Related papers: Matrix product states for $su(2)$ invariant quantu…
We propose a refined matrix product state representation for many-body quantum states that are invariant under SU(2) transformations, and indicate how to extend the time-evolving block decimation (TEBD) algorithm in order to simulate time…
We consider a one-parameter family of matrix product states of spin one particles on a periodic chain and study in detail the entanglement properties of such a state. In particular we calculate exactly the entanglement of one site with the…
We use the matrix product approach to construct all optimum ground states of general anisotropic spin-2 chains with nearest neighbour interactions and common symmetries. These states are exact ground states of the model and their properties…
The entanglement-sharing properties of an infinite spin-chain are studied when the state of the chain is a pure, translation-invariant state with a matrix-product structure. We study the entanglement properties of such states by means of…
In recent years, interest in expressing the success of neural networks to the quantum computing has increased significantly. Tensor network theory has become increasingly popular and widely used to simulate strongly entangled correlated…
A classification of SU(2)-invariant Projected Entangled Paired States (PEPS) on the square lattice, based on a unique site tensor, has been recently introduced by Mambrini et al.~\cite{Mambrini2016}. It is not clear whether such…
The order parameter cumulants of infinite matrix product ground states are evaluated across a quantum phase transition. A scheme using the Binder cumulant, finite-entanglement scaling and scaling functions to obtain the critical point and…
Matrix product states (MPS) are a central language for one-dimensional quantum matter and a practical target for near-term quantum simulators and variational algorithms. Yet, while substantial effort has focused on preparing MPS with…
Entangling properties of a mixed 2-qubit system can be described by the local homogeneous unitary invariant polynomials in elements of the density matrix. The structure of the corresponding invariant polynomial ring for the special subclass…
We implement and benchmark tensor network algorithms with $SU(2)$ symmetry for systems in two spatial dimensions and in the thermodynamic limit. Specifically, we implement $SU(2)$-invariant versions of the infinite Projected Entangled Pair…
Optimum ground states are constructed in two dimensions by using so called vertex state models. These models are graphical generalizations of the well-known matrix product ground states for spin chains. On the hexagonal lattice we obtain a…
The set of two-body reduced states of translation invariant, infinite quantum spin chains can be approximated from inside and outside using matrix product states and marginals of finite systems, respectively. These lead to hierarchies of…
Many fractional quantum Hall states can be expressed as a correlator of a given conformal field theory used to describe their edge physics. As a consequence, these states admit an economical representation as an exact Matrix Product States…
The Matrix Product method (MPM) has been used in the past to generate variational ansatzs of the ground state (GS) of spin chains and ladders. In this paper we apply the MPM to study the GS of conjugated polymers in the valence bond basis,…
We use uniform matrix product states (MPS) to study the (1+1)D $O(2)$ and $O(4)$ rotor models, which are equivalent to the Kogut-Susskind formulation of matter-free nonabelian lattice gauge theory on a "hawaiian earring" graph for $U(1)$…
This thesis is divided into two mainly independent parts: In the first part, we derive a criterion to determine when a translationally invariant Matrix Product State (MPS) has long range localizable entanglement, which indicates that the…
We extend the formalism of Matrix Product States (MPS) to describe one-dimensional gapped systems of fermions with both unitary and anti-unitary symmetries. Additionally, systems with orientation-reversing spatial symmetries are considered.…
Matrix product states are useful representations for a large variety of naturally occurring quantum states. Studying their typical properties is important for understanding universal behavior, including quantum chaos and thermalization, as…
Multipartite entanglement offers a powerful framework for understanding the complex collective phenomena in quantum many-body systems that are often beyond the description of conventional bipartite entanglement measures. Here, we propose a…
Entanglement properties of random multipartite quantum states which are invariant under global SU($d$) action are investigated. The random states live in the tensor power of an irreducible representation of SU($d$). We calculate and analyze…