Confinement, reduced entanglement, and spin-glass order in a random quantum spin-ice model

Menon, Anirudha; Pardini, Tom; Singh, Rajiv R. P.

doi:10.1103/physrevb.101.184423

Title: Confinement, reduced entanglement, and spin-glass order in a random quantum spin-ice model

Journal Article · Thu May 21 00:00:00 EDT 2020 · Physical Review B

DOI:https://doi.org/10.1103/physrevb.101.184423· OSTI ID:1642496

^[1]; Pardini, Tom ^[2]; Singh, Rajiv R. P. ^[1]

Univ. of California, Davis, CA (United States)
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

In this work, we study an effective spin model derived perturbatively from a random transverse-field Ising model on the pyrochlore lattice. The model consists of spin configurations on the pyrochlore lattice, restricted to the spin-ice subspace, with spins interacting with random Ising exchange couplings as well as ring exchanges along the hexagons of the lattice. This model is studied by exact diagonalization up to N=64 site systems. Furthermore, we calculate spin-glass correlation functions and local entanglement entropy S_T between spins in a single tetrahedron and the rest of the system. We find that the model undergoes two phase transitions. At weak randomness the model is in a quantum spin-ice phase where S_T=ln 6. Increasing randomness, at low transverse fields, first leads to a frozen phase, with long-range spin-glass order and S_T=ln 2 corresponding to the Cat states associated with Ising order. Further increase in randomness leads to a random resonating-hexagon phase with a frozen backbone of spins and a broad distribution of entanglement entropies. The implications of these studies for non-Kramers rare-earth pyrochlores are discussed.

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Research Organization:: Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); National Science Foundation (NSF)

Grant/Contract Number:: AC52-07NA27344; DMR 1855111; PHY 1748958

OSTI ID:: 1642496

Report Number(s):: LLNL-JRNL-796781; 996944; TRN: US2201912

Journal Information:: Physical Review B, Vol. 101, Issue 18; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 1 work

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References (38)

