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Gapped fracton phases of matter generalize the concept of topological order and broaden our fundamental understanding of entanglement in quantum many-body systems.
F. J. Wegner, Duality in Generalized Ising Models and Phase Transitions without Local Order Parameters, Journal of Mathematical Physics 12
1971
Earlier work this paper cites.
A. Polyakov, Quark confinement and topology of gauge theories, Nuclear Physics B 120
1977
Earlier work this paper cites.
J. B. Kogut, An introduction to lattice gauge theory and spin systems, Rev. Mod. Phys. 51
1979
Earlier work this paper cites.
M. Creutz, Monte carlo study of quantized su(2) gauge theory, Phys. Rev. D 21
1980
Earlier work this paper cites.
G. Bhanot and M. Creutz, Phase diagram of Z ( N ) Z(N) and U(1) gauge theories in three dimensions, Phys. Rev. D 21
1980
Earlier work this paper cites.
G. Savvidy and F. Wegner, Geometrical string and spin systems, Nuclear Physics B 413
1994
Earlier work this paper cites.
R. Pietig and F. Wegner, Low temperature expansion of the gonihedric Ising model, Nuclear Physics B 525
1998
Earlier work this paper cites.
M. Oshikawa, Ordered phase and scaling in Z n {Z}_{n} models and the three-state antiferromagnetic Potts model in three dimensions, Phys. Rev. B 61
2000
Earlier work this paper cites.
M. Campostrini, M. Hasenbusch, A. Pelissetto, P. Rossi, and E. Vicari, Critical behavior of the three-dimensional XY \mathrm{XY} universality class, Phys. Rev. B 63
2001
Earlier work this paper cites.
A. Kitaev, Fault-tolerant quantum computation by anyons, Annals of Physics 303
2003
Earlier work this paper cites.
E. Ardonne, P. Fendley, and E. Fradkin, Topological order and conformal quantum critical points, Annals of Physics 310
2004
Earlier work this paper cites.
C. L. Henley, From classical to quantum dynamics at Rokhsar–Kivelson points, Journal of Physics: Condensed Matter 16
2004
Earlier work this paper cites.
C. Xu and J. E. Moore, Strong-Weak Coupling Self-Duality in the Two-Dimensional Quantum Phase Transition of p + i p p+ip Superconducting Arrays, Phys. Rev. Lett. 93
2004
Earlier work this paper cites.
T. Senthil, A. Vishwanath, L. Balents, S. Sachdev, and M. P. A. Fisher, Deconfined Quantum Critical Points, Science 303
2004
Earlier work this paper cites.
C. Chamon, Quantum Glassiness in Strongly Correlated Clean Systems: An Example of Topological Overprotection, Phys. Rev. Lett. 94
2005
Earlier work this paper cites.
A. Hamma, P. Zanardi, and X.-G. Wen, String and membrane condensation on three-dimensional lattices, Phys. Rev. B 72
2005
Earlier work this paper cites.
C. Xu and J. Moore, Reduction of effective dimensionality in lattice models of superconducting arrays and frustrated magnets, Nuclear Physics B 716
2005
Earlier work this paper cites.
J. Nocedal and S. J. Wright, Numerical Optimization , 2nd ed. (Springer, New York, NY, USA, 2006)
2006
Earlier work this paper cites.
S. Trebst, P. Werner, M. Troyer, K. Shtengel, and C. Nayak, Breakdown of a Topological Phase: Quantum Phase Transition in a Loop Gas Model with Tension, Phys. Rev. Lett. 98
2007
Earlier work this paper cites.
C. Nayak, S. H. Simon, A. Stern, M. Freedman, and S. Das Sarma, Non-abelian anyons and topological quantum computation, Rev. Mod. Phys. 80
2008
Earlier work this paper cites.
C. Xu and C. Wu, Resonating plaquette phases in SU(4) Heisenberg antiferromagnet, Phys. Rev. B 77
2008
Earlier work this paper cites.
H. Li and F. D. M. Haldane, Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States, Phys. Rev. Lett. 101
2008
Earlier work this paper cites.
2010
Earlier work this paper cites.
