Gauge-free duality in pure square spin ice: Topological currents and monopoles
Abstract
We consider pure square spin ice, that is, square ice, where only nearest neighbors are coupled. The gauge-free duality between the perpendicular and collinear structure leads to a natural description in terms of topological currents and charges as the relevant degrees of freedom. That, in turn, can be expressed via a continuous field theory where the discrete spins are subsumed into entropic interactions among charges and currents. This approach produces structure factors, correlations, and susceptibilities for spins, monopoles, and currents. It also generalizes the height formalism of the disordered ground state to non-zero temperature. The framework can be applied to the zoology of recent experimental results, especially realizations on quantum annealers, and can be expanded to include longer range interactions.
- Publication Date:
- Research Org.:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE Laboratory Directed Research and Development (LDRD) Program
- OSTI Identifier:
- 1829635
- Alternate Identifier(s):
- OSTI ID: 1825209
- Report Number(s):
- LA-UR-21-28824
Journal ID: ISSN 2158-3226; TRN: US2216836
- Grant/Contract Number:
- 89233218CNA000001
- Resource Type:
- Accepted Manuscript
- Journal Name:
- AIP Advances
- Additional Journal Information:
- Journal Volume: 11; Journal Issue: 10; Journal ID: ISSN 2158-3226
- Publisher:
- American Institute of Physics (AIP)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 36 MATERIALS SCIENCE; Material Science; Statistical mechanics models; Geometric topology; Entropy; Electrostatics; Magnetism; Free energy; Electrodynamics; Chemical physics; Phase transitions; Magnetic ordering
Citation Formats
Nisoli, Cristiano. Gauge-free duality in pure square spin ice: Topological currents and monopoles. United States: N. p., 2021.
Web. doi:10.1063/5.0070545.
Nisoli, Cristiano. Gauge-free duality in pure square spin ice: Topological currents and monopoles. United States. https://doi.org/10.1063/5.0070545
Nisoli, Cristiano. Fri .
"Gauge-free duality in pure square spin ice: Topological currents and monopoles". United States. https://doi.org/10.1063/5.0070545. https://www.osti.gov/servlets/purl/1829635.
@article{osti_1829635,
title = {Gauge-free duality in pure square spin ice: Topological currents and monopoles},
author = {Nisoli, Cristiano},
abstractNote = {We consider pure square spin ice, that is, square ice, where only nearest neighbors are coupled. The gauge-free duality between the perpendicular and collinear structure leads to a natural description in terms of topological currents and charges as the relevant degrees of freedom. That, in turn, can be expressed via a continuous field theory where the discrete spins are subsumed into entropic interactions among charges and currents. This approach produces structure factors, correlations, and susceptibilities for spins, monopoles, and currents. It also generalizes the height formalism of the disordered ground state to non-zero temperature. The framework can be applied to the zoology of recent experimental results, especially realizations on quantum annealers, and can be expanded to include longer range interactions.},
doi = {10.1063/5.0070545},
journal = {AIP Advances},
number = 10,
volume = 11,
place = {United States},
year = {Fri Oct 08 00:00:00 EDT 2021},
month = {Fri Oct 08 00:00:00 EDT 2021}
}
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Works referenced in this record:
The color of magnetic monopole noise
journal, September 2021
- Nisoli, Cristiano
- EPL (Europhysics Letters)
Superferromagnetism and Domain-Wall Topologies in Artificial “Pinwheel” Spin Ice
journal, January 2019
- Li, Yue; Paterson, Gary W.; Macauley, Gavin M.
- ACS Nano
Interaction modifiers in artificial spin ices
journal, February 2018
- Östman, Erik; Stopfel, Henry; Chioar, Ioan-Augustin
- Nature Physics, Vol. 14, Issue 4
The concept of spin ice graphs and a field theory for their charges
journal, November 2020
- Nisoli, Cristiano
- AIP Advances, Vol. 10, Issue 11
Exactly Solvable Model for the Roughening Transition of a Crystal Surface
journal, May 1977
- van Beijeren, Henk
- Physical Review Letters, Vol. 38, Issue 18
Signatures of farther neighbor couplings in artificial square ice
journal, March 2021
- Brunn, O.; Perrin, Y.; Canals, B.
