Local entanglement and confinement transitions in the random transverse-field Ising model on the pyrochlore lattice

Pardini, Tom; Menon, Anirudha; Hau-Riege, Stefan P.; Singh, Rajiv R. P.

doi:10.1103/PhysRevB.100.144437

Title: Local entanglement and confinement transitions in the random transverse-field Ising model on the pyrochlore lattice

Journal Article · Mon Oct 28 00:00:00 EDT 2019 · Physical Review B

DOI:https://doi.org/10.1103/PhysRevB.100.144437· OSTI ID:1575863

Pardini, Tom ^[1];

^[2]; Hau-Riege, Stefan P. ^[1]; Singh, Rajiv R. P. ^[2]

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

We use numerical linked cluster expansions (NLC) and exact diagonalization to study confinement transitions out of the quantum spin liquid phase in the pyrochlore-lattice Ising antiferromagnet with random transverse fields. We calculate entanglement entropies associated with local regions defined by single tetrahedron to observe these transitions. The randomness-induced confinement transition is marked by a sharp reduction in the local entanglement and a concomitant increase in Ising correlations. In NLC, it is studied through the destruction of loop resonances due to random transverse-fields. As a result, the confining phase is characterized by a distribution of local entanglement entropies, which persists to large random fields.

View Accepted Manuscript (DOE)

Cite

Export

Save

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

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 1575863

Report Number(s):: LLNL-JRNL-778510; PRBMDO; 971948; TRN: US2100084

Journal Information:: Physical Review B, Vol. 100, Issue 14; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 4 works

Citation information provided by
Web of Science

References (51)

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
Entanglement at a Two-Dimensional Quantum Critical Point: A Numerical Linked-Cluster Expansion Study Kallin, Ann B.; Hyatt, Katharine; Singh, Rajiv R. P. Physical Review Letters, Vol. 110, Issue 13 https://doi.org/10.1103/PhysRevLett.110.135702	journal	March 2013
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
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
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
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
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
Theory of a Two-Dimensional Ising Model with Random Impurities. III. Boundary Effects McCOY, Barry M. Physical Review, Vol. 188, Issue 2 https://doi.org/10.1103/PhysRev.188.1014	journal	December 1969
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
The Structure and Entropy of Ice and of Other Crystals with Some Randomness of Atomic Arrangement Pauling, Linus Journal of the American Chemical Society, Vol. 57, Issue 12 https://doi.org/10.1021/ja01315a102	journal	December 1935
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
Numerical linked-cluster algorithms. I. Spin systems on square, triangular, and kagomé lattices Rigol, Marcos; Bryant, Tyler; Singh, Rajiv R. P. Physical Review E, Vol. 75, Issue 6 https://doi.org/10.1103/PhysRevE.75.061118	journal	June 2007
Quantum Spin Ice with Frustrated Transverse Exchange: From a $π$ -Flux Phase to a Nematic Quantum Spin Liquid Benton, Owen; Jaubert, L. D. C.; Singh, Rajiv R. P. Physical Review Letters, Vol. 121, Issue 6 https://doi.org/10.1103/PhysRevLett.121.067201	journal	August 2018
Superconductivity and the Quantum Hard-Core Dimer Gas Rokhsar, Daniel S.; Kivelson, Steven A. Physical Review Letters, Vol. 61, Issue 20 https://doi.org/10.1103/PhysRevLett.61.2376	journal	November 1988
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
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
Nonanalytic Behavior Above the Critical Point in a Random Ising Ferromagnet Griffiths, Robert B. Physical Review Letters, Vol. 23, Issue 1 https://doi.org/10.1103/PhysRevLett.23.17	journal	July 1969
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
Vindication of ${Yb}_{2} {Ti}_{2} O_{7}$ as a Model Exchange Quantum Spin Ice Applegate, R.; Hayre, N. R.; Singh, R. R. P. Physical Review Letters, Vol. 109, Issue 9 https://doi.org/10.1103/PhysRevLett.109.097205	journal	August 2012
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
Numerical Linked-Cluster Approach to Quantum Lattice Models Rigol, Marcos; Bryant, Tyler; Singh, Rajiv R. P. Physical Review Letters, Vol. 97, Issue 18 https://doi.org/10.1103/PhysRevLett.97.187202	journal	November 2006
Thermodynamic properties of Yb $_{2}$ Ti $_{2}$ O $_{7}$ pyrochlore as a function of temperature and magnetic field: Validation of a quantum spin ice exchange Hamiltonian Hayre, N. R.; Ross, K. A.; Applegate, R. Physical Review B, Vol. 87, Issue 18 https://doi.org/10.1103/PhysRevB.87.184423	journal	May 2013
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
A short introduction to numerical linked-cluster expansions Tang, Baoming; Khatami, Ehsan; Rigol, Marcos Computer Physics Communications, Vol. 184, Issue 3 https://doi.org/10.1016/j.cpc.2012.10.008	journal	March 2013
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
A Short Introduction to Numerical Linked-Cluster Expansions Tang, Baoming; Khatami, Ehsan; Rigol, Marcos arXiv https://doi.org/10.48550/arxiv.1207.3366	text	January 2012
Thermodynamic properties of the Yb2Ti2O7 pyrochlore as a function of temperature and magnetic field: validation of a quantum spin ice exchange Hamiltonian Hayre, N. R.; Ross, K. A.; Applegate, R. arXiv https://doi.org/10.48550/arxiv.1211.5934	text	January 2012
Generic spin model for the honeycomb iridates beyond the Kitaev limit Rau, Jeffrey G.; Lee, Eric Kin-Ho; Kee, Hae-Young arXiv https://doi.org/10.48550/arxiv.1310.7940	text	January 2013
Evidence for a Gapped Spin-Liquid Ground State in a Kagome Heisenberg Antiferromagnet Fu, M.; Imai, T.; Han, T. -H. arXiv https://doi.org/10.48550/arxiv.1511.02174	text	January 2015
Spin liquid and quantum phase transition without symmetry breaking in a frustrated three-dimensional Ising model Roechner, J.; Balents, L.; Schmidt, K. P. arXiv https://doi.org/10.48550/arxiv.1609.00484	text	January 2016
Randomness-induced quantum spin liquid behavior in the s=1/2 random J1-J2 Heisenberg antiferromagnet on the honeycomb lattice Uematsu, Kazuki; Kawamura, Hikaru arXiv https://doi.org/10.48550/arxiv.1701.02255	text	January 2017