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Advances on tensor network theory: symmetries, fermions, entanglement, and holography

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Abstract

This is a short review on selected theory developments on tensor network (TN) states for strongly correlated systems. Specifically, we briefly review the effect of symmetries in TN states, fermionic TNs, the calculation of entanglement Hamiltonians from projected entangled pair states (PEPS), and the relation between the multi-scale entanglement renormalization ansatz (MERA) and the AdS/CFT or gauge/gravity duality. We stress the role played by entanglement in the emergence of several physical properties and objects through the TN language. Some recent results along these lines are also discussed.

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References

  1. F. Verstratete, J.I. Cirac, V. Murg, Adv. Phys. 57, 143 (2008)

    ADS  Google Scholar 

  2. J.I. Cirac, F. Verstraete, J. Phys. A 42, 504004 (2009)

    MathSciNet  Google Scholar 

  3. R. Augusiak, F.M. Cucchietti, M. Lewenstein, in Modern Theories of Many-Particle Systems in Condensed Matter Physics, Lect. Not. Phys. (Springer-Verlag, Berlin, 2012), Vol. 843, p. 245

  4. J. Eisert, Mod. Simul. 3, 520 (2013)

    Google Scholar 

  5. N. Schuch, QIP, Lecture Notes of the 44th IFF Spring School, 2013

  6. R. Orús, Ann. Phys. 349, 117 (2014)

    ADS  Google Scholar 

  7. M. Lubasch, J.I. Cirac, M.-C. Bañuls, New J. Phys. 16, 033014 (2014)

    ADS  Google Scholar 

  8. F. Verstraete, M.M. Wolf, D. Perez-García, J.I. Cirac, Phys. Rev. Lett. 96, 220601 (2006)

    ADS  MathSciNet  Google Scholar 

  9. S.R. White, Phys. Rev. Lett. 69, 2863 (1992)

    ADS  Google Scholar 

  10. S.R. White, Phys. Rev. B 48, 10345 (1992)

    ADS  Google Scholar 

  11. G. Vidal, Phys. Rev. Lett. 99, 220405 (2007)

    ADS  Google Scholar 

  12. G. Evenbly, G. Vidal, Phys. Rev. Lett. 112, 240502 (2014)

    ADS  Google Scholar 

  13. G. Evenbly, G. Vidal, Phys. Rev. B 89, 235113 (2014)

    ADS  Google Scholar 

  14. A. Affleck, T. Kennedy, E.H. Lieb, H. Tasaki, Commun. Math. Phys. 115, 477 (1988)

    ADS  MathSciNet  Google Scholar 

  15. A. Affleck, T. Kennedy, E.H. Lieb, H. Tasaki, Phys. Rev. Lett. 59, 799 (1988)

    ADS  Google Scholar 

  16. F. Verstraete, J.I. Cirac, arXiv:cond-mat/0407066 (2004)

  17. M.B. Hastings, Phys. Rev. B 73, 085115 (2006)

    ADS  Google Scholar 

  18. D. Perez-Garcia, F. Verstraete, I. Cirac, M.M. Wolf, Quant. Inf. Comp. 8, 0650 (2008)

    MathSciNet  Google Scholar 