C. Castelnovo, S. Trebst, and M. Troyer, Topological Order and Quantum Criticality, in Understanding Quantum Phase Transitions (Taylor & Francis, 2010) pp. 169–192
2010
Earlier work this paper cites.
J. Haah, Local stabilizer codes in three dimensions without string logical operators, Phys. Rev. A 83
2011
Earlier work this paper cites.
S. V. Isakov, P. Fendley, A. W. W. Ludwig, S. Trebst, and M. Troyer, Dynamics at and near conformal quantum critical points, Phys. Rev. B 83
2011
Earlier work this paper cites.
J. I. Cirac, D. Poilblanc, N. Schuch, and F. Verstraete, Entanglement spectrum and boundary theories with projected entangled-pair states, Phys. Rev. B 83
2011
Earlier work this paper cites.
Z. Y. Xie, J. Chen, M. P. Qin, J. W. Zhu, L. P. Yang, and T. Xiang, Coarse-graining renormalization by higher-order singular value decomposition, Phys. Rev. B 86
2012
Earlier work this paper cites.
X.-L. Qi, H. Katsura, and A. W. W. Ludwig, General Relationship between the Entanglement Spectrum and the Edge State Spectrum of Topological Quantum States, Phys. Rev. Lett. 108
2012
Earlier work this paper cites.
B. Yoshida, Exotic topological order in fractal spin liquids, Phys. Rev. B 88
2013
Cited alongside, same era.
N. Schuch, D. Poilblanc, J. I. Cirac, and D. Pérez-García, Topological Order in the Projected Entangled-Pair States Formalism: Transfer Operator and Boundary Hamiltonians, Phys. Rev. Lett. 111
2013
Cited alongside, same era.
M. Mueller, W. Janke, and D. A. Johnston, Nonstandard Finite-Size Scaling at First-Order Phase Transitions, Phys. Rev. Lett. 112
2014
Cited alongside, same era.
O. Borisenko, V. Chelnokov, G. Cortese, M. Gravina, A. Papa, and I. Surzhikov, Critical behavior of 3D Z(N) lattice gauge theories at zero temperature, Nuclear Physics B 879
2014
Cited alongside, same era.
J. Haegeman, V. Zauner, N. Schuch, and F. Verstraete, Shadows of anyons and the entanglement structure of topological phases, Nature Communications 6
2015
H. Song, A. Prem, S.-J. Huang, and M. A. Martin-Delgado, Twisted fracton models in three dimensions, Phys. Rev. B 99
2019
Later among the works it cites.
M. Pretko, X. Chen, and Y. You, Fracton phases of matter, International Journal of Modern Physics A 35
2020
Later among the works it cites.
D. Aasen, D. Bulmash, A. Prem, K. Slagle, and D. J. Williamson, Topological defect networks for fractons of all types, Phys. Rev. Research 2
2020
Later among the works it cites.
M.-Y. Li and P. Ye, Fracton physics of spatially extended excitations, Phys. Rev. B 101
2020
Later among the works it cites.
N. Seiberg, Field theories with a vector global symmetry, SciPost Physics 8
2020
Later among the works it cites.
J.-K. Yuan, S. A. Chen, and P. Ye, Fractonic superfluids, Physical Review Research 2
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S. Vijay, J. Haah, and L. Fu, Fracton topological order, generalized lattice gauge theory, and duality, Phys. Rev. B 94
2016
Cited alongside, same era.
L. Vanderstraeten, J. Haegeman, P. Corboz, and F. Verstraete, Gradient methods for variational optimization of projected entangled-pair states, Phys. Rev. B 94
2016
Cited alongside, same era.
P. Corboz, Variational optimization with infinite projected entangled-pair states, Phys. Rev. B 94
2016
Cited alongside, same era.
X.-G. Wen, Colloquium: Zoo of quantum-topological phases of matter, Rev. Mod. Phys. 89
2017
Cited alongside, same era.
H. Ma, E. Lake, X. Chen, and M. Hermele, Fracton topological order via coupled layers, Phys. Rev. B 95
2017
Cited alongside, same era.
M. Pretko, Subdimensional particle structure of higher rank U ( 1 ) U(1) spin liquids, Phys. Rev. B 95
2017
Cited alongside, same era.
