Entanglement entropy production in deep inelastic scattering

Zhang, Kun; Hao, Kun; Kharzeev, Dmitri; Korepin, Vladimir

doi:10.1103/physrevd.105.014002

Title: Entanglement entropy production in deep inelastic scattering

Journal Article · 04 January 2022 · Physical Review. D.

DOI: https://doi.org/10.1103/physrevd.105.014002 · OSTI ID:1866113

^[1];

^[2]; Kharzeev, Dmitri ^[3]; Korepin, Vladimir ^[1]

Stony Brook Univ., NY (United States)
Northwest University, Xi’an (China); Stony Brook Univ., NY (United States)
Stony Brook Univ., NY (United States); Brookhaven National Lab. (BNL), Upton, NY (United States)

Deep inelastic scattering (DIS) samples a part of the wave function of a hadron in the vicinity of the light cone. Lipatov constructed a spin chain which describes the amplitude of DIS in leading logarithmic approximation. Kharzeev and Levin proposed the entanglement entropy as an observable in DIS [Phys. Rev. D 95, 114008 (2017)], and suggested a relation between the entanglement entropy and parton distributions. Here we represent the DIS process as a local quench in Lipatov’s spin chain and study the time evolution of the produced entanglement entropy. We show that the resulting entanglement entropy depends on time logarithmically, $$\mathcal{S}(t) = 1/3 ln(t/τ)$$ with $$τ = 1/m for 1/m ≤ t ≤ (mx)^{–1}$$, where m is the proton mass and $$\textit{x}$$ is the Bjorken $$\textit{x}$$. The central charge c of Lipatov’s spin chain is determined here to be $$\textit{c}$$ = 1; using the proposed relation between the entanglement entropy and parton distributions, this corresponds to the gluon structure function growing at small $$\textit{x}$$ as $$xG(x) ~ 1/x^{1/3}$$.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Brookhaven National Laboratory (BNL), Upton, NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES); National Natural Science Foundation of China; Shaanxi Natural Science Fundamental Research Program; Shaanxi Key Laboratory

Grant/Contract Number:: SC0012704

OSTI ID:: 1866113

Report Number(s):: BNL--222964-2022-JAAM

Journal Information:: Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 1 Vol. 105; ISSN 2470-0010

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (106)