  19. F. Verstraete, I. Cirac, Phys. Rev. Lett. 104, 190405 (2010)

    ADS  MathSciNet  Google Scholar 

  20. J. Haegeman, J.I. Cirac, T.J. Osborne, H. Verschelde, F. Verstraete, Phys. Rev. Lett. 105, 251601 (2010)

    ADS  MathSciNet  Google Scholar 

  21. J. Haegeman, J.I. Cirac, T.J. Osborne, F. Verstraete, Phys. Rev. B 88, 085118 (2013)

    ADS  Google Scholar 

  22. D. Jennings, J. Haegeman, T.J. Osborne, F. Verstraete, arXiv:1212.3833 (2012)

  23. J. Haegeman, T.J. Osborne, H. Verschelde, F. Verstraete, Phys. Rev. Lett. 110, 100402 (2013)

    ADS  Google Scholar 

  24. C. Brockt, J. Haegeman, D. Jennings, T.J. Osborne, F. Verstraete, arXiv:1210.5401 (2012)

  25. M. Nozaki, S. Ryu, T. Takayanagi, JHEP 10, 193 (2012)

    ADS  MathSciNet  Google Scholar 

  26. A. Mollabashi, M. Nozaki, S. Ryu, T. Takayanagi, arXiv:1311.6095 (2013)

  27. B. Swingle, arXiv:1209.3304 (2012)

  28. G. Vidal, Phys. Rev. Lett. 91, 147902 (2003)

    ADS  Google Scholar 

  29. G. Vidal, Phys. Rev. Lett. 939, 040502 (2004)

    Google Scholar 

  30. G. Vidal, Phys. Rev. Lett. 98, 070201 (2007)

    ADS  MathSciNet  Google Scholar 

  31. R. Orús, G. Vidal, Phys. Rev. B 78, 155117 (2008)

    ADS  Google Scholar 

  32. Y. Shi, L. Duan, G. Vidal, Phys. Rev. A 74, 022320 (2006)

    ADS  Google Scholar 

  33. P. Silvi, V. Giovannetti, S. Montangero, M. Rizzi, J.I. Cirac, R. Fazio, Phys. Rev. A 81, 062335 (2010)

    ADS  Google Scholar 

  34. V. Murg, Ö. Legeza, R.M. Noack, F. Verstraete, Phys. Rev. B 82, 205105 (2010)

    ADS  Google Scholar 

  35. M. Gerster, P. Silvi, M. Rizzi, R. Fazio, T. Calarco, S. Montangero, Phys. Rev. B 90, 125154 (2014)

    ADS  Google Scholar 

  36. L. Tagliacozzo, G. Evenbly, G. Vidal, Phys. Rev. B 80, 235127 (2009)

    ADS  Google Scholar 

  37. D. Porras, F. Verstraete, J.I. Cirac, Phys. Rev. Lett. 93, 227205 (2004)

    ADS  Google Scholar 

  38. P. Pippan, S.R. White, H.G. Evertz, Phys. Rev. B 81, 081103(R) (2010)

    ADS  Google Scholar 

  39. B. Pirvu, F. Verstraete, G. Vidal, Phys. Rev. B 83, 125104 (2011)

    ADS  Google Scholar 

  40. U. Schollwöck, Rev. Mod. Phys. 77, 259 (2005)

    ADS  Google Scholar 

  41. U. Schollwöck, Ann. Phys. 326, 96 (2011)

    ADS  MATH  Google Scholar 

  42. T. Nishino, K. Okunishi, J. Phys. Soc. Jpn 64, 4084 (1995)

    ADS  Google Scholar 

  43. K. Ueda, T. Nishino, K. Okunishi, Y. Hieida, R. Derian, A. Gendiar, J. Phys. Soc. Jpn 75, 014003 (2006)

    ADS  Google Scholar 

  44. W. Hackbusch, Tensor spaces and numerical tensor calculus (Springer, 2012)

  45. M.B. Hastings, J. Stat. Mech. 2007, P08024 (2007)

    MathSciNet  Google Scholar 

