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We consider the tensors generating matrix product states and density operators in a spin chain. For pure states, we revise the renormalization procedure introduced by F. Verstraete et al. in 2005 and characterize the tensors corresponding to the fixed points. We relate them to the states possessing zero correlation length, saturation of the area law, as well as to those which generate ground states of local and commuting Hamiltonians. For mixed states, we introduce the concept of renormalization fixed points and characterize the corresponding tensors. We also relate them to concepts like finite correlation length, saturation of the area law, as well as to those which generate Gibbs states of local and commuting Hamiltonians. One of the main result of this work is that the resulting fixed points can be associated to the boundary theories of two-dimensional topological states, through the bulk-boundary correspondence introduced by Cirac et al. in 2011.
Simulating quantum circuits with classical computers requires resources growing exponentially in terms of system size. Real quantum computer with noise, however, may be simulated polynomially with various methods considering different noise models. I
Matrix Product States form the basis of powerful simulation methods for ground state problems in one dimension. Their power stems from the fact that they faithfully approximate states with a low amount of entanglement, the area law. In this work, we
We devise a numerical scheme for the time evolution of matrix product operators by adapting the time-dependent variational principle for matrix product states [J. Haegeman et al, Phys. Rev. B 94, 165116 (2016)]. A simple augmentation of the initial o
We introduce the Nuclear Electronic All-Particle Density Matrix Renormalization Group (NEAP-DMRG) method for solving the time-independent Schrodinger equation simultaneously for electrons and other quantum species. In contrast to already existing mul
We present a matrix product state (MPS) algorithm to approximate ground states of translationally invariant systems with periodic boundary conditions. For a fixed value of the bond dimension D of the MPS, we discuss how to minimize the computational