- Physical Review B, Vol. 103, Issue 9
Dumping topological charges on neighbors: ice manifolds for colloids and vortices
journal, November 2014
- Nisoli, Cristiano
- New Journal of Physics, Vol. 16, Issue 11
Crystallites of magnetic charges in artificial spin ice
journal, August 2013
- Zhang, Sheng; Gilbert, Ian; Nisoli, Cristiano
- Nature, Vol. 500, Issue 7464
Realization of Rectangular Artificial Spin Ice and Direct Observation of High Energy Topology
journal, October 2017
- Ribeiro, I. R. B.; Nascimento, F. S.; Ferreira, S. O.
- Scientific Reports, Vol. 7, Issue 1
Thermal ground-state ordering and elementary excitations in artificial magnetic square ice
journal, November 2010
- Morgan, Jason P.; Stein, Aaron; Langridge, Sean
- Nature Physics, Vol. 7, Issue 1
Advances in artificial spin ice
journal, November 2019
- Skjærvø, Sandra H.; Marrows, Christopher H.; Stamps, Robert L.
- Nature Reviews Physics, Vol. 2, Issue 1
Magnetic order and energy-scale hierarchy in artificial spin-ice structures
journal, July 2018
- Stopfel, Henry; Östman, Erik; Chioar, Ioan-Augustin
- Physical Review B, Vol. 98, Issue 1
The Structure and Entropy of Ice and of Other Crystals with Some Randomness of Atomic Arrangement
journal, December 1935
- Pauling, Linus
- Journal of the American Chemical Society, Vol. 57, Issue 12
Observation of magnetic fragmentation in spin ice
journal, April 2016
- Petit, S.; Lhotel, E.; Canals, B.
- Nature Physics, Vol. 12, Issue 8
Defects dynamics following thermal quenches in square spin ice
journal, June 2013
- Levis, Demian; Cugliandolo, Leticia F.
- Physical Review B, Vol. 87, Issue 21
Dipolar Interactions and Origin of Spin Ice in Ising Pyrochlore Magnets
journal, April 2000
- den Hertog, Byron C.; Gingras, Michel J. P.
- Physical Review Letters, Vol. 84, Issue 15
A Theory of Water and Ionic Solution, with Particular Reference to Hydrogen and Hydroxyl Ions
journal, August 1933
- Bernal, J. D.; Fowler, R. H.
- The Journal of Chemical Physics, Vol. 1, Issue 8
Dispersion and Absorption in Dielectrics I. Alternating Current Characteristics
journal, April 1941
- Cole, Kenneth S.; Cole, Robert H.
- The Journal of Chemical Physics, Vol. 9, Issue 4
Thermodynamic phase transitions in a frustrated magnetic metamaterial
journal, September 2015
- Anghinolfi, L.; Luetkens, H.; Perron, J.
- Nature Communications, Vol. 6, Issue 1
Thermal fluctuations in artificial spin ice
journal, June 2014
- Kapaklis, Vassilios; Arnalds, Unnar B.; Farhan, Alan
- Nature Nanotechnology, Vol. 9, Issue 7, p. 514-519
Magnetic relaxation in rare-earth oxide pyrochlores
journal, September 2005
- Ryzhkin, I. A.
- Journal of Experimental and Theoretical Physics, Vol. 101, Issue 3
Generalized longitudinal susceptibility for magnetic monopoles in spin ice
journal, December 2012
- Bramwell, Steven T.
- Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 370, Issue 1981
The magnetic structure factor of the square ice: A phenomenological description
journal, March 2021
- Rougemaille, N.; Canals, B.
- Applied Physics Letters, Vol. 118, Issue 11
From confinement to deconfinement of magnetic monopoles in artificial rectangular spin ices
journal, November 2012
- Nascimento, F. S.; Mól, L. A. S.; Moura-Melo, W. A.
- New Journal of Physics, Vol. 14, Issue 11
Lattice Statistics of Hydrogen Bonded Crystals. I. The Residual Entropy of Ice
journal, August 1966
- Nagle, J. F.
