相关论文: Simple Hamiltonians for Matrix Product State model…

We introduce a simple representation for irreducible spherical tensor operators of the rotation group of arbitrary integer or half integer rank and use these tensor operators to construct matrix product states corresponding to all the…

We characterize the conditions under which a translationally invariant matrix product state (MPS) is invariant under local transformations. This allows us to relate the symmetry group of a given state to the symmetry group of a simple…

Motivated by the existence of exact many-body quantum scars in the AKLT chain, we explore the connection between Matrix Product State (MPS) wavefunctions and many-body quantum scarred Hamiltonians. We provide a method to systematically…

We investigate the relation between static correlation functions in the ground state of local quantum many-body Hamiltonians and the dispersion relations of the corresponding low energy excitations using the formalism of tensor network…

We focus on symmetries related to matrices and vectors appearing in the simulation of quantum many-body systems. Spin Hamiltonians have special matrix-symmetry properties such as persymmetry. Furthermore, the systems may exhibit physical…

We introduce Gaussian Matrix Product States (GMPS), a generalization of Matrix Product States (MPS) to lattices of harmonic oscillators. Our definition resembles the interpretation of MPS in terms of projected maximally entangled pairs,…

Using the Matrix Product State framework, we generalize the Affleck-Kennedy-Lieb-Tasaki (AKLT) construction to one-dimensional spin liquids with global color ${\rm SU}(N)$ symmetry, finite correlation lengths, and edge states that can…

The term Tensor Network States (TNS) refers to a number of families of states that represent different ans\"atze for the efficient description of the state of a quantum many-body system. Matrix Product States (MPS) are one particular case…

There are various research strategies used for non-Hermitian systems, which typically involve introducing non-Hermitian terms to pre-existing Hermitian Hamiltonians. It can be challenging to directly design non-Hermitian many-body models…

Over the last decade tensor network states (TNS) have emerged as a powerful tool for the study of quantum many body systems. The matrix product states (MPS) are one particular case of TNS and are used for the simulation of 1+1 dimensional…

We study the conditions under which Matrix Product States (MPS) or Matrix Product Operators are exact eigenvectors of an extensive local operator, such as a Hamiltonian. By suitably choosing the local operator, this covers a wide range of…

We exactly calculate the reduced density matrix of matrix product states (MPS). Our compact result enables one to perform analytic studies of entanglement in MPS. In particular, we consider the MPS ground states of two anisotropic spin…

For every Matrix Product State (MPS) one can always construct a so-called parent Hamiltonian. This is a local, frustration free, Hamiltonian which has the MPS as ground state and is gapped. Whenever that parent Hamiltonian has a degenerate…

We propose and study a specific adiabatic path to prepare those tensor network states that are unique ground states of few-body parent Hamiltonians in finite lattices, which include normal tensor network states, as well as other relevant…

Models whose ground states can be written as an exact matrix product state (MPS) provide valuable insights into phases of matter. While MPS-solvable models are typically studied as isolated points in a phase diagram, they can belong to a…

A platform for constructing microscopic Hamiltonians describing bosonic symmetry-protected topological (SPT) states is presented. The Hamiltonians we consider are examples of frustration-free Rokhsar-Kivelson models, which are known to be…

Matrix Product States can be defined as the family of quantum states that can be sequentially generated in a one-dimensional system. We introduce a new family of states which extends this definition to two dimensions. Like in Matrix Product…

Universal quantum computation can be achieved by simply performing single-qubit measurements on a highly entangled resource state. Resource states can arise from ground states of carefully designed two-body interacting Hamiltonians. This…

Matrix Product States (MPS) are a particular type of one dimensional tensor network states, that have been applied to the study of numerous quantum many body problems. One of their key features is the possibility to describe and encode…

The inverse problem of 'eigenstates-to-Hamiltonian' is considered for an open chain of $N$ quantum spins in the context of Many-Body-Localization. We first construct the simplest basis of the Hilbert space made of $2^N$ orthonormal…