Modern Scattering‐Type Scanning Near‐Field Optical Microscopy for Advanced Material Research Chen, Xinzhong; Hu, Debo; Mescall, Ryan Advanced Materials https://doi.org/10.1002/adma.201804774	journal	April 2019
Tunable Modal Birefringence in a Low‐Loss Van Der Waals Waveguide Hu, Debo; Chen, Ke; Chen, Xinzhong Advanced Materials, Vol. 31, Issue 27 https://doi.org/10.1002/adma.201807788	journal	May 2019
Nanoimaging and Nanospectroscopy of Polaritons with Time Resolved s ‐SNOM Yao, Ziheng; Xu, Suheng; Hu, Debo Advanced Optical Materials, Vol. 8, Issue 5 https://doi.org/10.1002/adom.201901042	journal	September 2019
Phonon Polaritons and Hyperbolic Response in van der Waals Materials Hu, Guangwei; Shen, Jialiang; Qiu, Cheng‐Wei Advanced Optical Materials, Vol. 8, Issue 5 https://doi.org/10.1002/adom.201901393	journal	November 2019
Fast Scanning Probe Microscopy via Machine Learning: Non‐Rectangular Scans with Compressed Sensing and Gaussian Process Optimization Kelley, Kyle P.; Ziatdinov, Maxim; Collins, Liam Small, Vol. 16, Issue 37 https://doi.org/10.1002/smll.202002878	journal	August 2020
Local Hamiltonians for integrable quantum models on a lattice Tarasov, V. O.; Takhtadzhyan, L. A.; Faddeev, L. D. Theoretical and Mathematical Physics, Vol. 57, Issue 2 https://doi.org/10.1007/BF01018648	journal	November 1983
Measurement of the proton structure functionF 2 from the 1993 HERA data Derrick, M.; Krakauer, D.; Magill, S. Zeitschrift für Physik C Particles and Fields, Vol. 65, Issue 3 https://doi.org/10.1007/BF01556128	journal	September 1995
Measurement of the proton structure function F2 in ep scattering at HERA Derrick, M.; Krakauer, D.; Magill, S. Physics Letters B, Vol. 316, Issue 2-3 https://doi.org/10.1016/0370-2693(93)90347-K	journal	October 1993
High energy QCD as a completely integrable model Faddeev, L. D.; Korchemsky, G. P. Physics Letters B, Vol. 342, Issue 1-4 https://doi.org/10.1016/0370-2693(94)01363-H	journal	January 1995
Lattice versions of quantum field theory models in two dimensions Izergin, A. G.; Korepin, V. E. Nuclear Physics B, Vol. 205, Issue 3 https://doi.org/10.1016/0550-3213(82)90365-0	journal	June 1982
Measurement of the proton structure function F2 (x, Q2) in the low-x region at HERA Abt, I.; Ahmed, T.; Andreev, V. Nuclear Physics B, Vol. 407, Issue 3 https://doi.org/10.1016/0550-3213(93)90090-C	journal	October 1993
Unitarity and the BFKL pomeron Mueller, A. H. Nuclear Physics B, Vol. 437, Issue 1 https://doi.org/10.1016/0550-3213(94)00480-3	journal	March 1995
Soft gluons in the infinite-momentum wave function and the BFKL pomeron Mueller, A. H. Nuclear Physics B, Vol. 415, Issue 2 https://doi.org/10.1016/0550-3213(94)90116-3	journal	March 1994
Geometric and renormalized entropy in conformal field theory Holzhey, Christoph; Larsen, Finn; Wilczek, Frank Nuclear Physics B, Vol. 424, Issue 3 https://doi.org/10.1016/0550-3213(94)90402-2	journal	August 1994
A measurement of the proton structure function F2(x, Q2) Ahmed, T.; Aid, S.; Akhundov, A. Nuclear Physics B, Vol. 439, Issue 3 https://doi.org/10.1016/0550-3213(95)98236-U	journal	April 1995
Wider or Deeper: Revisiting the ResNet Model for Visual Recognition Wu, Zifeng; Shen, Chunhua; van den Hengel, Anton Pattern Recognition, Vol. 90 https://doi.org/10.1016/j.patcog.2019.01.006	journal	June 2019
Collinearly-improved BK evolution meets the HERA data Iancu, E.; Madrigal, J. D.; Mueller, A. H. Physics Letters B, Vol. 750 https://doi.org/10.1016/j.physletb.2015.09.071	journal	November 2015
Principles of Nano-Optics Novotny, Lukas; Hecht, Bert Cambridge University Press https://doi.org/10.1017/CBO9780511813535	book	January 2006