- Journal of Mathematical Physics, Vol. 7, Issue 8
Direct Observation of Thermal Relaxation in Artificial Spin Ice
journal, August 2013
- Farhan, A.; Derlet, P. M.; Kleibert, A.
- Physical Review Letters, Vol. 111, Issue 5
Critical Behavior of Two-Dimensional Hydrogen-Bonded Antiferroelectrics
journal, June 1969
- Wu, F. Y.
- Physical Review Letters, Vol. 22, Issue 22
Long-Range Order at Low Temperatures in Dipolar Spin Ice
journal, July 2001
- Melko, Roger G.; den Hertog, Byron C.; Gingras, Michel J. P.
- Physical Review Letters, Vol. 87, Issue 6
Unhappy vertices in artificial spin ice: new degeneracies from vertex frustration
journal, April 2013
- Morrison, Muir J.; Nelson, Tammie R.; Nisoli, Cristiano
- New Journal of Physics, Vol. 15, Issue 4
Emergent magnetic monopole dynamics in macroscopically degenerate artificial spin ice
journal, February 2019
- Farhan, Alan; Saccone, Michael; Petersen, Charlotte F.
- Science Advances, Vol. 5, Issue 2
The “Coulomb Phase” in Frustrated Systems
journal, August 2010
- Henley, Christopher L.
- Annual Review of Condensed Matter Physics, Vol. 1, Issue 1
Correlation functions for two-dimensional ferroelectrics
journal, April 1968
- Sutherland, B.
- Physics Letters A, Vol. 26, Issue 11
Coulomb Phase Diagnostics as a Function of Temperature, Interaction Range, and Disorder
journal, March 2013
- Sen, Arnab; Moessner, R.; Sondhi, S. L.
- Physical Review Letters, Vol. 110, Issue 10
Exploring thermally induced states in square artificial spin-ice arrays
journal, May 2013
- Porro, J. M.; Bedoya-Pinto, A.; Berger, A.
- New Journal of Physics, Vol. 15, Issue 5
The configurational entropy in the Jaccard theory of the electrical properties of ice
journal, January 1997
- Ryzhkin, I. A.; Whitworth, R. W.
- Journal of Physics: Condensed Matter, Vol. 9, Issue 2
Equilibrium field theory of magnetic monopoles in degenerate square spin ice: Correlations, entropic interactions, and charge screening regimes
journal, December 2020
- Nisoli, Cristiano
- Physical Review B, Vol. 102, Issue 22
Effective Temperature in an Interacting Vertex System: Theory and Experiment on Artificial Spin Ice
journal, July 2010
- Nisoli, Cristiano; Li, Jie; Ke, Xianglin
- Physical Review Letters, Vol. 105, Issue 4
How ‘spin ice’ freezes
journal, September 2001
- Snyder, J.; Slusky, J. S.; Cava, R. J.
- Nature, Vol. 413, Issue 6851
Configurational Statistics
journal, January 1978
- Nagle, J. F.
- Journal of Glaciology, Vol. 21, Issue 85
Screening and the pinch point paradox in spin ice
journal, March 2020
- Twengström, Mikael; Henelius, Patrik; Bramwell, Steven T.
- Physical Review Research, Vol. 2, Issue 1
Magnetic Coulomb Phase in the Spin Ice Ho2Ti2O7
journal, September 2009
- Fennell, T.; Deen, P. P.; Wildes, A. R.
- Science, Vol. 326, Issue 5951
Theory of the dielectric constant of ice
journal, November 1979
- Nagle, J. F.
- Chemical Physics, Vol. 43, Issue 3
Fragmentation of magnetism in artificial kagome dipolar spin ice
journal, May 2016
- Canals, Benjamin; Chioar, Ioan-Augustin; Nguyen, Van-Dai
- Nature Communications, Vol. 7, Issue 1
Zero-point entropy in ‘spin ice’
journal, May 1999
- Ramirez, A. P.; Hayashi, A.; Cava, R. J.
