Related papers: Product vacua with boundary states
We have developed a new approach based on matrix product representations of ground states to study Quantum Phase Transitions (QPT). As confirmation of the power of our approach we have analytically analyzed the XXZ spin-one chain with…
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…
Devising schemes for testing the amount of entanglement in quantum systems has played a crucial role in quantum computing and information theory. Here, we study the problem of testing whether an unknown state $|\psi\rangle$ is a matrix…
We prove that ground states of gapped local Hamiltonians on an infinite spin chain can be efficiently approximated by matrix product states with a bond dimension which scales as D~(L-1)/epsilon, where any local quantity on L consecutive…
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 study thermal states of strongly interacting quantum spin chains and prove that those can be represented in terms of convex combinations of matrix product states. Apart from revealing new features of the entanglement structure of Gibbs…
We consider the square lattice $S$=1/2 quantum compass model (QCM) parameterized by $J_x, J_z$, under a field, $\mathbf{h}$, in the $x$-$z$ plane. At the special field value, $(h_x^\star,h_z^\star)$=$2S(J_x,J_z)$, we show that the QCM…
We study $S=1$ quantum spin systems on the infinite chain with short ranged Hamiltonians which have certain rotational and discrete symmetry. We define a $\mathbb{Z}_2$ index for any gapped unique ground state, and prove that it is…
A complete classification is given for one dimensional chains with nearest neighbor interactions having two states in each site, for which a matrix product ground state exists. The Hamiltonians and their corresponding matrix product ground…
We describe a class of spin chains with new physical and computational properties. On the physical side, the spin chains give examples of symmetry-protected topological phases that are defined by non-onsite symmetries, i.e. symmetries that…
Relativistic continuous matrix product states (RCMPS) are a powerful variational ansatz for quantum field theories of a single field. However, they inherit a property of their non-relativistic counterpart that makes them divergent for…
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…
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…
We investigate quantum phase transitions in which a change in the type of entanglement from bound entanglement to either free entanglement or separability may occur. In particular, we present a theoretical method to construct a class of…
The matrix product state (MPS) belongs to the most important mathematical models in, for example, condensed matter physics and quantum information sciences. However, to realize an $N$-qubit MPS with large $N$ and large entanglement on a…
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…
The steady states of three families of one-dimensional non-equilibrium models with open boundaries, first proposed in [22], are studied using a matrix product formalism. It is shown that their associated quadratic algebras have…
In this paper, we study the entanglement properties of a spin-1 model the exact ground state of which is given by a Matrix Product state. The model exhibits a critical point transition at a parameter value a=0. The longitudinal and…
Numerical simulations are a powerful tool to study quantum systems beyond exactly solvable systems lacking an analytic expression. For one-dimensional entangled quantum systems, tensor network methods, amongst them Matrix Product States…
The matrix product state formalism is used to simulate Hamiltonian lattice gauge theories. To this end, we define matrix product state manifolds which are manifestly gauge invariant. As an application, we study 1+1 dimensional one flavour…