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This article reviews recent developments in the theoretical understanding and the numerical implementation of variational renormalization group methods using matrix product states and projected entangled pair states.
Proc. Roy. Soc. London
P. Dirac · 1926
Earlier work this paper cites.
Relationship between systems of impenetrable bosons and fermions in one dimension
M. Girardeau · 1960
Earlier work this paper cites.
Prog. Theor. Phys
J. Kondo · 1964
Earlier work this paper cites.
One-Dimensional Chain of Anisotropic Spin-Spin Interactions
C.N.Yang and C.P.Yang · 1966
Earlier work this paper cites.
J. Funct. Anal
E. Størmer · 1969
Earlier work this paper cites.
The renormalization group: Critical phenomena and the kondo problem
K. G. Wilson · 1975
Earlier work this paper cites.
Renormalization-group approach to the anderson model of dilute magnetic alloys. II. static properties for the asymmetric case
H. R. Krishna-murthy, J. W. Wilkins, and K. G. Wilson · 1980
Earlier work this paper cites.
Topics in quantum probability
L. Accardi · 1981
Earlier work this paper cites.
On the computational complexity of Ising spin-glass models
F. Barahona · 1982
Earlier work this paper cites.
Continuum dynamics of the 1-d heisenberg antiferromagnet: Identification with the o(3) nonlinear sigma model
F. D. Haldane · 1983
Earlier work this paper cites.
Nonlinear field theory of large-spin heisenberg antiferromagnets: Semiclassically quantized solitons of the one-dimensional easy-axis néel state
F. D. Haldane · 1983
Earlier work this paper cites.
On the quantum structure of a black hole
G.’Hooft · 1985
Earlier work this paper cites.
Quantum source of entropy for black holes
L. Bombelli, R. K. Koul, J. H. Lee, and R. D. Sorkin · 1986
Earlier work this paper cites.
Graph minors. ii. algorithmic aspects of tree-width
N. Robertson and P. D. Seymour · 1986
Earlier work this paper cites.
Commun. Math. Phys
I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki · 1988
Earlier work this paper cites.
The xy model has long-range order for all spins and all dimensions greater than 1
T. Kennedy, E. H. Lieb, and B. S. Shastry · 1988
Earlier work this paper cites.
Antiferromagnetic ground states of quantum spin chains
M. Fannes, B. Nachtergaele, and R. Werner · 1989
Earlier work this paper cites.
Boson localization and the superfluid-insulator transition
M. P. Fisher, P. B. Weichmann, G. Grinstein, and D. S. Fisher · 1989
Earlier work this paper cites.
Phys. Lett. A
M. Suzuki · 1990
Earlier work this paper cites.
J. Math. Phys
M. Suzuki · 1991
Earlier work this paper cites.
Ground states of vbs models on cayley trees
M. Fannes, B. Nachtergaele, and R. Werner · 1992
Earlier work this paper cites.
Comm. Math. Phys
M. Fannes, B. Nachtergaele, and R. F. Werner · 1992
Earlier work this paper cites.
Density-matrix algorithms for quantum renormalization groups
S. R. White · 1992
Earlier work this paper cites.
Density Matrix Formulation for Quantum Renormalization Groups
S. R. White · 1992
Earlier work this paper cites.
Europhys. Lett
A. Klümper, A. Schadschneider, and J. Zittartz · 1993
Earlier work this paper cites.
Entropy and area
M. Srednicki · 1993
Earlier work this paper cites.
On geometric entropy
C. Callan and F. Wilczek · 1994
Earlier work this paper cites.
Black hole thermodynamics and information loss in two dimensions
T. M. Fiola, J. Preskill, A. Strominger, and S. P. Trivedi · 1994
Earlier work this paper cites.
Z. Phys. B
C. Lange, A. Klümper, and J. Zittartz · 1994
Earlier work this paper cites.
Density-matrix algorithm for the calculation of dynamical properties of low-dimensional systems
K. A. Hallberg · 1995
Earlier work this paper cites.
Density Matrix Renormatlization Group Method for 2D Classical Models
T. Nishino · 1995
Earlier work this paper cites.
Thermodynamic limit of density matrix renormalization
S. Östlund and S. Rommer · 1995
Earlier work this paper cites.
J. Phys. Conden. Matter
R. J. Bursill, T. Xiang, and G. A. Gehring · 1996
Earlier work this paper cites.
