Anomalies and entanglement renormalization

L. D. Landau and E. M. Lifshitz, Course of theoretical physics (Pergamon Press, 1965)

1965

Earlier work this paper cites.

L. P. Kadanoff, Scaling laws for Ising models near T c

1966

Earlier work this paper cites.

F. J. Wegner, Duality in generalized Ising models and phase transitions without local order parameters, J. Math. Phys. 12

1971

Earlier work this paper cites.

J. Wess and B. Zumino, Consequences of anomalous ward identities, Phys. Lett. B 37

1971

Earlier work this paper cites.

J. M. Kosterlitz and D. J. Thouless, Ordering, metastability and phase transitions in two-dimensional systems, J. Phys. C: Solid State Phys. 6

1973

Earlier work this paper cites.

K. G. Wilson, The renormalization group: Critical phenomena and the Kondo problem, Rev. Mod. Phys. 47

1975

Earlier work this paper cites.

G. ’t Hooft, Naturalness, chiral symmetry, and spontaneous chiral symmetry breaking, Recent Developments in Gauge Theories , 135 (1980)

1980

Earlier work this paper cites.

F. D. M. Haldane, Nonlinear Field Theory of Large-Spin Heisenberg Antiferromagnets: Semiclassically Quantized Solitons of the One-Dimensional Easy-Axis Néel State, Phys. Rev. Lett. 50

1983

Earlier work this paper cites.

V. Drinfel’d, Quantum groups, Proc. Int. Congr. Math. 1

1986

Earlier work this paper cites.

I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, Rigorous results on valence-bond ground states in antiferromagnets, Phys. Rev. Lett. 59

1987

Earlier work this paper cites.

S.-K. Yang, Modular invariant partition function of the Ashkin-Teller model on the critical line and N= 2 superconformal invariance, Nucl. Phys. B 285

1987

Earlier work this paper cites.

M. Baake, G. von Gehlen, and V. Rittenberg, Operator content of the Ashkin-Teller quantum chain-superconformal and Zamolodchikov-Fateev invariance: II. Boundary conditions compatible with the torus, J. Phys. A: Math. Gen. 20

1987

Earlier work this paper cites.

G. von Gehlen and V. Rittenberg, The Ashkin-Teller quantum chain and conformal invariance, J. Phys. A: Math. Gen 20

1987

Earlier work this paper cites.

X.-G. Wen, Vacuum degeneracy of chiral spin states in compactified space, Phys. Rev. B 40

1989

Earlier work this paper cites.

G. Moore and N. Seiberg, Classical and quantum conformal field theory, Commun. Math. Phys. 123

1989

Earlier work this paper cites.

T. Einarsson, Fractional statistics on a torus, Phys. Rev. Lett. 64

1990

Earlier work this paper cites.

X.-G. Wen, Topological Orders in Rigid States, Int. J. Mod. Phys. B 04

1990

Earlier work this paper cites.

P. Ginsparg, in Fields, Strings and Critical Phenomena , Les Houches 1988, Session XLIX, edited by E. Brézin and J. Z. Justin (North-Holland, Amsterdam, 1990) arXiv:hep-th/9108028

1990

Earlier work this paper cites.

S. R. White, Density matrix formulation for quantum renormalization groups, Phys. Rev. Lett. 69

1992

Earlier work this paper cites.

M. Fannes, B. Nachtergaele, and R. F. Werner, Finitely correlated states on quantum spin chains, Commun. Math. Phys. 144

1992

Earlier work this paper cites.

T. Kennedy and H. Tasaki, Hidden ℤ 2 × ℤ 2 {\mathbb{Z}}_{2}\times{\mathbb{Z}}_{2} symmetry breaking in Haldane-gap antiferromagnets, Phys. Rev. B 45

1992

Earlier work this paper cites.

A. Klümper, A. Schadschneider, and J. Zittartz, Matrix Product Ground States for One-Dimensional Spin-1 Quantum Antiferromagnets, EPL 24

1993

Earlier work this paper cites.

P. Christe and M. Henkel, Introduction to Conformal Invariance and Its Applications to Critical Phenomena (Springer-Verlag, Berlin, 1993) arXiv:cond-mat/9304035

1993

Earlier work this paper cites.