  46. C. Holzhey, F. Larsen, F. Wilczek, Nucl. Phys. B 424, 443 (1994)

    ADS  MATH  MathSciNet  Google Scholar 

  47. G. Vidal, J.I. Latorre, E. Rico, A. Kitaev, Phys. Rev. Lett. 90, 227902 (2003)

    ADS  Google Scholar 

  48. J.I. Latorre, E. Rico, G. Vidal, QIC 4, 48 (2004)

    MATH  MathSciNet  Google Scholar 

  49. P. Calabrese, J. Cardy, J. Stat. Mech. 0406, P06002 (2004)

    Google Scholar 

  50. F. Pollmann, A. Turner, E. Berg, M. Oshikawa, Phys. Rev. B 81, 064439 (2010)

    ADS  Google Scholar 

  51. F. Pollmann, A. Turner, arXiv:1204.0704 (2012)

  52. J. Jordan, R. Orús, G. Vidal, F. Verstraete, J.I. Cirac, Phys. Rev. Lett. 101, 250602 (2008)

    ADS  Google Scholar 

  53. M. Levin, C.P. Nave, Phys. Rev. Lett. 99, 120601 (2007)

    ADS  Google Scholar 

  54. Z.Y. Xie, H.C. Jiang, Q.N. Chen, Z.Y. Weng, T. Xiang, Phys. Rev. Lett. 103, 160601 (2009)

    ADS  Google Scholar 

  55. H.H. Zhao, Z.Y. Xie, Q.N. Chen, Z.C. Wei, J.W. Cai, T. Xiang, Phys. Rev. B 81, 174411 (2010)

    ADS  Google Scholar 

  56. Z.Y. Xie, J. Chen, M.P. Qin, J.W. Zhu, L.P. Yang, T. Xiang, Phys. Rev. B 86, 045139 (2012)

    ADS  Google Scholar 

  57. R. Orús, G. Vidal, Phys. Rev. B 80, 094403 (2009)

    ADS  Google Scholar 

  58. T. Nishino, K. Okunishi, J. Phys. Soc. Jpn 65, 891 (1996)

    ADS  MATH  Google Scholar 

  59. T. Nishino, K. Okunishi, J. Phys. Soc. Jpn 66, 3040 (1997)

    ADS  MATH  Google Scholar 

  60. R. Orús, Phys. Rev. B 85, 205117 (2012)

    ADS  Google Scholar 

  61. M. Srednicki, Phys. Rev. Lett. 71, 666 (1993)

    ADS  MATH  MathSciNet  Google Scholar 

  62. M. Plenio, J. Eisert, J. Dreißig, M. Cramer, Phys. Rev. Lett. 94, 060503 (2005)

    ADS  MathSciNet  Google Scholar 

  63. A. Riera, J.I. Latorre, Phys. Rev. A 74, 052326 (2006)

    ADS  Google Scholar 

  64. H. Kalis, D. Klagges, R. Orús, K.P. Schmidt, Phys. Rev. A 86, 022317 (2012)

    ADS  Google Scholar 

  65. R. Orús, H. Kalis, M. Bornemann, K.P. Schmidt, Phys. Rev. A 87, 062312 (2013)

    ADS  Google Scholar 

  66. H.C. Jiang, Z.Y. Weng, T. Xiang, Phys. Rev. Lett. 101, 090603 (2008)

    ADS  Google Scholar 

  67. M. Lubasch, I. Cirac, M.C. Bañuls, arXiv:1405.3259

  68. R. Hübener, V. Nebendahl, W. Dür, New J. Phys. 12, 025004 (2010)

    Google Scholar 

  69. O. Legeza, J. Solyom, Phys. Rev. B 68, 195116 (2003)

    ADS  Google Scholar 

  70. J. Rissler, R.M. Noack, S.R. White, Chem. Phys. 323, 519 (2006)

    ADS  Google Scholar 

  71. O. Legeza, R.M. Noack, J. Solyom, L. Tincani, in Computational Many-Particle Physics, Lect. Not. Phys. (Springer-Verlag, Berlin, 2008), Vol. 739, p. 655