Quantum Computation and Quantum Information Nielsen, Michael A.; Chuang, Isaac L. Cambridge University Press https://doi.org/10.1017/CBO9780511976667	book	January 2011
Charge-Transfer Plasmon Polaritons at Graphene/α-RuCl ₃ Interfaces Rizzo, Daniel J.; Jessen, Bjarke S.; Sun, Zhiyuan Nano Letters, Vol. 20, Issue 12 https://doi.org/10.1021/acs.nanolett.0c03466	journal	November 2020
Hyperbolic Cooper-Pair Polaritons in Planar Graphene/Cuprate Plasmonic Cavities Berkowitz, Michael E.; Kim, Brian S. Y.; Ni, Guangxin Nano Letters, Vol. 21, Issue 1 https://doi.org/10.1021/acs.nanolett.0c03684	journal	December 2020
Edge and Surface Plasmons in Graphene Nanoribbons Fei, Z.; Goldflam, M. D.; Wu, J. -S. Nano Letters, Vol. 15, Issue 12 https://doi.org/10.1021/acs.nanolett.5b03834	journal	November 2015
Nanoscale Near-Field Tomography of Surface States on (Bi _0.5 Sb _0.5 ) ₂ Te ₃ Mooshammer, Fabian; Sandner, Fabian; Huber, Markus A. Nano Letters, Vol. 18, Issue 12 https://doi.org/10.1021/acs.nanolett.8b03008	journal	November 2018
Nano-photocurrent Mapping of Local Electronic Structure in Twisted Bilayer Graphene Sunku, Sai S.; McLeod, Alexander S.; Stauber, Tobias Nano Letters, Vol. 20, Issue 5 https://doi.org/10.1021/acs.nanolett.9b04637	journal	February 2020
Machine Learning for Integrated Quantum Photonics Kudyshev, Zhaxylyk A.; Shalaev, Vladimir M.; Boltasseva, Alexandra ACS Photonics, Vol. 8, Issue 1 https://doi.org/10.1021/acsphotonics.0c00960	journal	December 2020
Hybrid Machine Learning for Scanning Near-Field Optical Spectroscopy Chen, Xinzhong; Yao, Ziheng; Xu, Suheng ACS Photonics, Vol. 8, Issue 10 https://doi.org/10.1021/acsphotonics.1c00915	journal	September 2021
Infrared Nanoscopy of Dirac Plasmons at the Graphene–SiO ₂ Interface Fei, Zhe; Andreev, Gregory O.; Bao, Wenzhong Nano Letters, Vol. 11, Issue 11 https://doi.org/10.1021/nl202362d	journal	October 2011
Quantum Spin Chain, Toeplitz Determinants and the Fisher–Hartwig Conjecture Jin, B. -Q.; Korepin, V. E. Journal of Statistical Physics, Vol. 116, Issue 1-4 https://doi.org/10.1023/B:JOSS.0000037230.37166.42	journal	August 2004
Gate-tuning of graphene plasmons revealed by infrared nano-imaging Fei, Z.; Rodin, A. S.; Andreev, G. O. Nature, Vol. 487, Issue 7405 https://doi.org/10.1038/nature11253	journal	June 2012
Optical nano-imaging of gate-tunable graphene plasmons Chen, Jianing; Badioli, Michela; Alonso-González, Pablo Nature, Vol. 487, Issue 7405 https://doi.org/10.1038/nature11254	journal	June 2012
Near-field photocurrent nanoscopy on bare and encapsulated graphene Woessner, Achim; Alonso-González, Pablo; Lundeberg, Mark B. Nature Communications, Vol. 7, Issue 1 https://doi.org/10.1038/ncomms10783	journal	February 2016
Scattering-type scanning near-field optical microscopy with reconstruction of vertical interaction Wang, Le; Xu, Xiaoji G. Nature Communications, Vol. 6, Issue 1 https://doi.org/10.1038/ncomms9973	journal	November 2015
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
Polaritons in layered two-dimensional materials Low, Tony; Chaves, Andrey; Caldwell, Joshua D. Nature Materials, Vol. 16, Issue 2 https://doi.org/10.1038/nmat4792	journal	November 2016
Electronic and plasmonic phenomena at graphene grain boundaries Fei, Z.; Rodin, A. S.; Gannett, W. Nature Nanotechnology, Vol. 8, Issue 11 https://doi.org/10.1038/nnano.2013.197	journal	October 2013
Direct observation of ultraslow hyperbolic polariton propagation with negative phase velocity Yoxall, Edward; Schnell, Martin; Nikitin, Alexey Y. Nature Photonics, Vol. 9, Issue 10 https://doi.org/10.1038/nphoton.2015.166	journal	September 2015
Real-space mapping of tailored sheet and edge plasmons in graphene nanoresonators Nikitin, A. Y.; Alonso-González, P.; Vélez, S. Nature Photonics, Vol. 10, Issue 4 https://doi.org/10.1038/nphoton.2016.44	journal	March 2016
