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We show how fermionic statistics can be naturally incorporated in tensor networks on arbitrary graphs through the use of graded Hilbert spaces.
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Existence of long-range order in one and two dimensions ,
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There are no goldstone bosons in two dimensions ,
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Quantum mechanics of fractional-spin particles ,
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Density matrix formulation for quantum renormalization groups ,
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Corner transfer matrix renormalization group method ,
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Corner transfer matrix algorithm for classical renormalization group ,
T. Nishino and K. Okunishi, · 1997
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Valence-bond states for quantum computation ,
F. Verstraete and J. I. Cirac, · 2004
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Renormalization algorithms for quantum-many body systems in two and higher dimensions ,
F. Verstraete and J. I. Cirac, · 2004
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The One-Dimensional Hubbard Model ,
F. H. L. Essler, H. Frahm, F. Göhmann, A. Klümper and V. E. Korepin, · 2005
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Matrix product states represent ground states faithfully ,
F. Verstraete and J. I. Cirac, · 2006
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An area law for one-dimensional quantum systems ,
M. B. Hastings, · 2007
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Classical simulation of infinite-size quantum lattice systems in one spatial dimension ,
G. Vidal, · 2007
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Scaling of entanglement support for matrix product states ,
L. Tagliacozzo, T. R. de Oliveira, S. Iblisdir and J. I. Latorre, · 2008
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Class of quantum many-body states that can be efficiently simulated ,
G. Vidal, · 2008
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String order and symmetries in quantum spin lattices ,
D. Pérez-García, M. M. Wolf, M. Sanz, F. Verstraete and J. I. Cirac, · 2008
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Infinite size density matrix renormalization group, revisited (2008), arXiv:0804.2509
I. P. McCulloch, · 2008
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Accurate determination of tensor network state of quantum lattice models in two dimensions ,
H. C. Jiang, Z. Y. Weng and T. Xiang, · 2008
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Classical simulation of infinite-size quantum lattice systems in two spatial dimensions ,
J. Jordan, R. Orús, G. Vidal, F. Verstraete and J. I. Cirac, · 2008
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Finite automata for caching in matrix product algorithms ,
G. M. Crosswhite and D. Bacon, · 2008
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Theory of finite-entanglement scaling at one-dimensional quantum critical points ,
F. Pollmann, S. Mukerjee, A. M. Turner and J. E. Moore, · 2009
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Simulation of two-dimensional quantum systems on an infinite lattice revisited: Corner transfer matrix for tensor contraction ,
R. Orús and G. Vidal, · 2009
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Fermionic multiscale entanglement renormalization ansatz ,
P. Corboz and G. Vidal, · 2009
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Contraction of fermionic operator circuits and the simulation of strongly correlated fermions ,
T. Barthel, C. Pineda and J. Eisert, · 2009
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Quantum circuits for strongly correlated quantum systems ,
F. Verstraete, J. I. Cirac and J. I. Latorre, · 2009
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Z.-C. Gu, F. Verstraete and X.-G. Wen, · 2010
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Simulation of interacting fermions with entanglement renormalization ,
P. Corboz, G. Evenbly, F. Verstraete and G. Vidal, · 2010
Cited alongside, same era.
Fermionic projected entangled pair states ,
C. V. Kraus, N. Schuch, F. Verstraete and J. I. Cirac, · 2010
Cited alongside, same era.
Unitary circuits for strongly correlated fermions ,
C. Pineda, T. Barthel and J. Eisert, · 2010
Cited alongside, same era.
Simulation of strongly correlated fermions in two spatial dimensions with fermionic projected entangled-pair states ,
P. Corboz, R. Orús, B. Bauer and G. Vidal, · 2010
Cited alongside, same era.
Simulation of fermionic lattice models in two dimensions with projected entangled-pair states: Next-nearest neighbor hamiltonians ,
P. Corboz, J. Jordan and G. Vidal, · 2010
Cited alongside, same era.
Schur Forms of Matrix Product Operators in the Infinite Limit ,
Classifying parafermionic gapped phases using matrix product states ,
W.-T. Xu and G.-M. Zhang, · 2018
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Period 4 stripe in the extended two-dimensional hubbard model ,
B. Ponsioen, S. S. Chung and P. Corboz, · 2019
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Tangent-space methods for uniform matrix product states ,
L. Vanderstraeten, J. Haegeman and F. Verstraete, · 2019
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Differentiable programming tensor networks ,
H.-J. Liao, J.-G. Liu, L. Wang and T. Xiang, · 2019
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A programming guide for tensor networks with global su2 symmetry ,
P. Schmoll, S. Singh, M. Rizzi and R. Orús, · 2020
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Local matrix product operators: Canonical form, compression, and control theory ,
D. E. Parker, X. Cao and M. P. Zaletel, · 2020
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L. Michel and I. P. McCulloch, · 2010
Cited alongside, same era.