Equilibrium dynamics of the dissipative two-state system
T. A. Costi and C. Kieffer · 1996
Earlier work this paper cites.
Phys. Rev. Lett
A. Kolezhuk, R. Roth, and U. Schollwöck · 1996
Earlier work this paper cites.
Z. Phys. B
H. Niggeman, A. Klümper, and J. Zittartz · 1997
Earlier work this paper cites.
Class of ansatz wave functions for one-dimensional spin systems and their relation to the density matrix renormalization group
S. Rommer and S. Östlund · 1997
Earlier work this paper cites.
Thermodynamics of the Anisotropic Heisenberg Chain Calculated by the Density Matrix Renormalization Group Method
N. Shibata · 1997
Earlier work this paper cites.
Transfer-matrix density-matrix renormalization-group theory for thermodynamics of one-dimensional quantum systems
X. Wang and T. Xiang · 1997
Earlier work this paper cites.
Robust convex optimization, Mathematics of Operational Research
A. Ben-Tal and A. Nemirovski · 1998
Earlier work this paper cites.
Scaling and universality in the anisotropic kondo model and the dissipative two-state system
T. A. Costi · 1998
Earlier work this paper cites.
Equivalence of the variational matrix product method and the density matrix renormalization group applied to spin chains
J. Dukelsky, M. A. Martin-Delgado, T. Nishino, and G. Sierra · 1998
Earlier work this paper cites.
Cold bosonic atoms in optical lattices
D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller · 1998
Earlier work this paper cites.
Phys. Rev. Lett
A. Kolezhuk and H. Mikeska · 1998
Earlier work this paper cites.
Density-Matrix Renormalization
I. Peschel, X. Wang, M. Kaulke, and K. Hallberg · 1998
Earlier work this paper cites.
New J. Phys
Y. Hieida, K. Okunishi, and Y. Akutsu · 1999
Cited alongside, same era.
Phys. Rev. B
A. Kolezhuk, H. Mikeska, K. Maisinger, and U. Schollwöck · 1999
Cited alongside, same era.
Dynamical correlation functions using the density matrix renormalization group
T. D. Kühner and S. R. White · 1999
Cited alongside, same era.
Ann. Physik (Leipzig)
I. Peschel, M. Kaulke, and O. Legeza · 1999
Cited alongside, same era.
Higher-order methods for quantum simulations
A. T. Sornborger and E. D. Stewart · 1999
Cited alongside, same era.
Distributed entanglement
V. Coffman, J. Kundu, and W. K. Wootters · 2000
Cited alongside, same era.
Quantum Computation and Quantum Information
M. A. Nielsen and I. L. Chuang · 2000
Real time evolution using the density matrix renormalization group
S. R. White and A. E. Feiguin · 2004
Later among the works it cites.
Entanglement frustration for gaussian states on symmetric graphs
M. M. Wolf, F. Verstraete, and J. Cirac · 2004
Later among the works it cites.
Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm
M. Zwolak and G. Vidal · 2004
Later among the works it cites.
Phys. Rev. B
A. Feiguin and S. White · 2005
Later among the works it cites.
Real-time dynamics in spin-(1/2) chains with adaptive time-dependent density matrix renormalization group
D. Gobert, C. Kollath, U. Schollwöck, and G. Schütz · 2005
Later among the works it cites.
A de finetti representation for finite symmetric quantum states
R. Koenig and R. Renner · 2005
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Cited alongside, same era.
Prog. Theor. Phys
K. Okunishi and T. Nishino · 2000
Cited alongside, same era.
Variational characterizations of separability and entanglement of formation
K. Audenaert, F. Verstraete, and B. D. Moor · 2001
Cited alongside, same era.
Exact diagonalization and quantum monte carlo study of the spin-1/2 XXZ model on the square lattice
H. Q. Lin, J. S. Flynn, and D. D. Betts · 2001
Cited alongside, same era.
Phys. Rev. B
M. A. Martin-Delgado, M. Roncaglia, and G. Sierra · 2001
Cited alongside, same era.
A one-way quantum computer
R. Raussendorf and H. J. Briegel · 2001
Cited alongside, same era.
Later among the works it cites.
Efficient evaluation of partition functions of frustrated and inhomogeneous spin systems
V. Murg, F. Verstraete, and J. I. Cirac · 2005
Later among the works it cites.