S. Östlund and S. Rommer, Thermodynamic Limit of Density Matrix Renormalization, Phys. Rev. Lett. 75

1995

Earlier work this paper cites.

M. de Wild Propitius, Topological interactions in broken gauge theories , Ph.D. thesis, University of Amsterdam, arXiv:hep-th/9511195 (1995)

1995

Earlier work this paper cites.

D. Evans and Y. Kawahigashi, On Ocneanu’s theory of asymptotic inclusions for subfactors, topological quantum field theories and quantum doubles, Int. J. Math. 6

1995

Earlier work this paper cites.

P. Di Francesco, Conformal field theory (Springer, New York, 1997)

1997

Earlier work this paper cites.

M. de Wild Propitius, (Spontaneously broken) Abelian Chern-Simons theories, Nucl. Phys. B 489

1997

Earlier work this paper cites.

J. Dukelsky, M. A. Martín-Delgado, T. Nishino, and G. Sierra, Equivalence of the variational matrix product method and the density matrix renormalization group applied to spin chains, EPL 43

1998

Earlier work this paper cites.

T. Nishino, Y. Hieida, K. Okunishi, N. Maeshima, Y. Akutsu, and A. Gendiar, Two-Dimensional Tensor Product Variational Formulation, Progr. Theor. Phys. 105

2001

Earlier work this paper cites.

B. Bakalov and A. A. Kirillov, Lectures on tensor categories and modular functors , Vol. 21 (American Mathematical Soc., 2001)

2001

Earlier work this paper cites.

M. Muger, From subfactors to categories and topology II: The quantum double of tensor categories and subfactors, J. Pure Appl. Algebr. 180

2003

Earlier work this paper cites.

F. Verstraete and J. I. Cirac, Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions, arXiv:cond-mat/0407066 (2004)

2004

Earlier work this paper cites.

J. Fröhlich, J. Fuchs, I. Runkel, and C. Schweigert, Kramers-wannier duality from conformal defects, Phys. Rev. Lett. 93

2004

Earlier work this paper cites.

P. Etingof, D. Nikshych, and V. Ostrik, On fusion categories, Ann. Math. , 581 arXiv:math/0203060 (2005)

2005

Earlier work this paper cites.

A. Kitaev and J. Preskill, Topological Entanglement Entropy, Phys. Rev. Lett. 96

2006

Earlier work this paper cites.

M. Levin and X.-G. Wen, Detecting Topological Order in a Ground State Wave Function, Phys. Rev. Lett. 96

2006

Cited alongside, same era.

A. Feiguin, S. Trebst, A. W. W. Ludwig, M. Troyer, A. Kitaev, Z. Wang, and M. H. Freedman, Interacting anyons in topological quantum liquids: The golden chain, Phys. Rev. Lett 95

2007

Cited alongside, same era.

D. Pérez-García, F. Verstraete, M. M. Wolf, and J. I. Cirac, Matrix Product State Representations, Quantum Info. Comput. 7

2007

Cited alongside, same era.

G. Vidal, Entanglement Renormalization, Phys. Rev. Lett. 99

2007

Cited alongside, same era.

J. Fröhlich, J. Fuchs, I. Runkel, and C. Schweigert, Duality and defects in rational conformal field theory, Nucl. Phys. B 763

2007

Cited alongside, same era.

D. V. Else, S. D. Bartlett, and A. C. Doherty, The hidden symmetry-breaking picture of symmetry-protected topological order, Phys. Rev. B 88

Original

2013

Later among the works it cites.

L. H. Santos and J. Wang, Symmetry-protected many-body Aharonov-Bohm effect, Phys. Rev. B 89

Original

2014

Later among the works it cites.

A. Kapustin, Symmetry protected topological phases, anomalies, and cobordisms: beyond group cohomology, arXiv:1403.1467 (2014)

Original

2014

Later among the works it cites.

D. V. Else and C. Nayak, Classifying symmetry-protected topological phases through the anomalous action of the symmetry on the edge, Phys. Rev. B 90

Original

2014

Later among the works it cites.

R. Orús, A practical introduction to tensor networks: Matrix product states and projected entangled pair states, Ann. Phys. 349