  72. G. Barcza, O. Legeza, K.H. Marti, M. Reiher, Phys. Rev. A 83, 012508 (2011)

    ADS  Google Scholar 

  73. K.H. Marti, B. Bauer, M. Reiher, M. Troyer, F. Verstraete, New J. Phys. 12, 103008 (2010)

    ADS  Google Scholar 

  74. N. Nakatani, G.K.-Lic Chan, J. Chem. Phys. 138, 134113 (2013)

    ADS  Google Scholar 

  75. G. Vidal, in Understanding Quantum Phase Transitions, edited by L.D. Carr (Taylor & Francis, Boca Raton, 2010)

  76. M.M. Wolf, Phys. Rev. Lett. 96, 010404 (2006)

    ADS  Google Scholar 

  77. M.P.A. Fisher, O.I. Motrunich, D.N. Sheng, in Proceeding 24th Solvay conf., 2008

  78. S. Ostlund, S. Rommer, Phys. Rev. Lett. 75, 3537 (1995)

    ADS  Google Scholar 

  79. M. Fannes, B. Nachtergaele, R. Werner, Commun. Math. Phys. 144, 443 (1992)

    ADS  MATH  MathSciNet  Google Scholar 

  80. G. Sierra, T. Nishino, Nucl. Phys. B 495, 505 (1997)

    ADS  MATH  MathSciNet  Google Scholar 

  81. I. McCulloch, M. Gulacsi, Europhys. Lett. 57, 852 (2002)

    ADS  Google Scholar 

  82. I. McCulloch, J. Stat. Mech. 2007, P10014 (2007)

    Google Scholar 

  83. S. Singh, H.-Q. Zhou, G. Vidal, New J. Phys. 12, 033029 (2010)

    ADS  Google Scholar 

  84. S. Singh, R. Pfeifer, G. Vidal, Phys. Rev. A 82, 050301 (2010)

    ADS  MathSciNet  Google Scholar 

  85. S. Singh, R. Pfeifer, G. Vidal, Phys. Rev. B 83, 115125 (2011)

    ADS  Google Scholar 

  86. S. Singh, G. Vidal, Phys. Rev. B 86, 195114 (2012)

    ADS  Google Scholar 

  87. S. Singh, G. Vidal, Phys. Rev. B 88, 121108(R) (2013)

    ADS  Google Scholar 

  88. B. Bauer, P. Corboz, R. Orus, M. Troyer, Phys. Rev. B 83, 125106 (2011)

    ADS  Google Scholar 

  89. A. Weichselbaum, Ann. Phys. 327, 2972 (2012)

    ADS  MATH  MathSciNet  Google Scholar 

  90. R. Penrose, Angular momentum: an approach to combinatorial space-time 1971, http://math.ucr.edu/home/baez/penrose/

  91. C. Rovelli, L. Smolin, Phys. Rev. D 52, 5743 (1995)

    ADS  MathSciNet  Google Scholar 

  92. C. Rovelli, Living Reviews in Relativity, http://www.livingreviews.org/lrr-2008-5

  93. J.F. Cornwell, Group Theory in Physics (Academic Press, 1997)

  94. S. Singh, G. Vidal, Phys. Rev. B 88, 115147 (2013)

    ADS  Google Scholar 

  95. N. Schuch, I. Cirac, D. Pérez-García, Ann. Phys. 325, 2153 (2010)

    ADS  MATH  Google Scholar 

  96. L. Tagliacozzo, G. Vidal, Phys. Rev. B 83, 115127 (2011)

    ADS  Google Scholar 

  97. S. Dusuel, M. Kamfor, R. Orús, K.P. Schmidt, J. Vidal, Phys. Rev. Lett. 106, 107203 (2011)

    ADS  Google Scholar 

  98. L. Tagliacozzo, A. Celi, M. Lewenstein, Phys. Rev. X 4, 041024 (2014)

    Google Scholar 

  99. E. Rico, T. Pichler, M. Dalmonte, P. Zoller, S. Montangero, Phys. Rev. Lett. 112, 201601 (2014)

    ADS  Google Scholar 

  100. B. Buyens, J. Haegeman, K. Van Acoleyen, H. Verschelde, F. Verstraete, Phys. Rev. Lett. 113, 091601 (2014)

    ADS  Google Scholar 

  101. J. Haegeman, K. Van Acoleyen, N. Schuch, J.I. Cirac, F. Verstraete, arxiv:1407.1025 (2014)

