Related papers: Fermionic topological quantum states as tensor net…
We study fermionic matrix product operator algebras and identify the associated algebraic data. Using this algebraic data we construct fermionic tensor network states in two dimensions that have non-trivial symmetry-protected or intrinsic…
We introduce a systematic mathematical language for describing fixed point models and apply it to the study to topological phases of matter. The framework is reminiscent of state-sum models and lattice topological quantum field theories,…
The Z_2 topological order in Z_2 spin liquid and in exactly soluble Kitaev toric code model is the simplest topological order for 2+1D bosonic systems. More general 2+1D bosonic topologically ordered states can be constructed via exact…
Tensor network states and specifically matrix-product states have proven to be a powerful tool for simulating ground states of strongly correlated spin models. Recently, they have also been applied to interacting fermionic problems,…
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…
The ground state of the toric code, that of the two-dimensional class D superconductor, and the partition sum of the two-dimensional Ising model are dual to each other. This duality is remarkable inasmuch as it connects systems commonly…
Developing non-perturbative methods to reveal exotic properties of strongly correlated fermionic systems remains one of the most essential tasks of theoretical physics. Tensor network methods with Grassmann algebra offer powerful numerical…
A brief pedagogical overview of recent advances in tensor network state methods are presented that have the potential to broaden their scope of application radically for strongly correlated molecular systems. These include global fermionic…
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…
Artificial neural networks and machine learning have now reached a new era after several decades of improvement where applications are to explode in many fields of science, industry, and technology. Here, we use artificial neural networks…
The projective construction (the slave-particle approach) has played an very important role in understanding strongly correlated systems, such as the emergence of fermions, anyons, and gauge theory in quantum spin liquids and quantum Hall…
Neural-network quantum states have been successfully used to study a variety of lattice and continuous-space problems. Despite a great deal of general methodological developments, representing fermionic matter is however still early…
We show how fermionic statistics can be naturally incorporated in tensor networks on arbitrary graphs through the use of graded Hilbert spaces. This formalism allows to use tensor network methods for fermionic lattice systems in a local…
Tensor network states and methods have erupted in recent years. Originally developed in the context of condensed matter physics and based on renormalization group ideas, tensor networks lived a revival thanks to quantum information theory…
We describe a class of neuralized fermionic tensor network states (NN-fTNS) that introduce non-linearity into fermionic tensor networks through configuration-dependent neural network transformations of the local tensors. The construction…
The study of topological band insulators has revealed fascinating phases characterized by band topology indices and anomalous boundary modes protected by global symmetries. In strongly correlated systems, where the traditional notion of…
We present and implement an efficient variational method to simulate two-dimensional finite size fermionic quantum systems by fermionic projected entangled pair states. The approach differs from the original one due to the fact that there…
Tensor network states and parton wave functions are two pivotal methods for studying quantum many-body systems. This work connects these two subjects as we demonstrate that a variety of parton wave functions, such as projected Fermi sea and…
We describe our implementation of fermionic tensor network contraction on arbitrary lattices within both a globally ordered and locally ordered formalism. We provide a pedagogical description of these two conventions as implemented for the…
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…