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In these lecture notes we give a technical overview of tangent-space methods for matrix product states in the thermodynamic limit.
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1997
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T. Nishino and K. Okunishi, “Corner Transfer Matrix Algorithm for Classical Renormalization Group,”
1997
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F. Verstraete, J. J. García-Ripoll, and J. I. Cirac, “Matrix Product Density Operators: Simulation of Finite-Temperature and Dissipative Systems,”
2004
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G. Vidal, “Efficient simulation of one-dimensional quantum many-body systems,”
2004
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S. R. White and A. E. Feiguin, “Real-time evolution using the density matrix renormalization group,”
2004
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A. J. Daley, C. Kollath, U. Schollwöck, and G. Vidal, “Time-dependent density-matrix renormalization-group using adaptive effective hilbert spaces,”
2004
Earlier work this paper cites.
F. Verstraete and J. I. Cirac, “Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions,”
2004
Earlier work this paper cites.
D. Pérez-García, F. Verstraete, M. M. Wolf, and J. I. Cirac, “Matrix Product State Representations,”
2006
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J. F. Bonnans, J. C. Gilbert, C. Lemaréchal, and C. A. Sagastizábal, Numerical Optimization (Springer-Verlag Berlin Heidelberg, 2006)
2006
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G. Vidal, “Classical Simulation of Infinite-Size Quantum Lattice Systems in One Spatial Dimension,”
2007
Earlier work this paper cites.
F. Verstraete, V. Murg, and J. I. Cirac, “Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems,”
2008
Earlier work this paper cites.
D. Pérez-García, M. Wolf, M. Sanz, F. Verstraete, and J. I. Cirac, “String Order and Symmetries in Quantum Spin Lattices,”
2008
Earlier work this paper cites.
R. Orús and G. Vidal, “Infinite time-evolving block decimation algorithm beyond unitary evolution,”
2008
Earlier work this paper cites.
I. P. McCulloch, “Infinite size density matrix renormalization group, revisited,”
2008
Earlier work this paper cites.
C. Lubich, From Quantum to Classical Molecular Dynamics: Reduced Models and Numerical Analysis (Zurich Lectures in Advanced Mathematics, 2008)
2008
Earlier work this paper cites.
H. Jiang, Z. Weng, and T. Xiang, “Accurate Determination of Tensor Network State of Quantum Lattice Models in Two Dimensions,”
2008
Cited alongside, same era.
J. Jordan, R. Orús, G. Vidal, F. Verstraete, and J. I. Cirac, “Classical Simulation of Infinite-Size Quantum Lattice Systems in Two Spatial Dimensions,”
2008
Cited alongside, same era.
R. Orús and G. Vidal, “Simulation of two-dimensional quantum systems on an infinite lattice revisited: Corner transfer matrix for tensor contraction,”
2009
Cited alongside, same era.
B. Pirvu, V. Murg, J. I. Cirac, and F. Verstraete, “Matrix product operator representations,”
2010
Cited alongside, same era.
F. Verstraete and J. I. Cirac, “Continuous matrix product states for quantum fields,”
2010
Cited alongside, same era.
L. Vanderstraeten, F. Verstraete, and J. Haegeman, “Scattering particles in quantum spin chains,”
2015
Later among the works it cites.
J. Haegeman, V. Zauner, N. Schuch, and F. Verstraete, “Shadows of anyons and the entanglement structure of topological phases,”
2015
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L. Vanderstraeten, M. Mariën, F. Verstraete, and J. Haegeman, “Excitations and the tangent space of projected entangled-pair states,”
2015
Later among the works it cites.
J. Rincón, M. Ganahl, and G. Vidal, “Lieb-liniger model with exponentially decaying interactions: A continuous matrix product state study,”
2015
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H. N. Phien, J. A. Bengua, H. D. Tuan, P. Corboz, and R. Orús, “Infinite projected entangled pair states algorithm improved: Fast full update and gauge fixing,”
2015
Later among the works it cites.
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T. J. Osborne, J. Eisert, and F. Verstraete, “Holographic quantum states,”
2010
Cited alongside, same era.
J. Haegeman, J. I. Cirac, T. J. Osborne, H. Verschelde, and F. Verstraete, “Applying the variational principle to ( 1 + 1 1+1 )-dimensional quantum field theories,”
2010
Cited alongside, same era.