  102. P. Corboz, G. Evenbly, F. Verstraete, G. Vidal, Phys. Rev. A 81, 010303(R) (2010)

    ADS  Google Scholar 

  103. P. Corboz, G. Vidal, Phys. Rev. B 80, 165129 (2009)

    ADS  Google Scholar 

  104. P. Corboz, R. Orús, B. Bauer, G. Vidal, Phys. Rev. B 81, 165104 (2010)

    ADS  Google Scholar 

  105. D. Pérez-García, M.M. Wolf, M. Sanz, F. Verstraete, J.I. Cirac, Phys. Rev. Lett. 100, 167202 (2008)

    ADS  Google Scholar 

  106. M. Sanz, M.M. Wolf, D. Pérez-García, J.I. Cirac, Phys. Rev. A 79, 042308 (2009)

    ADS  Google Scholar 

  107. A. Altand, B. Simons, in Condensed Matter Field Theory (Cambridge University Press, 2006), p. 58

  108. M.P. Nightingale, J.C. Umrigar, Quantum Monte Carlo Methods in Physics and Chemistry (Springer, 1999)

  109. C.V. Kraus, N. Schuch, F. Verstraete, J.I. Cirac, Phys. Rev. A 81, 052338 (2010)

    ADS  MathSciNet  Google Scholar 

  110. I. Pizorn, F. Verstraete, Phys. Rev. B 81, 245110 (2010)

    ADS  Google Scholar 

  111. Q.-Q. Shi, S.-H. Li, J.-H. Zhao, H.-Q. Zhou, arXiv:0907.5520 (2009)

  112. C. Pineda, T. Barthel, J. Eisert, Phys. Rev. A 81, 050303(R) (2010)

    ADS  Google Scholar 

  113. T. Barthel, C. Pineda, J. Eisert, Phys. Rev. A 80, 042333 (2009)

    ADS  Google Scholar 

  114. P. Corboz, S. Capponi, A.M. Läuchli, B. Bauer, R. Orús, Europhys. Lett. 98, 27005 (2012)

    ADS  Google Scholar 

  115. L. Wang, P. Corboz, M. Troyer, New J. Phys. 16, 103008 (2014)

    ADS  Google Scholar 

  116. P. Corboz, S.R. White, G. Vidal, M. Troyer, Phys. Rev. B 84, 041108 (2011)

    ADS  Google Scholar 

  117. P. Corboz, T.M. Rice, M. Troyer, Phys. Rev. Lett. 113, 046402 (2014)

    ADS  Google Scholar 

  118. D. Poilblanc, P. Corboz, N. Schuch, J.I. Cirac, Phys. Rev. B 89, 241106 (2014)

    ADS  Google Scholar 

  119. J.I. Latorre, A. Riera, J. Phys. A 42, 504002 (2009)

    MathSciNet  Google Scholar 

  120. L. Amico, R. Fazio, A. Osterloh, V. Vedral, Rev. Mod. Phys. 80, 517 (2008)

    ADS  MATH  MathSciNet  Google Scholar 

  121. H. Li, F.D.M. Haldane, Phys. Rev. Lett. 101, 010504 (2008)

    ADS  Google Scholar 

  122. J.I. Cirac, D. Poilblanc, N. Schuch, F. Verstraete, Phys. Rev. B 83, 245134 (2011)

    ADS  Google Scholar 

  123. R. Orús, T.-C. Wei, O. Buerschaper, A. García-Saez, arXiv:1406.0585 (2014)

  124. D. Poilblanc, N. Schuch, D. Pérez-García, J.I. Cirac, Phys. Rev. B 86, 014404 (2012)

    ADS  Google Scholar 

  125. N. Schuch, D. Poilblanc, J.I. Cirac, D. Pérez-García, Phys. Rev. B 86, 115108 (2012)

    ADS  Google Scholar 

  126. N. Schuch, D. Poilblanc, J.I. Cirac, D. Pérez-García, Phys. Rev. Lett. 111, 090501 (2013)

    ADS  Google Scholar 

  127. D. Poilblanc, N. Schuch, Phys. Rev. B 87, 140407 (2013)

    ADS  Google Scholar 

  128. D. Poilblanc, N. Schuch, J.I. Cirac, Phys. Rev. B 88, 144414 (2013)

    ADS  Google Scholar 

  129. S. Yang, L. Lehman, D. Poilblanc, K. Van Acoleyen, F. Verstraete, J.I. Cirac, N. Schuch, Phys. Rev. Lett. 112, 036402 (2014)

