20. References#

BC17

Jacob C Bridgeman and Christopher T Chubb. Hand-waving and interpretive dance: an introductory course on tensor networks. Journal of Physics A: Mathematical and Theoretical, 50(22):223001, 2017. arXiv:1603.03039, doi:10.1088/1751-8121/aa6dc3.

CC05

Pasquale Calabrese and John Cardy. Evolution of entanglement entropy in one-dimensional systems. Journal of Statistical Mechanics: Theory and Experiment, 2005(04):P04010, 2005. arXiv:cond-mat/0503393, doi:10.1088/1742-5468/2005/04/p04010.

DHMV23

Maarten Van Damme, Jutho Haegeman, Ian McCulloch, and Laurens Vanderstraeten. Efficient higher-order matrix product operators for time evolution. 2023. arXiv:2302.14181.

EY36

Carl Eckart and Gale Young. The approximation of one matrix by another of lower rank. Psychometrika, 1(3):211–218, Sep 1936. doi:10.1007/BF02288367.

FTL+07

Adrian Feiguin, Simon Trebst, Andreas WW Ludwig, Matthias Troyer, Alexei Kitaev, Zhenghan Wang, and Michael H Freedman. Interacting anyons in topological quantum liquids: the golden chain. Physical Review Letters, 98(16):160409, 2007. arXiv:cond-mat/0612341, doi:10.1103/PhysRevLett.98.160409.

HCO+11

Jutho Haegeman, J Ignacio Cirac, Tobias J Osborne, Iztok Pižorn, Henri Verschelde, and Frank Verstraete. Time-dependent variational principle for quantum lattices. Physical Review Letters, 107(7):070601, 2011. arXiv:1103.0936, doi:10.1103/PhysRevLett.107.070601.

HLO+16

Jutho Haegeman, Christian Lubich, Ivan Oseledets, Bart Vandereycken, and Frank Verstraete. Unifying time evolution and optimization with matrix product states. Physical Review B, 94:165116, 2016. arXiv:1408.5056, doi:10.1103/PhysRevB.94.165116.

HS05

Naomichi Hatano and Masuo Suzuki. Finding Exponential Product Formulas of Higher Orders. In Quantum Annealing and Other Optimization Methods, volume 679, pages 37–68. 2005. arXiv:math-ph/0506007, doi:10.1007/11526216_2.

HMSchollwock17

C. Hubig, I. P. McCulloch, and U. Schollwöck. Generic construction of efficient matrix product operators. Phys. Rev. B, 95:035129, Jan 2017. URL: https://link.aps.org/doi/10.1103/PhysRevB.95.035129, doi:10.1103/PhysRevB.95.035129.

JWX08

H. C. Jiang, Z. Y. Weng, and T. Xiang. Accurate determination of tensor network state of quantum lattice models in two dimensions. Physical Review Letters, 101(9):090603, 2008. arXiv:0806.3719, doi:10.1103/PhysRevLett.101.090603.

JOrusV+08

J. Jordan, R. Orús, G. Vidal, F. Verstraete, and J. I. Cirac. Classical Simulation of Infinite-Size Quantum Lattice Systems in Two Spatial Dimensions. Physical Review Letters, 101(25):250602, 2008. arXiv:cond-mat/0703788, doi:10.1103/PhysRevLett.101.250602.

Lan37

L. D. Landau. On the theory of phase transitions. Journal of Experimental and Theoretical Physics, 7:19–32, 1937. doi:10.1016/B978-0-08-010586-4.50034-1.

LOV15

Christian Lubich, Ivan V. Oseledets, and Bart Vandereycken. Time integration of tensor trains. SIAM Journal on Numerical Analysis, 53(2):917–941, 2015. arXiv:1407.2042, doi:10.1137/140976546.

Ons44

Lars Onsager. Crystal statistics. i. a two-dimensional model with an order-disorder transition. Physical Review, 65:117–149, 1944. doi:10.1103/PhysRev.65.117.

PHV14

Robert N. C. Pfeifer, Jutho Haegeman, and Frank Verstraete. Faster identification of optimal contraction sequences for tensor networks. Physical Review E, 90:033315, 2014. arXiv:1304.6112, doi:10.1103/PhysRevE.90.033315.

RCC18

Marek M. Rams, Piotr Czarnik, and Lukasz Cincio. Precise extrapolation of the correlation function asymptotics in uniform tensor network states with application to the Bose-Hubbard and XXZ models. Physical Review X, 8(4):041033, 2018. arXiv:1801.08554, doi:10.1103/PhysRevX.8.041033.

VHV19

Laurens Vanderstraeten, Jutho Haegeman, and Frank Verstraete. Tangent-space methods for uniform matrix product states. SciPost Physics Lecture Notes, pages 007, 2019. arXiv:1810.07006, doi:10.21468/SciPostPhysLectNotes.7.

VGarciaRC04

F. Verstraete, J. J. Garc\'ıa-Ripoll, and J. I. Cirac. Matrix product density operators: simulation of finite-temperature and dissipative systems. Physical Review Letters, 93:207204, 2004. arXiv:cond-mat/0406426, doi:10.1103/PhysRevLett.93.207204.

ZaunerStauberVF+18

V. Zauner-Stauber, L. Vanderstraeten, M. T. Fishman, F. Verstraete, and J. Haegeman. Variational optimization algorithms for uniform matrix product states. Physical Review B, 97(4):045145, 2018. arXiv:1701.07035, doi:10.1103/PhysRevB.97.045145.