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News on tensor network algorithms Romn Ors Donostia International Physics Center (DIPC) December 6th 2018 S. S. Jahromi, RO, M. Kargarian, A. Langari, PRB 97, 115162 (2018) S. S. Jahromi, RO, PRB 98, 155108 (2018) S. S. Jahromi, RO,

  1. News on tensor network algorithms Román Orús Donostia International Physics Center (DIPC) December 6th 2018 S. S. Jahromi, RO, M. Kargarian, A. Langari, PRB 97, 115162 (2018) S. S. Jahromi, RO, PRB 98, 155108 (2018) S. S. Jahromi, RO, arXiv:1808.00680 P. Schmoll, S. Singh, M. Rizzi, RO, arXiv:1809.08180 A. Kshetrimayum, M. Rizzi, J. Eisert, RO, arXiv:1809.08258 P. Schmoll, A. Haller, M. Rizzi, RO, arXiv:1812.01311

  2. Applications welcomed

  3. Tens nsor ne networks ks everyw ywhe here Quantum gravity, HEP and lattice gauge theories string theory and AdS/CFT Quantum information Strongly correlated systems and computation Classical statistical mechanics Quantum simulations Entanglement and Tensor Networks Numerical tensor calculus Nuclear physics Quantum chemistry AI, Deep learning & Linguistics Materials science

  4. Outli line ne 1) iPEPS for the ruby model 2) iPEPS & VBS phases on the star lattice 3) gPEPS and the structure matrix 4) iDMRG for SU(2)-invariant chiral ladder Overview, omit many technical details

  5. Outli line ne 1) iPEPS for the ruby model 2) iPEPS & VBS phases on the star lattice 3) gPEPS and the structure matrix 4) iDMRG for SU(2)-invariant chiral ladder S. S. Jahromi, RO, M. Kargarian, A. Langari, PRB 97, 115162 (2018)

  6. <latexit sha1_base64="4ZPoby6jmn0eEuamn8SqoWsFkI4=">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</latexit> <latexit sha1_base64="4ZPoby6jmn0eEuamn8SqoWsFkI4=">ACTHicbVBNSwMxEM3Wr1q/qh69BIvgocquCHoRil6KpwrWFrp1mU3TNjbZXZKsWJf9gV48ePNXePGgiGBaV9HqQODNe2+YyfMjzpS27UcrNzU9MzuXny8sLC4trxRX1y5UGEtC6yTkoWz6oChnAa1rpjltRpKC8Dlt+IOTkd64plKxMDjXw4i2BfQC1mUEtKG8IqniI7yDXRUL3GBR30wxE0ZD8v4NsWnXsb9MuzgxJUCm50DlaZGYz0BHrv89o7q6/eK5bsXtc+C9wMlBCWdW84oPbCUksaKAJB6Vajh3pdgJSM8JpWnBjRSMgA+jRloEBCKrayTiMFG8ZpoO7oTQv0HjM/pxIQCg1FL5xCtB9NamNyP+0Vqy7h+2EBVGsaUA+F3VjnWIR8niDpOUaD40AIhk5lZM+iCBaJN/wYTgTH75L7jY23UMPtsvVY6zOPJoA2ibeSgA1RBVRDdUTQHXpCL+jVurerTfr/dOas7KZdfSrcrMfMKqyZw=</latexit> <latexit sha1_base64="4ZPoby6jmn0eEuamn8SqoWsFkI4=">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</latexit> <latexit sha1_base64="4ZPoby6jmn0eEuamn8SqoWsFkI4=">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</latexit> The he rub ruby mo model X X σ α i σ α H = − J α j α = x,y,z α − links Reproduces the low-energy sector of the topological color code model in its gapped phase (Z 2 x Z 2 topological order) E. Bombin, M. A. Martin-Delgado, PRL 97, 180501 (2006) Coarse-graining triangles leads to brickwall lattice Study with iPEPS