    ADS  Google Scholar 

  130. N. Schuch, M.M. Wolf, F. Verstraete, J.I. Cirac, Phys. Rev. Lett. 98, 140506 (2007)

    ADS  MathSciNet  Google Scholar 

  131. J.M. Maldecena, Adv. Theor. Math. Phys. 2, 231 (1998)

    ADS  MathSciNet  Google Scholar 

  132. S.S. Gubser, I.R. Klebanov, A.M. Polyakov, Phys. Lett. B 428, 105 (1998)

    ADS  MathSciNet  Google Scholar 

  133. E. Witten, Adv. Theor. Math. Phys. 2, 253 (1998)

    ADS  MATH  MathSciNet  Google Scholar 

  134. B. Swingle, Phys. Rev. D 86, 065007 (2012)

    ADS  Google Scholar 

  135. H. Matsueda, arXiv:1208.5103 (2014)

  136. H. Matsueda, arXiv:1208.5305 (2012)

  137. J. Molina-Vilaplana, P. Sodano, JHEP 10, 011 (2011)

    ADS  Google Scholar 

  138. J. Molina-Vilaplana, arXiv:1109.5592 (2011)

  139. H. Matsueda, M. Ishihara, Y. Hashizume, arXiv:1208.0206 (2012)

  140. H. Matsueda, arXiv:1208.5106 (2012)

  141. J. Molina-Vilaplana, JHEP 05, 024 (2013)

    ADS  Google Scholar 

  142. J. Molina-Vilaplana, J. Prior, Gen. Relativ. Gravit. 46, 1823 (2014)

    ADS  MathSciNet  Google Scholar 

  143. S. Ryu, T. Takayanagi, Phys. Rev. Lett. 96, 181602 (2006)

    ADS  MathSciNet  Google Scholar 

  144. T. Nishioka, S. Ryu, T. Takayanagi, J. Phys. A 42, 504008 (2009)

    MathSciNet  Google Scholar 

  145. S. Sachdev, arXiv:1002.2947 (2010)

  146. G. Evenbly, G. Vidal, J. Stat. Phys. 145, 891 (2011)

    ADS  MATH  MathSciNet  Google Scholar 

  147. M. Van Raamsdonk, Gen. Rel. Grav. 42, 2323 (2010)

    ADS  MATH  Google Scholar 

  148. M. Van Raamsdonk, Int. J. Mod. Phys. D 19, 2429 (2010)

    ADS  MATH  Google Scholar 

  149. M. Van Raamsdonk, arXiv:0907.2939 (2010)

  150. T. Faulkner, M. Guica, T. Hartman, R.C. Myers, M. Van Raamsdonk, arXiv:1312.7856 (2013)

  151. B. Swingle, M. Van Raamsdonk, arXiv:1405.2933 (2014)

  152. J. Maldacena, L. Susskind, arXiv:1306.0533 (2013)

  153. J. Sonner, Phys. Rev. Lett. 1119, 211603 (2013)

    ADS  Google Scholar 

  154. M. Chernicoff, A. Guijosa, J.F. Pedraza, JHEP 1310, 211 (2013)

    ADS  Google Scholar 

  155. C. Fernández-González, N. Schuch, M.M. Wolf, J.I. Cirac, D. Pérez-García, Phys. Rev. Lett. 109, 260401 (2012)

    ADS  Google Scholar 

  156. R.N.C. Pfeifer, P. Corboz, O. Buerschaper, M. Aguado, M. Troyer, G. Vidal, Phys. Rev. B 82, 115126 (2010)

    ADS  Google Scholar 

  157. S. Singh, R.N.C. Pfeifer, G. Vidal, G.K. Brennen, Phys. Rev. B 89, 075112 (2014)

    ADS  Google Scholar 

  158. X. Chen, Z.-C. Gu, X.-G. Wen, Phys. Rev. B 84, 235128 (2011)

    ADS  Google Scholar 

  159. N. Schuch, D. Pérez-García, I. Cirac, Phys. Rev. B 84, 165139 (2011)

    ADS  Google Scholar 

  160. O. Buerschaper, Ann. Phys. 351, 447 (2014)

    ADS  Google Scholar 

  161. J. Dubail, N. Read, arXiv:1307.7726 (2013)

  162. T.B. Wahl, H.-H. Tu, N. Schuch, J.I. Cirac, Phys. Rev. Lett. 111, 236805 (2013)

    ADS  Google Scholar 

  163. T.B. Wahl, S.T. Haßler, H.-H. Tu, J.I. Cirac, N. Schuch, Phys. Rev. B 90, 115133 (2014)

    ADS  Google Scholar 

  164. V. Murg, V.E. Korepin, F. Verstraete, Phys. Rev. B 86, 045125 (2012)

    ADS  Google Scholar 

  165. A.J. Ferris, Phys. Rev. Lett. 113, 010401 (2014)

    ADS  Google Scholar 

  166. A.W. Sandvik, G. Vidal, Phys. Rev. Lett. 99, 220602 (2007)

    ADS  Google Scholar 

  167. N. Schuch, M.M. Wolf, F. Verstraete, J.I. Cirac, Phys. Rev. Lett. 100, 040501 (2008)

    ADS  MathSciNet  Google Scholar 

  168. F. Mezzacapo, N. Schuch, M. Boninsegni, J.I. Cirac, New J. Phys. 11, 083026 (2009)

    ADS  Google Scholar 

  169. I. Pizorn, L. Wang, F. Verstraete, Phys. Rev. A 83, 052321 (2011)

    ADS  Google Scholar 

  170. R.J. Baxter, Physica A 106, 18 (1981)

    ADS  MathSciNet  Google Scholar 

  171. R.J. Baxter, Exactly Solved Models in Statistical Mechanics (Academic Press, London, 1982)

  172. R.J. Baxter, J. Math. Phys. 9, 650 (1968)

    ADS  Google Scholar 

  173. R.J. Baxter, J. Stat. Phys. 19, 461 (1978)

    ADS  MathSciNet  Google Scholar 

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Orús, R. Advances on tensor network theory: symmetries, fermions, entanglement, and holography. Eur. Phys. J. B 87, 280 (2014). https://doi.org/10.1140/epjb/e2014-50502-9

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