K. Slagle and Y. B. Kim, Fracton topological order from nearest-neighbor two-spin interactions and dualities, Phys. Rev. B 96
2017
Cited alongside, same era.
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Later among the works it cites.
M. Mühlhauser, M. R. Walther, D. A. Reiss, and K. P. Schmidt, Quantum robustness of fracton phases, Phys. Rev. B 101
2020
Later among the works it cites.
W.-T. Xu, Q. Zhang, and G.-M. Zhang, Tensor Network Approach to Phase Transitions of a Non-Abelian Topological Phase, Phys. Rev. Lett. 124
2020
Later among the works it cites.
Q. Zhang, W.-T. Xu, Z.-Q. Wang, and G.-M. Zhang, Non-Hermitian effects of the intrinsic signs in topologically ordered wavefunctions, Communications Physics 3
2020
Later among the works it cites.
J.-Y. Chen, S. Capponi, A. Wietek, M. Mambrini, N. Schuch, and D. Poilblanc, SU ( 3 ) 1 \mathrm{SU}(3{)}_{1} Chiral Spin Liquid on the Square Lattice: A View from Symmetric Projected Entangled Pair States, Phys. Rev. Lett. 125
2020
Later among the works it cites.
K. J. S. et al
2021
Later among the works it cites.
G. Semeghini, H. Levine, A. Keesling, S. Ebadi, T. T. Wang, D. Bluvstein, R. Verresen, H. Pichler, M. Kalinowski, R. Samajdar, A. Omran, S. Sachdev, A. Vishwanath, M. Greiner, V. Vuletić, and M. D. Lukin, Probing topological spin liquids on a programmable quantum simulator, Science 374
2021
Later among the works it cites.
K. Slagle, Foliated Quantum Field Theory of Fracton Order, Phys. Rev. Lett. 126
2021
Later among the works it cites.
M.-Y. Li and P. Ye, Fracton physics of spatially extended excitations. II. Polynomial ground state degeneracy of exactly solvable models, Phys. Rev. B 104
2021
Later among the works it cites.
N. Seiberg and S.-H. Shao, Exotic ℤ N \mathbb{Z}_{N} Symmetries, Duality, and Fractons in 3+1-Dimensional Quantum Field Theory, SciPost Phys. 10
2021
Later among the works it cites.
S. A. Chen, J.-K. Yuan, and P. Ye, Fractonic superfluids. II. Condensing subdimensional particles, Phys. Rev. Research 3
2021
Later among the works it cites.
H. Li and P. Ye, Renormalization group analysis on emergence of higher rank symmetry and higher moment conservation, Physical Review Research 3
2021
Later among the works it cites.
T. F. J. Poon and X.-J. Liu, Quantum phase transition of fracton topological orders, Phys. Rev. Research 3
2021
Later among the works it cites.
E. Lake and M. Hermele, Subdimensional criticality: Condensation of lineons and planons in the X-cube model, Phys. Rev. B 104
2021
Later among the works it cites.
J. I. Cirac, D. Pérez-García, N. Schuch, and F. Verstraete, Matrix product states and projected entangled pair states: Concepts, symmetries, theorems, Rev. Mod. Phys. 93
2021
Later among the works it cites.
M. Iqbal and N. Schuch, Entanglement Order Parameters and Critical Behavior for Topological Phase Transitions and Beyond, Phys. Rev. X 11
2021
Later among the works it cites.
N. Tantivasadakarn, W. Ji, and S. Vijay, Hybrid fracton phases: Parent orders for liquid and nonliquid quantum phases, Phys. Rev. B 103
2021
Later among the works it cites.
D. J. Williamson, C. Delcamp, F. Verstraete, and N. Schuch, On the stability of topological order in tensor network states, Phys. Rev. B 104
2021
Later among the works it cites.
P. C. G. Vlaar and P. Corboz, Simulation of three-dimensional quantum systems with projected entangled-pair states, Phys. Rev. B 103
2021
Later among the works it cites.
C. Stahl, E. Lake, and R. Nandkishore, Spontaneous breaking of multipole symmetries, Phys. Rev. B 105
2022
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2022
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