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W. Shirley, K. Slagle, and X. Chen, Twisted foliated fracton phases
Original
1907
Earlier work this paper cites.
N. Seiberg, Field Theories With a Vector Global Symmetry
Original
1909
Earlier work this paper cites.
J. Haah, Local stabilizer codes in three dimensions without string logical operators
Original
1962
Earlier work this paper cites.
C. Hooley, On Artin’s conjecture
1967
Earlier work this paper cites.
K. A. Berman, Bicycles and spanning trees
1986
Earlier work this paper cites.
D. Dhar, Self-organized critical state of sandpile automaton models
1990
Earlier work this paper cites.
D. J. Lorenzini, A finite group attached to the laplacian of a graph
1991
Earlier work this paper cites.
Wiley, 5th ed., 1991
I. Niven, H. Zuckerman, and H. Montgomery, An Introduction to the Theory of Numbers · 1991
Earlier work this paper cites.
Published for the Conference Board of the mathematical sciences by the American Mathematical Society, 1997
F. Chung, Spectral Graph Theory · 1997
Earlier work this paper cites.
N. L. Biggs, Chip-firing and the critical group of a graph
1999
Earlier work this paper cites.
M. Pretko, X. Chen, and Y. You, Fracton Phases of Matter
Original
2001
Earlier work this paper cites.
S. Gao, Absolute irreducibility of polynomials via newton polytopes
2001
Earlier work this paper cites.
N. Seiberg and S.-H. Shao, Exotic Symmetries, Duality, and Fractons in 2+1-Dimensional Quantum Field Theory
Original
2003
Earlier work this paper cites.
S. Gao and V. M. Rodrigues, Irreducibility of polynomials modulo p via newton polytopes
2003
Earlier work this paper cites.
N. Seiberg and S.-H. Shao, Exotic U ⁡ ( 1 ) U(1) Symmetries, Duality, and Fractons in 3+1-Dimensional Quantum Field Theory
Original
2004
Earlier work this paper cites.
N. Seiberg and S.-H. Shao, Exotic ℤ N \mathbb{Z}_{N} Symmetries, Duality, and Fractons in 3+1-Dimensional Quantum Field Theory
Original
2004
Earlier work this paper cites.

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Wiley, 3rd ed., 2004
D. S. Dummit and R. M. Foote, Abstract Algebra · 2004
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2005
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P. Gorantla, H. T. Lam, N. Seiberg, and S.-H. Shao, More Exotic Field Theories in 3+1 Dimensions
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Then

H. Ma, M. Hermele, and X. Chen, Fracton topological order from the Higgs and partial-confinement mechanisms of rank-two gauge theory
Original
2018
Later among the works it cites.
R. M. Nandkishore and M. Hermele, Fractons
Original
2019
Later among the works it cites.
W. Shirley, K. Slagle, and X. Chen, Fractional excitations in foliated fracton phases
Original
2019
Later among the works it cites.
W. Shirley, K. Slagle, and X. Chen, Foliated fracton order in the checkerboard model
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W. Shirley, K. Slagle, and X. Chen, Foliated fracton order from gauging subsystem symmetries
Original

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2022

Gapped Lineon and Fracton Models on Graphs

Gorantla, Pranay, Lam, Ho Tat, Seiberg, Nathan et al.

Understand

We introduce a $\mathbb{Z}_N$ stabilizer code that can be defined on any spatial lattice of the form $\Gamma\times C_{L_z}$, where $\Gamma$ is a general graph.

We also present the low-energy limit of this stabilizer code as a Euclidean lattice action, which we refer to as the anisotropic $\mathbb{Z}_N$ Laplacian model.
It is gapped, robust (i.e., stable under small deformations), and has lineons.
Its ground state degeneracy (GSD) is expressed in terms of a "mod $N$-reduction" of the Jacobian group of the graph $\Gamma$.