- Nature, Vol. 399, Issue 6734
Extensive degeneracy, Coulomb phase and magnetic monopoles in artificial square ice
journal, November 2016
- Perrin, Yann; Canals, Benjamin; Rougemaille, Nicolas
- Nature, Vol. 540, Issue 7633
Phase transition in the two-dimensional Coulomb gas, and the interfacial roughening transition
journal, December 1976
- Chui, S. T.; Weeks, J. D.
- Physical Review B, Vol. 14, Issue 11
New two-color dimer models with critical ground states
journal, February 1997
- Raghavan, R.; Henley, Christopher L.; Arouh, Scott L.
- Journal of Statistical Physics, Vol. 86, Issue 3-4
Artificial ‘spin ice’ in a geometrically frustrated lattice of nanoscale ferromagnetic islands
journal, January 2006
- Wang, R. F.; Nisoli, C.; Freitas, R. S.
- Nature, Vol. 439, Issue 7074
Polarization fluctuations in ferroelectric models
journal, January 1981
- Youngblood, R. W.; Axe, J. D.
- Physical Review B, Vol. 23, Issue 1
Ordering, metastability and phase transitions in two-dimensional systems
journal, April 1973
- Kosterlitz, J M; Thouless, D J
- Journal of Physics C: Solid State Physics, Vol. 6, Issue 7, p. 1181-1203
Low-energy states, ground states, and variable frustrations of the finite-size dipolar Cairo lattices
journal, April 2021
- Makarova, Kseniia; Strongin, Vladislav; Titovets, Iuliia
- Physical Review E, Vol. 103, Issue 4
Emergent dynamic chirality in a thermally driven artificial spin ratchet
journal, October 2017
- Gliga, Sebastian; Hrkac, Gino; Donnelly, Claire
- Nature Materials, Vol. 16, Issue 11
Thermalized ground state of artificial kagome spin ice building blocks
journal, September 2012
- Arnalds, Unnar B.; Farhan, Alan; Chopdekar, Rajesh V.
- Applied Physics Letters, Vol. 101, Issue 11
Magnetic monopole noise
journal, July 2019
- Dusad, Ritika; Kirschner, Franziska K. K.; Hoke, Jesse C.
- Nature, Vol. 571, Issue 7764
Spin Ice State in Frustrated Magnetic Pyrochlore Materials
journal, November 2001
- Bramwell, S. T.
- Science, Vol. 294, Issue 5546
Artificial ferroic systems: novel functionality from structure, interactions and dynamics
journal, August 2013
- Heyderman, L. J.; Stamps, R. L.
- Journal of Physics: Condensed Matter, Vol. 25, Issue 36
Deliberate exotic magnetism via frustration and topology
journal, March 2017
- Nisoli, Cristiano; Kapaklis, Vassilios; Schiffer, Peter
- Nature Physics, Vol. 13, Issue 3
Brownian motion and quantum dynamics of magnetic monopoles in spin ice
journal, February 2013
- Bovo, L.; Bloxsom, J. A.; Prabhakaran, D.
- Nature Communications, Vol. 4, Issue 1
Thermal Quenches in Spin Ice
journal, March 2010
- Castelnovo, C.; Moessner, R.; Sondhi, S. L.
- Physical Review Letters, Vol. 104, Issue 10
Magnetic monopoles in spin ice
journal, January 2008
- Castelnovo, C.; Moessner, R.; Sondhi, S. L.
- Nature, Vol. 451, Issue 7174
Qubit spin ice
journal, July 2021
- King, Andrew D.; Nisoli, Cristiano; Dahl, Edward D.
- Science, Vol. 373, Issue 6554
Classical height models with topological order
journal, April 2011
- Henley, Christopher L.
- Journal of Physics: Condensed Matter, Vol. 23, Issue 16
Artificial spin ice: Paths forward
journal, March 2021
- Schiffer, Peter; Nisoli, Cristiano
- Applied Physics Letters, Vol. 118, Issue 11
Thermodynamics of irreversible processes applied to ice
journal, December 1964
- Jaccard, C.
- Physik der Kondensierten Materie, Vol. 3, Issue 2
Works referencing / citing this record:
The early-time Lieb-Robinson correlation function for qubit arrays
preprint, January 2022
- Mahoney, Brendan J.; Lent, Craig S.
- arXiv