Coulombic Quantum Liquids in Spin- $1 / 2$ Pyrochlores Savary, Lucile; Balents, Leon Physical Review Letters, Vol. 108, Issue 3 https://doi.org/10.1103/PhysRevLett.108.037202	journal	January 2012
Proximate Kitaev quantum spin liquid behaviour in a honeycomb magnet Banerjee, A.; Bridges, C. A.; Yan, J. -Q. Nature Materials, Vol. 15, Issue 7 https://doi.org/10.1038/nmat4604	journal	April 2016
Spin liquids in frustrated magnets Balents, Leon Nature, Vol. 464, Issue 7286 https://doi.org/10.1038/nature08917	journal	March 2010
Anyons in an exactly solved model and beyond Kitaev, Alexei Annals of Physics, Vol. 321, Issue 1 https://doi.org/10.1016/j.aop.2005.10.005	journal	January 2006
Cluster-Glass Phase in Pyrochlore $X Y$ Antiferromagnets with Quenched Disorder Andrade, Eric C.; Hoyos, José A.; Rachel, Stephan Physical Review Letters, Vol. 120, Issue 9 https://doi.org/10.1103/PhysRevLett.120.097204	journal	March 2018
Topography of Spin Liquids on a Triangular Lattice Zhu, Zhenyue; Maksimov, P. A.; White, Steven R. Physical Review Letters, Vol. 120, Issue 20 https://doi.org/10.1103/PhysRevLett.120.207203	journal	May 2018
Valence Bond Glass Phase in Dilute Kagome Antiferromagnets Singh, R. R. P. Physical Review Letters, Vol. 104, Issue 17 https://doi.org/10.1103/PhysRevLett.104.177203	journal	April 2010
Disorder-Induced Quantum Spin Liquid in Spin Ice Pyrochlores Savary, Lucile; Balents, Leon Physical Review Letters, Vol. 118, Issue 8 https://doi.org/10.1103/PhysRevLett.118.087203	journal	February 2017
“Magnetic monopole” condensation of the pyrochlore ice U(1) quantum spin liquid: Application to $\Pr_{2} {Ir}_{2} O_{7}$ and ${Yb}_{2} {Ti}_{2} O_{7}$ Chen, Gang Physical Review B, Vol. 94, Issue 20 https://doi.org/10.1103/PhysRevB.94.205107	journal	November 2016
Unusual Liquid State of Hard-Core Bosons on the Pyrochlore Lattice Banerjee, Argha; Isakov, Sergei V.; Damle, Kedar Physical Review Letters, Vol. 100, Issue 4 https://doi.org/10.1103/PhysRevLett.100.047208	journal	January 2008
Competing Spin Liquids and Hidden Spin-Nematic Order in Spin Ice with Frustrated Transverse Exchange Taillefumier, Mathieu; Benton, Owen; Yan, Han Physical Review X, Vol. 7, Issue 4 https://doi.org/10.1103/PhysRevX.7.041057	journal	December 2017
Bond-Disordered Spin Liquid and the Honeycomb Iridate $H_{3} {LiIr}_{2} O_{6}$ : Abundant Low-Energy Density of States from Random Majorana Hopping Knolle, Johannes; Moessner, Roderich; Perkins, Natalia B. Physical Review Letters, Vol. 122, Issue 4 https://doi.org/10.1103/PhysRevLett.122.047202	journal	February 2019
Spinon Fermi surface $U (1)$ spin liquid in the spin-orbit-coupled triangular-lattice Mott insulator ${YbMgGaO}_{4}$ Li, Yao-Dong; Lu, Yuan-Ming; Chen, Gang Physical Review B, Vol. 96, Issue 5 https://doi.org/10.1103/PhysRevB.96.054445	journal	August 2017
Disorder-Induced Mimicry of a Spin Liquid in ${YbMgGaO}_{4}$ Zhu, Zhenyue; Maksimov, P. A.; White, Steven R. Physical Review Letters, Vol. 119, Issue 15 https://doi.org/10.1103/PhysRevLett.119.157201	journal	October 2017
Pyrochlore photons: The $U (1)$ spin liquid in a $S = \frac{1}{2}$ three-dimensional frustrated magnet Hermele, Michael; Fisher, Matthew P. A.; Balents, Leon Physical Review B, Vol. 69, Issue 6 https://doi.org/10.1103/PhysRevB.69.064404	journal	February 2004
Ice: A strongly correlated proton system Castro Neto, A. H.; Pujol, P.; Fradkin, Eduardo Physical Review B, Vol. 74, Issue 2 https://doi.org/10.1103/PhysRevB.74.024302	journal	July 2006
Dzyaloshinskii-Moriya anisotropy and nonmagnetic impurities in the $s = \frac{1}{2}$ kagome system ${ZnCu}_{3} {(OH)}_{6} {Cl}_{2}$ Rousochatzakis, Ioannis; Manmana, Salvatore R.; Läuchli, Andreas M. Physical Review B, Vol. 79, Issue 21 https://doi.org/10.1103/PhysRevB.79.214415	journal	June 2009
Short-ranged resonating valence bond physics, quantum dimer models, and Ising gauge theories Moessner, R.; Sondhi, S. L.; Fradkin, Eduardo Physical Review B, Vol. 65, Issue 2 https://doi.org/10.1103/PhysRevB.65.024504	journal	December 2001
Quantum spin liquids: a review Savary, Lucile; Balents, Leon Reports on Progress in Physics, Vol. 80, Issue 1 https://doi.org/10.1088/0034-4885/80/1/016502	journal	November 2016
