, to study the ground state properties of quantum many-body systems. In this…

In the references [HL1]--[HL5] and [H1], a theory of tensor products of modules for a vertex operator algebra is being developed. To use this theory, one first has to verify that the vertex operator algebra satisfies certain conditions. We…

Tensor networks are a powerful tool to simulate a variety of different physical models, including those that suffer from the sign problem in Monte Carlo simulations. The Hubbard model on the honeycomb lattice with non-zero chemical…

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…

We investigate in details how the Virasoro algebra appears in the scaling limit of the simplest lattice models of XXZ or RSOS type. Our approach is straightforward but to our knowledge had never been tried so far. We simply formulate a…

In this work, we develop a stochastic matrix product state (stoMPS) approach that combines the MPS technique and Monte Carlo samplings and can be applied to simulate quantum lattice models down to low temperature. In particular, we exploit…

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 $\beta$…

Producing large complex simulation datasets can often be a time and resource consuming task. Especially when these experiments are very expensive, it is becoming more reasonable to generate synthetic data for downstream tasks. Recently,…