Built on

W. Shirley, K. Slagle, and X. Chen, Twisted foliated fracton phases
Original
1907
Earlier work this paper cites.
N. Seiberg, Field Theories With a Vector Global Symmetry
Original
1909
Earlier work this paper cites.
J. Haah, Local stabilizer codes in three dimensions without string logical operators
Original
1962
Earlier work this paper cites.
C. Hooley, On Artin’s conjecture
1967
Earlier work this paper cites.
K. A. Berman, Bicycles and spanning trees
1986
Earlier work this paper cites.
D. Dhar, Self-organized critical state of sandpile automaton models
1990
Earlier work this paper cites.
D. J. Lorenzini, A finite group attached to the laplacian of a graph
1991
Earlier work this paper cites.
Wiley, 5th ed., 1991
I. Niven, H. Zuckerman, and H. Montgomery, An Introduction to the Theory of Numbers · 1991
Earlier work this paper cites.
Published for the Conference Board of the mathematical sciences by the American Mathematical Society, 1997
F. Chung, Spectral Graph Theory · 1997
Earlier work this paper cites.
N. L. Biggs, Chip-firing and the critical group of a graph
1999
Earlier work this paper cites.
M. Pretko, X. Chen, and Y. You, Fracton Phases of Matter
Original
2001
Earlier work this paper cites.
S. Gao, Absolute irreducibility of polynomials via newton polytopes
2001
Earlier work this paper cites.
N. Seiberg and S.-H. Shao, Exotic Symmetries, Duality, and Fractons in 2+1-Dimensional Quantum Field Theory
Original
2003
Earlier work this paper cites.
S. Gao and V. M. Rodrigues, Irreducibility of polynomials modulo p via newton polytopes
2003
Earlier work this paper cites.
N. Seiberg and S.-H. Shao, Exotic U ⁡ ( 1 ) U(1) Symmetries, Duality, and Fractons in 3+1-Dimensional Quantum Field Theory
Original
2004
Earlier work this paper cites.
N. Seiberg and S.-H. Shao, Exotic ℤ N \mathbb{Z}_{N} Symmetries, Duality, and Fractons in 3+1-Dimensional Quantum Field Theory
Original
2004
Earlier work this paper cites.

Similar

Wiley, 3rd ed., 2004
D. S. Dummit and R. M. Foote, Abstract Algebra · 2004
Cited alongside, same era.
C. Chamon, Quantum glassiness in strongly correlated clean systems: An example of topological overprotection
2005
Cited alongside, same era.
P. Gorantla, H. T. Lam, N. Seiberg, and S.-H. Shao, More Exotic Field Theories in 3+1 Dimensions
Original
2007
Cited alongside, same era.
K. Slagle, Foliated Quantum Field Theory of Fracton Order
Original
2008
Cited alongside, same era.
D. Lorenzini, Smith normal form and laplacians
2008
Cited alongside, same era.
J. Haah, A degeneracy bound for homogeneous topological order

Then

H. Ma, M. Hermele, and X. Chen, Fracton topological order from the Higgs and partial-confinement mechanisms of rank-two gauge theory
Original
2018
Later among the works it cites.
R. M. Nandkishore and M. Hermele, Fractons
Original
2019
Later among the works it cites.
W. Shirley, K. Slagle, and X. Chen, Fractional excitations in foliated fracton phases
Original
2019
Later among the works it cites.
W. Shirley, K. Slagle, and X. Chen, Foliated fracton order in the checkerboard model
Original
2019
Later among the works it cites.
W. Shirley, K. Slagle, and X. Chen, Foliated fracton order from gauging subsystem symmetries
Original

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

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Original

2009

Cited alongside, same era.

P. Gorantla, H. T. Lam, N. Seiberg, and S.-H. Shao, fcc lattice, checkerboards, fractons, and quantum field theory

Original

2010

Cited alongside, same era.

T. Rudelius, N. Seiberg, and S.-H. Shao, Fractons with Twisted Boundary Conditions and Their Symmetries

Original

2012

Cited alongside, same era.

P. Moree, Artin’s primitive root conjecture - a survey

2012

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John Wiley & Sons, Ltd, 2nd ed., 2012

D. A. Cox, Galois Theory · 2012

Cited alongside, same era.

J. Haah, Commuting pauli hamiltonians as maps between free modules

Original

2013

Cited alongside, same era.

Springer New York, 2013

D. Eisenbud, Commutative Algebra: with a View Toward Algebraic Geometry · 2013

Cited alongside, same era.

2019