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Renormalization algorithm with graph enhancement

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Abstract
We introduce a class of variational states to describe quantum many-body systems. This class generalizes matrix product states which underlie the density-matrix renormalization-group approach by combining them with weighted graph states. States within this class may (i) possess arbitrarily long-ranged two-point correlations, (ii) exhibit an arbitrary degree of block entanglement entropy up to a volume law, (iii) be taken translationally invariant, while at the same time (iv) local properties and two-point correlations can be computed efficiently. This variational class of states can be thought of as being prepared from matrix product states, followed by commuting unitaries on arbitrary constituents, hence truly generalizing both matrix product and weighted graph states. We use this class of states to formulate a renormalization algorithm with graph enhancement and present numerical examples, demonstrating that improvements over density-matrix renormalization-group simulations can be achieved in the simulation of ground states and quantum algorithms. Further generalizations, e.g., to higher spatial dimensions, are outlined.
Keywords
DENSITY-MATRIX RENORMALIZATION, QUANTUM SPIN CHAINS, ENTANGLEMENT, STATES, entropy, ground states, many-body problems, matrix algebra, quantum, entanglement, renormalisation

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MLA
Huebener, R et al. “Renormalization Algorithm with Graph Enhancement.” PHYSICAL REVIEW A 79.2 (2009): n. pag. Print.
APA
Huebener, R., Kruszynska, C., Hartmann, L., Duer, W., Verstraete, F., Eisert, J., & Plenio, M. (2009). Renormalization algorithm with graph enhancement. PHYSICAL REVIEW A, 79(2).
Chicago author-date
Huebener, R, C Kruszynska, L Hartmann, W Duer, Frank Verstraete, J Eisert, and MB Plenio. 2009. “Renormalization Algorithm with Graph Enhancement.” Physical Review A 79 (2).
Chicago author-date (all authors)
Huebener, R, C Kruszynska, L Hartmann, W Duer, Frank Verstraete, J Eisert, and MB Plenio. 2009. “Renormalization Algorithm with Graph Enhancement.” Physical Review A 79 (2).
Vancouver
1.
Huebener R, Kruszynska C, Hartmann L, Duer W, Verstraete F, Eisert J, et al. Renormalization algorithm with graph enhancement. PHYSICAL REVIEW A. 2009;79(2).
IEEE
[1]
R. Huebener et al., “Renormalization algorithm with graph enhancement,” PHYSICAL REVIEW A, vol. 79, no. 2, 2009.
@article{8589248,
  abstract     = {We introduce a class of variational states to describe quantum many-body systems. This class generalizes matrix product states which underlie the density-matrix renormalization-group approach by combining them with weighted graph states. States within this class may (i) possess arbitrarily long-ranged two-point correlations, (ii) exhibit an arbitrary degree of block entanglement entropy up to a volume law, (iii) be taken translationally invariant, while at the same time (iv) local properties and two-point correlations can be computed efficiently. This variational class of states can be thought of as being prepared from matrix product states, followed by commuting unitaries on arbitrary constituents, hence truly generalizing both matrix product and weighted graph states. We use this class of states to formulate a renormalization algorithm with graph enhancement and present numerical examples, demonstrating that improvements over density-matrix renormalization-group simulations can be achieved in the simulation of ground states and quantum algorithms. Further generalizations, e.g., to higher spatial dimensions, are outlined.},
  articleno    = {022317},
  author       = {Huebener, R and Kruszynska, C and Hartmann, L and Duer, W and Verstraete, Frank and Eisert, J and Plenio, MB},
  issn         = {1050-2947},
  journal      = {PHYSICAL REVIEW A},
  keywords     = {DENSITY-MATRIX RENORMALIZATION,QUANTUM SPIN CHAINS,ENTANGLEMENT,STATES,entropy,ground states,many-body problems,matrix algebra,quantum,entanglement,renormalisation},
  language     = {eng},
  number       = {2},
  pages        = {6},
  title        = {Renormalization algorithm with graph enhancement},
  url          = {http://dx.doi.org/10.1103/PhysRevA.79.022317},
  volume       = {79},
  year         = {2009},
}

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