Built on

G. Moore and N. Seiberg, Classical and quantum conformal field theory, Communications in Mathematical Physics 123
1989
Earlier work this paper cites.
R. Dijkgraaf and E. Witten, Topological gauge theories and group cohomology, Communications in Mathematical Physics 129
1990
Earlier work this paper cites.
D. N. YETTER, TQFTs From Homotopy 2-Types, Journal of Knot Theory and Its Ramifications 02
1993
Earlier work this paper cites.
L. Crane and D. Yetter, in Quantum (WORLD SCIENTIFIC, 1993) pp. 1–11, arXiv:arXiv:hep-th/9301062v1
1993
Earlier work this paper cites.
L. Crane and I. B. Frenkel, Four-dimensional topological quantum field theory, Hopf categories, and the canonical bases, Journal of Mathematical Physics 35
1994
Earlier work this paper cites.
A. R. Calderbank and P. W. Shor, Good quantum error-correcting codes exist, Physical Review A - Atomic, Molecular, and Optical Physics 54
1996
Earlier work this paper cites.
A. Steane, Multiple-particle interference and quantum error correction, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 452
1996
Earlier work this paper cites.
J. Scott Carter, L. H. Kauffman, and M. Saito, Structures and diagrammatics of four dimensional topological lattice field theories, Advances in Mathematics 146
1999
Earlier work this paper cites.
S. Lang, Algebra (Springer-Verlag New York, 2002)
2002
Earlier work this paper cites.
A. Y. Kitaev, Fault-tolerant quantum computation by anyons, Annals of Physics 303
2003
Earlier work this paper cites.
D. Eisenbud, Commutative Algebra: with a View Toward Algebraic Geometry , 1st ed., Graduate Texts in Mathematics, Vol. 150 (Springer-Verlag New York, 2004)
2004
Earlier work this paper cites.
C. Chamon, Quantum glassiness in strongly correlated clean systems: An example of topological overprotection, Physical Review Letters 94
2005
Earlier work this paper cites.
A. Kitaev and J. Preskill, Topological entanglement entropy, Physical Review Letters 96
2005
Earlier work this paper cites.
Kitaev Alexei, Anyons in an exactly solved model and beyond, Annals of Physics 321
2006
Earlier work this paper cites.
M. Levin and X. G. Wen, Detecting topological order in a ground state wave function, Physical Review Letters 96
2006
Earlier work this paper cites.
C. Castelnovo, C. Chamon, and D. Sherrington, Quantum mechanical and information theoretic view on classical glass transitions, Physical Review B 81
Original
2010
Earlier work this paper cites.
J. Haah, Local stabilizer codes in three dimensions without string logical operators, Physical Review A - Atomic, Molecular, and Optical Physics 83
Original
2011
Earlier work this paper cites.
S. Bravyi and J. Haah, Energy landscape of 3D spin hamiltonians with topological order, Physical Review Letters 107
Original
2011
Earlier work this paper cites.
I. H. Kim, 3D local qupit quantum code without string logical operator, arXiv , 9 arXiv:1202.0052 (2012)
Original
2012
Earlier work this paper cites.
C. Castelnovo and C. Chamon, Topological quantum glassiness, Philosophical Magazine 92
Original
2012
Earlier work this paper cites.
K. Walker and Z. Wang, (3+1)-TQFTs and topological insulators, Frontiers of Physics 7
Original
2012
Earlier work this paper cites.
B. Yoshida, Exotic topological order in fractal spin liquids, Physical Review B 88
Original
2013
Earlier work this paper cites.
S. Bravyi and J. Haah, Quantum self-correction in the 3D cubic code model, Physical Review Letters 111
Original
2013
Earlier work this paper cites.

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2019

Compactifying fracton stabilizer models

Dua, Arpit, Williamson, Dominic J., Haah, Jeongwan et al.

Understand

We investigate two dimensional compactifications of three dimensional fractonic stabilizer models.

