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A variational ansatz for momentum eigenstates of translation invariant quantum spin chains is formulated. The matrix product state ansatz works directly in the thermodynamic limit and allows for an efficient implementation (cubic scaling in the bond dimension) of the variational principle. Unlike previous approaches, the ansatz includes topologically non-trivial states (kinks, domain walls) for systems with symmetry breaking. The method is benchmarked using the spin-1/2 XXZ antiferromagnet and the spin-1 Heisenberg antiferromagnet and we obtain surprisingly accurate results.
In one-dimensional quantum systems with short-range interactions, a set of leading numerical methods is based on matrix product states, whose bond dimension determines the amount of computational resources required by these methods. We prove that a t
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 states our
The theory of entanglement provides a fundamentally new language for describing interactions and correlations in many body systems. Its vocabulary consists of qubits and entangled pairs, and the syntax is provided by tensor networks. We review how ma
We combine the Density Matrix Renormalization Group (DMRG) with Matrix Product State tangent space concepts to construct a variational algorithm for finding ground states of one dimensional quantum lattices in the thermodynamic limit. A careful compa
In stochastic modeling, there has been a significant effort towards finding predictive models that predict a stochastic process future using minimal information from its past. Meanwhile, in condensed matter physics, matrix product states (MPS) are kn