Evidence for a spinon Fermi surface in a triangular-lattice quantum-spin-liquid candidate Shen, Yao; Li, Yao-Dong; Wo, Hongliang Nature, Vol. 540, Issue 7634 https://doi.org/10.1038/nature20614	journal	December 2016
Quantum Excitations in Quantum Spin Ice Ross, Kate A.; Savary, Lucile; Gaulin, Bruce D. Physical Review X, Vol. 1, Issue 2 https://doi.org/10.1103/PhysRevX.1.021002	journal	October 2011
Generic Spin Model for the Honeycomb Iridates beyond the Kitaev Limit Rau, Jeffrey G.; Lee, Eric Kin-Ho; Kee, Hae-Young Physical Review Letters, Vol. 112, Issue 7 https://doi.org/10.1103/PhysRevLett.112.077204	journal	February 2014
Majorana quantization and half-integer thermal quantum Hall effect in a Kitaev spin liquid Kasahara, Y.; Ohnishi, T.; Mizukami, Y. Nature, Vol. 559, Issue 7713 https://doi.org/10.1038/s41586-018-0274-0	journal	July 2018
Zero-point entropy in ‘spin ice’ Ramirez, A. P.; Hayashi, A.; Cava, R. J. Nature, Vol. 399, Issue 6734 https://doi.org/10.1038/20619	journal	May 1999
Probing $α - {RuCl}_{3}$ Beyond Magnetic Order: Effects of Temperature and Magnetic Field Winter, Stephen M.; Riedl, Kira; Kaib, David Physical Review Letters, Vol. 120, Issue 7 https://doi.org/10.1103/PhysRevLett.120.077203	journal	February 2018
Spin liquid and quantum phase transition without symmetry breaking in a frustrated three-dimensional Ising model Röchner, Julia; Balents, Leon; Schmidt, Kai Phillip Physical Review B, Vol. 94, Issue 20 https://doi.org/10.1103/PhysRevB.94.201111	journal	November 2016
Monte Carlo study of the discontinuous quantum phase transition in the transverse-field Ising model on the pyrochlore lattice Emonts, Patrick; Wessel, Stefan Physical Review B, Vol. 98, Issue 17 https://doi.org/10.1103/PhysRevB.98.174433	journal	November 2018
Instabilities of a U(1) Quantum Spin Liquid in Disordered Non-Kramers Pyrochlores Benton, Owen Physical Review Letters, Vol. 121, Issue 3 https://doi.org/10.1103/PhysRevLett.121.037203	journal	July 2018
Fractionalized excitations in the spin-liquid state of a kagome-lattice antiferromagnet Han, Tian-Heng; Helton, Joel S.; Chu, Shaoyan Nature, Vol. 492, Issue 7429 https://doi.org/10.1038/nature11659	journal	December 2012
Random antiferromagnetic quantum spin chains Fisher, Daniel S. Physical Review B, Vol. 50, Issue 6 https://doi.org/10.1103/PhysRevB.50.3799	journal	August 1994
Evidence for a gapped spin-liquid ground state in a kagome Heisenberg antiferromagnet Fu, M.; Imai, T.; Han, T. -H. Science, Vol. 350, Issue 6261 https://doi.org/10.1126/science.aab2120	journal	November 2015
Disordered Route to the Coulomb Quantum Spin Liquid: Random Transverse Fields on Spin Ice in $\Pr_{2} {Zr}_{2} O_{7}$ Wen, J. -J.; Koohpayeh, S. M.; Ross, K. A. Physical Review Letters, Vol. 118, Issue 10 https://doi.org/10.1103/PhysRevLett.118.107206	journal	March 2017
Spin-glass transition in geometrically frustrated antiferromagnets with weak disorder Andreanov, A.; Chalker, J. T.; Saunders, T. E. Physical Review B, Vol. 81, Issue 1 https://doi.org/10.1103/PhysRevB.81.014406	journal	January 2010
Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models Jackeli, G.; Khaliullin, G. Physical Review Letters, Vol. 102, Issue 1 https://doi.org/10.1103/PhysRevLett.102.017205	journal	January 2009
Valence Bonds in Random Quantum Magnets: Theory and Application to ${YbMgGaO}_{4}$ Kimchi, Itamar; Nahum, Adam; Senthil, T. Physical Review X, Vol. 8, Issue 3 https://doi.org/10.1103/PhysRevX.8.031028	journal	July 2018
Local entanglement and confinement transitions in the random transverse-field Ising model on the pyrochlore lattice Pardini, Tom; Menon, Anirudha; Hau-Riege, Stefan P. Physical Review B, Vol. 100, Issue 14 https://doi.org/10.1103/PhysRevB.100.144437	journal	October 2019
Quantum Ice: A Quantum Monte Carlo Study Shannon, Nic; Sikora, Olga; Pollmann, Frank Physical Review Letters, Vol. 108, Issue 6 https://doi.org/10.1103/PhysRevLett.108.067204	journal	February 2012
Scaling Studies of Highly Disordered Spin-½ Antiferromagnetic Systems Bhatt, R. N.; Lee, P. A. Physical Review Letters, Vol. 48, Issue 5 https://doi.org/10.1103/PhysRevLett.48.344	journal	February 1982

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