Journal of Pure and Applied Mathematics: Advances and Applications[1] A. M. Goldsborough and R. A. Römer, Self-assembling tensor
networks and holography in disordered spin chains, Phys. Rev. B 89(21)
(2014), Article 214203.
DOI: https://doi.org/10.1103/PhysRevB.89.214203
[2] A. M. Goldsborough and G. Evenbly, Entanglement renormalization
for disordered systems, Phys. Rev. B 96(15) (2017), Article 155136.
DOI: https://doi.org/10.1103/PhysRevB.96.155136
[3] G. Evenbly and G. Vidal, Tensor network states and geometry, J.
Stat. Phys. 145(4) (2011), 891-918.
DOI: https://doi.org/10.1007/s10955-011-0237-4
[4] B. Swingle, Entanglement renormalization and holography, Phys.
Rev. D 86(6) (2012), Article 065007.
DOI: https://doi.org/10.1103/PhysRevD.86.065007
[5] J. Molina-Vilaplana, Holographic geometries of one-dimensional
gapped quantum systems from tensor network states, J. High Energy
Phys. 2013, (2013), 1-25.
DOI: https://doi.org/10.1007/JHEP05(2013)024
[6] J. Maldacena, The large-N limit of superconformal field theories
and supergravity, Int. J. Theor. Phys. 38(4) (1999), 1113-1133.
DOI: https://doi.org/10.1023/A:1026654312961
[7] J. McGreevy, Holographic duality with a view toward many-body
physics, Adv. High Energy Phys. (2010) Article ID 723105, 54 pages.
DOI: http://dx.doi.org/10.1155/2010/723105
[8] K. H. Rosen, Discrete Mathematics and its Applications, Seventh
Edition, McGraw Hill, New York, NY, 2012.
[9] R. Oŕus, A practical introduction to tensor networks: Matrix
product states and projected entangled pair states, Ann. Phys. 349
(2014), 117-158.
DOI: https://doi.org/10.1016/j.aop.2014.06.013
[10] R. Oŕus, Advances on tensor network theory: Symmetries,
fermions, entanglement, and holography, Eur. Phys. J. B 87(11) (2014),
280.
DOI: https://doi.org/10.1140/epjb/e2014-50502-9
[11] S. R. White, Density matrix formulation for quantum
renormalization groups, Phys. Rev. Lett. 69(19) (1992), 2863-2866.
DOI: https://doi.org/10.1103/PhysRevLett.69.2863
[12] S. Östlund and S. Rommer, Thermodynamic limit of density matrix
renormalization, Phys. Rev. Lett. 75(19) (1995), 3537-3540.
DOI: https://doi.org/10.1103/PhysRevLett.75.3537
[13] U. Schollwöck, The density-matrix renormalization group in the
age of matrix product states, Ann. Phys. 326(1) (2011), 96-192.
DOI: https://doi.org/10.1016/j.aop.2010.09.012
[14] F. Verstraete and J. I. Cirac, Renormalization algorithms for
quantum-many body systems in two and higher dimensions,
arXiv:cond-mat/0407066 (2004).
[15] F. Verstraete, V. Murg and J. I. Cirac, Matrix product states,
projected entangled pair states, and variational renormalization group
methods for quantum spin systems, Adv. Phys. 57(2) (2008), 143-224.
DOI: https://doi.org/10.1080/14789940801912366
[16] V. Murg et al., Simulating strongly correlated quantum systems
with tree tensor networks, Phys. Rev. B 82(20) (2010), Article
205105.
DOI: https://doi.org/10.1103/PhysRevB.82.205105
[17] K. Gunst et al., T3NS: Three-legged tree tensor network states,
arXiv:1801.09998 (2018).
[18] N. Nakatani and G. K.-L. Chan, Efficient tree tensor network
states (TTNS) for quantum chemistry: Generalizations of the density
matrix renormalization group algorithm, J. Chem. Phys. 138(13) (2013),
Article 134113.
DOI: https://doi.org/10.1063/1.4798639
[19] S. Szalay et al., Tensor product methods and entanglement
optimization for ab initio quantum chemistry, Int. J. Quantum
Chem. 115(19) (2015), 1342-1391.
DOI: https://doi.org/10.1002/qua.24898
[20] V. Murg et al., Tree tensor network state with variable tensor
order: An efficient multireference method for strongly correlated
systems, J. Chem. Theory Comput. 11(3) (2015), 1027-1036.
DOI: http://dx.doi.org/10.1021/ct501187j
[21] G. Vidal, Entanglement renormalization, Phys. Rev. Lett. 99(22)
(2007), Article 220405.
DOI: https://doi.org/10.1103/PhysRevLett.99.220405
[22] G. Vidal, Class of quantum many-body states that can be
efficiently simulated, Phys. Rev. Lett. 101(11) (2008), Article
110501.
DOI: https://doi.org/10.1103/PhysRevLett.101.110501
[23] G. Evenbly and G. Vidal, Algorithms for entanglement
renormalization, Phys. Rev. B 79(14) (2009), Article 144108.
DOI: https://doi.org/10.1103/PhysRevB.79.144108
[24] A. M. Goldsborough, S. A. Rautu and R. A. Römer, Leaf-to-leaf
distances and their moments in finite and infinite ordered
m-ary tree graphs, Phys. Rev. E 91(4) (2015), Article
042133.
DOI: https://doi.org/10.1103/PhysRevE.91.042133
[25] R. Sedgewick and P. Flajolet, An Introduction to the Analysis of
Algorithms, Addison-Wesley, Westford, MA, Second Edition, 2013.
[26] T. Koshy, Catalan Numbers with Applications, Oxford University
Press, Oxford, Second Edition, 2009.
[27] H. S. Wilf, Generating Functionology, Academic Press, London,
Second Edition, 1994.
[28] P. Kirschenhofer, On the height of leaves in binary trees, J.
Comb. Inform. System Sci. 8 (1983), 44-60.
[29] A. M. Goldsborough et al., Leaf-to-leaf distances in ordered
Catalan tree graphs, arXiv:1502.07893v1 [math-ph] (2015).
[30] A. Panholzer and H. Prodinger, Moments of level numbers of leaves
in binary trees, J. Stat. Plan. Inference 101(1-2) (2002), 267-279.
DOI: https://doi.org/10.1016/S0378-3758(01)00187-2
[31] P. Kirschenhofer, Some new results on the average height of
binary trees, Ars Combinatoria 16A (1983), 255-260.
[32] B. Haas, J. Pitman and M. Winkel, Spinal partitions and
invariance under re-rooting of continuum random trees, Ann. Probab.
37(4) (2009), 1381-1411.
DOI: http://dx.doi.org/10.1214/08-AOP434