Local tensor network for strongly correlated projective states ,
B. Béri and N. R. Cooper, · 2011
Cited alongside, same era.
Stripes in the two-dimensional t t - j j model with infinite projected entangled-pair states ,
P. Corboz, S. R. White, G. Vidal and M. Troyer, · 2011
Cited alongside, same era.
Time-dependent variational principle for quantum lattices ,
J. Haegeman, J. I. Cirac, T. J. Osborne, I. Pižorn, H. Verschelde and F. Verstraete, · 2011
Cited alongside, same era.
Matrix product states for critical spin chains: Finite-size versus finite-entanglement scaling ,
B. Pirvu, G. Vidal, F. Verstraete and L. Tagliacozzo, · 2012
Cited alongside, same era.
Variational matrix product ansatz for dispersion relations ,
J. Haegeman, B. Pirvu, D. J. Weir, J. I. Cirac, T. J. Osborne, H. Verschelde and F. Verstraete, · 2012
Cited alongside, same era.
Efficient simulation of grassmann tensor product states ,
Z.-C. Gu, · 2013
Cited alongside, same era.
Efficient variational contraction of two-dimensional tensor networks with a non-trivial unit cell ,
A. Nietner, B. Vanhecke, F. Verstraete, J. Eisert and L. Vanderstraeten, · 2020
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Matrix product states and projected entangled pair states: Concepts, symmetries, theorems ,
J. I. Cirac, D. Pérez-García, N. Schuch and F. Verstraete, · 2021
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A beginner’s guide to non-abelian ipeps for correlated fermions ,
B. Bruognolo, J.-W. Li, J. von Delft and A. Weichselbaum, · 2021
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Study of spin symmetry in the doped t − j t-j model using infinite projected entangled pair states ,
J.-W. Li, B. Bruognolo, A. Weichselbaum and J. von Delft, · 2021
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Efficient matrix product state methods for extracting spectral information on rings and cylinders ,
M. Van Damme, R. Vanhove, J. Haegeman, F. Verstraete and L. Vanderstraeten, · 2021
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Investigation of the néel phase of the frustrated heisenberg antiferromagnet by differentiable symmetric tensor networks ,
J. Hasik, D. Poilblanc and F. Becca, · 2021
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Variational methods for contracting projected entangled-pair states ,
L. Vanderstraeten, L. Burgelman, B. Ponsioen, M. Van Damme, B. Vanhecke, P. Corboz, J. Haegeman and F. Verstraete, · 2022
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Automatic differentiation applied to excitations with projected entangled pair states ,
B. Ponsioen, F. F. Assaad and P. Corboz, · 2022
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Simulating chiral spin liquids with projected entangled-pair states ,
J. Hasik, M. Van Damme, D. Poilblanc and L. Vanderstraeten, · 2022
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Tensor networks can resolve fermi surfaces ,
Q. Mortier, N. Schuch, F. Verstraete and J. Haegeman, · 2022
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Finite projected entangled pair states for the hubbard model ,
M. Scheb and R. M. Noack, · 2023
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Frustration-induced superconductivity in the t t - t ′ t^{\prime} hubbard model (2023), 2307.14835
C. Zhang, J.-W. Li and J. von Delft, · 2023
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Dualities in one-dimensional quantum lattice models: symmetric hamiltonians and matrix product operator intertwiners ,
L. Lootens, C. Delcamp, G. Ortiz and F. Verstraete, · 2023
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Differentiable programming tensor networks for kitaev magnets ,
X.-Y. Zhang, S. Liang, H.-J. Liao, W. Li and L. Wang, · 2023
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Finite-entanglement scaling of 2d metals ,
Q. Mortier, M.-H. Li, J. Haegeman and N. Bultinck, · 2023
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Unveiling correlated topological insulators through fermionic tensor network states – classification, edge theories and variational wavefunctions (2023), 2308.06543
C. Xu, Y. Ma and S. Jiang, · 2023
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Local jordan-wigner transformations on the torus ,
O. O’Brien, L. Lootens and F. Verstraete, · 2024
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Fermionic isometric tensor network states in two dimensions (2024), 2211.00043
Z. Dai, Y. Wu, T. Wang and M. P. Zaletel, · 2024
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TensorTrack ,
L. Devos, L. Burgelman, B. Vanhecke, J. Haegeman, F. Verstraete and L. Vanderstraeten, · 2024
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MPSKit ,
M. Van Damme, L. Devos and J. Haegeman, · 2024
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Dualities in one-dimensional quantum lattice models: topological sectors ,
L. Lootens, C. Delcamp and F. Verstraete, · 2024
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