Exploiting quantum parallelism to simulate quantum random many-body systems
B. Paredes, F. Verstraete, and J. I. Cirac · 2005
Later among the works it cites.
Entropy, entanglement, and area: analytical results for harmonic lattice systems
M. B. Plenio, J. Eisert, J. Dreissig, and M. Cramer · 2005
Later among the works it cites.
The density-matrix renormalization group
U. Schollwöck · 2005
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Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
M. Troyer and U. Wiese · 2005
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Mapping local hamiltonians of fermions to local hamiltonians of spins
F. Verstraete and J. Cirac · 2005
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Renormalization group transformations on quantum states
F. Verstraete, J. Cirac, J. Latorre, E. Rico, and M. Wolf · 2005
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Variational matrix product state approach to quantum impurity models
F. Verstraete, A. Weichselbaum, U. Schollwöck, J. I. Cirac, and J. v. Delft · 2005
Later among the works it cites.
Phys. Rev. B
S. White · 2005
Later among the works it cites.
Ground-state approximation for strongly interacting spin systems in arbitrary spatial dimension
S. Anders, M. B. Plenio, W. Dür, F. Verstraete, and H. J. Briegel · 2006
Later among the works it cites.
Entanglement scaling in critical two-dimensional fermionic and bosonic systems
T. Barthel, M.-C. Chung, and U. Schollwöck · 2006
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Lieb-robinson bounds and the generation of correlations and topological quantum order
S. Bravyi, M. B. Hastings, and F. Verstraete · 2006
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One-and-a-half quantum de finetti theorems
M. Christandl, R. Koenig, G. Mitchison, and R. Renner · 2006
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Quantum fidelity and quantum phase transitions in matrix product states
M. Cozzini, R. Ionicioiu, and P. Zanardi · 2006
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Computational difficulty of global variations in the density matrix renormalization group
J. Eisert · 2006
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Time evolution algorithms for matrix product states and DMRG
J. J. García-Ripoll · 2006
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Entanglement entropy of fermions in any dimension and the widom conjecture
D. Gioev and I. Klich · 2006
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Solving gapped hamiltonians locally
M. B. Hastings · 2006
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Variational treatment of the Shastry-Sutherland antiferromagnet using Projected Entangled Pair States (PEPS)
A. Isacsson and O. F. Syljuasen · 2006
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Detecting topological order in a ground state wave function
M. Levin and X. G. Wen · 2006
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A renormalisation-group algorithm for eigenvalue density functions of interacting quantum systems
T. J. Osborne · 2006
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General monogamy inequality for bipartite qubit entanglement
T. J. Osborne and F. Verstraete · 2006
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Matrix product state representations
D. Perez-Garcia, F. Verstraete, M. Wolf, and J. Cirac · 2006
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Renormalization algorithm for the calculation of spectra of interacting quantum systems
D. Porras, F. Verstraete, and J. I. Cirac · 2006
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Classical simulation of quantum many-body systems with a tree tensor network
Y. Shi, L. Duan, and G. Vidal · 2006
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Matrix product states represent ground states faithfully
F. Verstraete and J. Cirac · 2006
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Criticality, the area law, and the computational power of peps
F. Verstraete, M. M. Wolf, D. Perez-Garcia, and J. I. Cirac · 2006
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A class of quantum many-body states that can be efficiently simulated
G. Vidal · 2006
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Violation of the entropic area law for fermions
M. M. Wolf · 2006
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Statistics dependence of the entanglement entropy
M. Cramer, J. Eisert, and M. B. Plenio · 2007
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An area law for one dimensional quantum systems
M. Hastings · 2007
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Entropy and entanglement in quantum ground states
M. B. Hastings · 2007
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Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
J. Jordan, R. Orus, G. Vidal, F. Verstraete, and J. I. Cirac · 2007
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Variational study of hard-core bosons in a two-dimensional optical lattice using projected entangled pair states
V. Murg, F. Verstraete, and J. I. Cirac · 2007
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Classical simulation of infinite-size quantum lattice systems in one spatial dimension
G. Vidal · 2007
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Entanglement renormalization
G. Vidal · 2007
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Phys. Rev. Lett
S. R. White and A. Chernyshev · 2007
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Area laws in quantum systems: mutual information and correlations
M. Wolf, F. Verstraete, M. Hastings, and J. Cirac · 2007
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