F. Pollmann, A. M. Turner, E. Berg, and M. Oshikawa, “Entanglement spectrum of a topological phase in one dimension,”
2010
Cited alongside, same era.
U. Schollwöck, “The density-matrix renormalization group in the age of matrix product states,”
2011
Cited alongside, same era.
J. Haegeman, J. I. Cirac, T. J. Osborne, I. Pizorn, H. Verschelde, and F. Verstraete, “Time-Dependent Variational Principle for Quantum Lattices,”
2011
Cited alongside, same era.
X. Chen, Z.-C. Gu, and X.-G. Wen, “Classification of gapped symmetric phases in one-dimensional spin systems,”
2011
Cited alongside, same era.
T. Koffel, M. Lewenstein, and L. Tagliacozzo, “Entanglement Entropy for the Long-Range Ising Chain in a Transverse Field,”
2012
Cited alongside, same era.
J. Haegeman, C. Lubich, I. Oseledets, B. Vandereycken, and F. Verstraete, “Unifying time evolution and optimization with matrix product states,”
2016
Later among the works it cites.
B. Buyens, J. Haegeman, H. Verschelde, F. Verstraete, and K. Van Acoleyen, “Confinement and string breaking for QED 2 \text{QED}_{2} in the hamiltonian picture,”
2016
Later among the works it cites.
V. Zauner, D. Draxler, L. Vanderstraeten, J. Haegeman, and F. Verstraete, “Symmetry breaking and the geometry of reduced density matrices,”
2016
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P. Corboz, “Variational optimization with infinite projected entangled-pair states,”
2016
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J. C. Halimeh and V. Zauner-Stauber, “Dynamical phase diagram of quantum spin chains with long-range interactions,”
2017
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J. C. Halimeh, V. Zauner-Stauber, I. P. McCulloch, I. de Vega, U. Schollwöck, and M. Kastner, “Prethermalization and persistent order in the absence of a thermal phase transition,”
2017
Later among the works it cites.
L. Vanderstraeten, Tensor Network States and Effective Particles for Low-Dimensional Quantum Spin Systems (Springer International Publishing, 2017)
2017
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J. Haegeman and F. Verstraete, “Diagonalizing Transfer Matrices and Matrix Product Operators: A Medley of Exact and Computational Methods,”
2017
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J. Haegeman, D. Draxler, V. Stojevic, J. I. Cirac, T. J. Osborne, and F. Verstraete, “Quantum Gross-Pitaevskii Equation,”
2017
Later among the works it cites.
M. Ganahl, J. Rincón, and G. Vidal, “Continuous matrix product states for quantum fields: An energy minimization algorithm,”
2017
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N. Bultinck, D. J. Williamson, J. Haegeman, and F. Verstraete, “Fermionic matrix product states and one-dimensional topological phases,”
2017
Later among the works it cites.
2017
Later among the works it cites.
D. Draxler, J. Haegeman, F. Verstraete, and M. Rizzi, “Continuous matrix product states with periodic boundary conditions and an application to atomtronics,”
2017
Later among the works it cites.
2017
Later among the works it cites.
M. M. Rams, P. Czarnik, and L. Cincio, “Precise extrapolation of the correlation function asymptotics in uniform tensor network states with application to the bose-hubbard and xxz models,”
2018
Closest in time.
C. Hubig, J. Haegeman, and U. Schollwöck, “Error estimates for extrapolations with matrix-product states,”
2018
Closest in time.
L. Vanderstraeten, M. Van Damme, H. P. Büchler, and F. Verstraete, “Quasiparticles in quantum spin chains with long-range interactions,”
2018
Closest in time.
M. T. Fishman, L. Vanderstraeten, V. Zauner-Stauber, J. Haegeman, and F. Verstraete, “Faster methods for contracting infinite two-dimensional tensor networks,”
2018
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A. Hallam, J. Morley, and A. G. Green, “The Lyapunov Spectrum of Quantum Thermalisation,”
2018
Closest in time.
M. Ganahl and G. Vidal, “Continuous matrix product states for nonrelativistic quantum fields: A lattice algorithm for inhomogeneous systems,”
2018
Closest in time.