We find the two dimensional topological phases produced as a function of compactification radius for the X-cube model and Haah's cubic code.
Furthermore, we uncover translation symmetry-enrichment in the compactified cubic code that leads to twisted boundary conditions.

Built on

G. Moore and N. Seiberg, Classical and quantum conformal field theory, Communications in Mathematical Physics 123
1989
Earlier work this paper cites.
R. Dijkgraaf and E. Witten, Topological gauge theories and group cohomology, Communications in Mathematical Physics 129
1990
Earlier work this paper cites.
D. N. YETTER, TQFTs From Homotopy 2-Types, Journal of Knot Theory and Its Ramifications 02
1993
Earlier work this paper cites.
L. Crane and D. Yetter, in Quantum (WORLD SCIENTIFIC, 1993) pp. 1–11, arXiv:arXiv:hep-th/9301062v1
1993
Earlier work this paper cites.
L. Crane and I. B. Frenkel, Four-dimensional topological quantum field theory, Hopf categories, and the canonical bases, Journal of Mathematical Physics 35
1994
Earlier work this paper cites.
A. R. Calderbank and P. W. Shor, Good quantum error-correcting codes exist, Physical Review A - Atomic, Molecular, and Optical Physics 54
1996
Earlier work this paper cites.
A. Steane, Multiple-particle interference and quantum error correction, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 452
1996
Earlier work this paper cites.
J. Scott Carter, L. H. Kauffman, and M. Saito, Structures and diagrammatics of four dimensional topological lattice field theories, Advances in Mathematics 146
1999
Earlier work this paper cites.
S. Lang, Algebra (Springer-Verlag New York, 2002)
2002
Earlier work this paper cites.
A. Y. Kitaev, Fault-tolerant quantum computation by anyons, Annals of Physics 303
2003
Earlier work this paper cites.
D. Eisenbud, Commutative Algebra: with a View Toward Algebraic Geometry , 1st ed., Graduate Texts in Mathematics, Vol. 150 (Springer-Verlag New York, 2004)
2004
Earlier work this paper cites.
C. Chamon, Quantum glassiness in strongly correlated clean systems: An example of topological overprotection, Physical Review Letters 94
2005
Earlier work this paper cites.
A. Kitaev and J. Preskill, Topological entanglement entropy, Physical Review Letters 96
2005
Earlier work this paper cites.
Kitaev Alexei, Anyons in an exactly solved model and beyond, Annals of Physics 321
2006
Earlier work this paper cites.
M. Levin and X. G. Wen, Detecting topological order in a ground state wave function, Physical Review Letters 96
2006
Earlier work this paper cites.
C. Castelnovo, C. Chamon, and D. Sherrington, Quantum mechanical and information theoretic view on classical glass transitions, Physical Review B 81
Original
2010
Earlier work this paper cites.
J. Haah, Local stabilizer codes in three dimensions without string logical operators, Physical Review A - Atomic, Molecular, and Optical Physics 83
Original
2011
Earlier work this paper cites.
S. Bravyi and J. Haah, Energy landscape of 3D spin hamiltonians with topological order, Physical Review Letters 107
Original
2011
Earlier work this paper cites.
I. H. Kim, 3D local qupit quantum code without string logical operator, arXiv , 9 arXiv:1202.0052 (2012)
Original
2012
Earlier work this paper cites.
C. Castelnovo and C. Chamon, Topological quantum glassiness, Philosophical Magazine 92
Original
2012
Earlier work this paper cites.
K. Walker and Z. Wang, (3+1)-TQFTs and topological insulators, Frontiers of Physics 7
Original
2012
Earlier work this paper cites.
B. Yoshida, Exotic topological order in fractal spin liquids, Physical Review B 88
Original
2013
Earlier work this paper cites.
S. Bravyi and J. Haah, Quantum self-correction in the 3D cubic code model, Physical Review Letters 111
Original
2013
Earlier work this paper cites.