  7. <latexit sha1_base64="VAfDML2SnCzWpqlIkq/yMgNv+Eg=">AB/HicbZDLSgMxFIbP1Fut9Eu3QSLIAhlpgi6EYpupKsK9gLtMGTSTBuauZBkxLHUV3HjQhG3Pog738Z0OgtPZDw8f/nkJPfizmTyrK+jcLK6tr6RnGztLW9s7tn7h+0ZQIQlsk4pHoelhSzkLaUkx2o0FxYHacbX8/8zj0VkXhnUpj6gR4GDKfEay05JrlhvuATlHDTbP7EV2imtWrKqVFVoGO4cK5NV0za/+ICJQENFOJayZ1uxciZYKEY4nZb6iaQxJmM8pD2NIQ6odCbZ8lN0rJUB8iOhT6hQpv6emOBAyjTwdGeA1UguejPxP6+XKP/CmbAwThQNyfwhP+FIRWiWBowQYniqQZMBNO7IjLCAhOl8yrpEOzFLy9Du1a1Nd+eVepXeRxFOIQjOAEbzqEON9CEFhBI4Rle4c14Ml6Md+Nj3low8pky/Cnj8wflfZJU</latexit> <latexit sha1_base64="VAfDML2SnCzWpqlIkq/yMgNv+Eg=">AB/HicbZDLSgMxFIbP1Fut9Eu3QSLIAhlpgi6EYpupKsK9gLtMGTSTBuauZBkxLHUV3HjQhG3Pog738Z0OgtPZDw8f/nkJPfizmTyrK+jcLK6tr6RnGztLW9s7tn7h+0ZQIQlsk4pHoelhSzkLaUkx2o0FxYHacbX8/8zj0VkXhnUpj6gR4GDKfEay05JrlhvuATlHDTbP7EV2imtWrKqVFVoGO4cK5NV0za/+ICJQENFOJayZ1uxciZYKEY4nZb6iaQxJmM8pD2NIQ6odCbZ8lN0rJUB8iOhT6hQpv6emOBAyjTwdGeA1UguejPxP6+XKP/CmbAwThQNyfwhP+FIRWiWBowQYniqQZMBNO7IjLCAhOl8yrpEOzFLy9Du1a1Nd+eVepXeRxFOIQjOAEbzqEON9CEFhBI4Rle4c14Ml6Md+Nj3low8pky/Cnj8wflfZJU</latexit> <latexit sha1_base64="VAfDML2SnCzWpqlIkq/yMgNv+Eg=">AB/HicbZDLSgMxFIbP1Fut9Eu3QSLIAhlpgi6EYpupKsK9gLtMGTSTBuauZBkxLHUV3HjQhG3Pog738Z0OgtPZDw8f/nkJPfizmTyrK+jcLK6tr6RnGztLW9s7tn7h+0ZQIQlsk4pHoelhSzkLaUkx2o0FxYHacbX8/8zj0VkXhnUpj6gR4GDKfEay05JrlhvuATlHDTbP7EV2imtWrKqVFVoGO4cK5NV0za/+ICJQENFOJayZ1uxciZYKEY4nZb6iaQxJmM8pD2NIQ6odCbZ8lN0rJUB8iOhT6hQpv6emOBAyjTwdGeA1UguejPxP6+XKP/CmbAwThQNyfwhP+FIRWiWBowQYniqQZMBNO7IjLCAhOl8yrpEOzFLy9Du1a1Nd+eVepXeRxFOIQjOAEbzqEON9CEFhBI4Rle4c14Ml6Md+Nj3low8pky/Cnj8wflfZJU</latexit> <latexit sha1_base64="VAfDML2SnCzWpqlIkq/yMgNv+Eg=">AB/HicbZDLSgMxFIbP1Fut9Eu3QSLIAhlpgi6EYpupKsK9gLtMGTSTBuauZBkxLHUV3HjQhG3Pog738Z0OgtPZDw8f/nkJPfizmTyrK+jcLK6tr6RnGztLW9s7tn7h+0ZQIQlsk4pHoelhSzkLaUkx2o0FxYHacbX8/8zj0VkXhnUpj6gR4GDKfEay05JrlhvuATlHDTbP7EV2imtWrKqVFVoGO4cK5NV0za/+ICJQENFOJayZ1uxciZYKEY4nZb6iaQxJmM8pD2NIQ6odCbZ8lN0rJUB8iOhT6hQpv6emOBAyjTwdGeA1UguejPxP6+XKP/CmbAwThQNyfwhP+FIRWiWBowQYniqQZMBNO7IjLCAhOl8yrpEOzFLy9Du1a1Nd+eVepXeRxFOIQjOAEbzqEON9CEFhBI4Rle4c14Ml6Md+Nj3low8pky/Cnj8wflfZJU</latexit> Ene nergies a and nd pha hase di diag agram ram Ground state energy Multicritical point −1.05 −0.55 J c =(0.8, 0.8, 0.4) J=(1, 1, 1) −1.06 −0.56 iPEPS FU iPEPS FU Comparison to exact diag. ED (N=24) −1.07 ED (N=24) −0.57 −1.08 for 24 sites. −0.58 −1.09 ε 0 ε 0 −1.1 −0.59 Good convergence. −1.11 −0.6 Multicritical point challenging. −1.12 −0.61 −1.13 −1.14 −0.62 0.1 0.2 0.3 0.4 0.5 0.6 0.1 0.2 0.3 0.4 0.5 0.6 1/D 1/D Phase diagram 3 phases separated by 2nd order QPTs. J x + J y + J z = 2 QPTs meet at a multicritical point. A 1 phase: gapped, Z 2 x Z 2 TO. A 2 & A 3 phases: gapless. Gapped by a perturbation, colored Ising anyons. S. S. Jahromi, M. Kargarian, S. F. Masoudi, A. Langari, PRB 94, 125145 (2016)

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