Ultrafast optical switching of infrared plasmon polaritons in high-mobility graphene Ni, G. X.; Wang, L.; Goldflam, M. D. Nature Photonics, Vol. 10, Issue 4 https://doi.org/10.1038/nphoton.2016.45	journal	March 2016
Imaging exciton–polariton transport in MoSe2 waveguides Hu, F.; Luan, Y.; Scott, M. E. Nature Photonics, Vol. 11, Issue 6 https://doi.org/10.1038/nphoton.2017.65	journal	May 2017
Probing optical anisotropy of nanometer-thin van der waals microcrystals by near-field imaging Hu, Debo; Yang, Xiaoxia; Li, Chi Nature Communications, Vol. 8, Issue 1 https://doi.org/10.1038/s41467-017-01580-7	journal	November 2017
Multi-messenger nanoprobes of hidden magnetism in a strained manganite McLeod, A. S.; Zhang, Jingdi; Gu, M. Q. Nature Materials, Vol. 19, Issue 4 https://doi.org/10.1038/s41563-019-0533-y	journal	December 2019
Real-space observation of vibrational strong coupling between propagating phonon polaritons and organic molecules Bylinkin, Andrei; Schnell, Martin; Autore, Marta Nature Photonics, Vol. 15, Issue 3 https://doi.org/10.1038/s41566-020-00725-3	journal	November 2020
Fundamental limits to graphene plasmonics Ni, G. X.; McLeod, A. S.; Sun, Z. Nature, Vol. 557, Issue 7706 https://doi.org/10.1038/s41586-018-0136-9	journal	May 2018
Machine learning in electronic-quantum-matter imaging experiments Zhang, Yi; Mesaros, A.; Fujita, K. Nature, Vol. 570, Issue 7762 https://doi.org/10.1038/s41586-019-1319-8	journal	June 2019
Efficient Fizeau drag from Dirac electrons in monolayer graphene Zhao, Wenyu; Zhao, Sihan; Li, Hongyuan Nature, Vol. 594, Issue 7864 https://doi.org/10.1038/s41586-021-03574-4	journal	June 2021
Fizeau drag in graphene plasmonics Dong, Y.; Xiong, L.; Phinney, I. Y. Nature, Vol. 594, Issue 7864 https://doi.org/10.1038/s41586-021-03640-x	journal	June 2021
Ghost hyperbolic surface polaritons in bulk anisotropic crystals Ma, Weiliang; Hu, Guangwei; Hu, Debo Nature, Vol. 596, Issue 7872 https://doi.org/10.1038/s41586-021-03755-1	journal	August 2021
Artificial-intelligence-driven scanning probe microscopy Krull, A.; Hirsch, P.; Rother, C. Communications Physics, Vol. 3, Issue 1 https://doi.org/10.1038/s42005-020-0317-3	journal	March 2020
Computer-inspired quantum experiments Krenn, Mario; Erhard, Manuel; Zeilinger, Anton Nature Reviews Physics, Vol. 2, Issue 11 https://doi.org/10.1038/s42254-020-0230-4	journal	September 2020
Thermodynamics of a One‐Dimensional System of Bosons with Repulsive Delta‐Function Interaction Yang, C. N.; Yang, C. P. Journal of Mathematical Physics, Vol. 10, Issue 7 https://doi.org/10.1063/1.1664947	journal	July 1969
Nano-optical imaging and spectroscopy of order, phases, and domains in complex solids Atkin, Joanna M.; Berweger, Samuel; Jones, Andrew C. Advances in Physics, Vol. 61, Issue 6 https://doi.org/10.1080/00018732.2012.737982	journal	December 2012
Machine learning for quantum matter Carrasquilla, Juan Advances in Physics: X, Vol. 5, Issue 1 https://doi.org/10.1080/23746149.2020.1797528	journal	January 2020
Nanoscale electrodynamics of strongly correlated quantum materials Liu, Mengkun; Sternbach, Aaron J.; Basov, D. N. Reports on Progress in Physics, Vol. 80, Issue 1 https://doi.org/10.1088/0034-4885/80/1/014501	journal	November 2016
Conformal dimensions in Bethe ansatz solvable models Izergin, A. G.; Korepin, V. E.; Reshetikhin, N. Y. Journal of Physics A: Mathematical and General, Vol. 22, Issue 13 https://doi.org/10.1088/0305-4470/22/13/052	journal	July 1989
Machine learning for condensed matter physics Bedolla, Edwin; Padierna, Luis Carlos; Castañeda-Priego, Ramón Journal of Physics: Condensed Matter, Vol. 33, Issue 5 https://doi.org/10.1088/1361-648X/abb895	journal	November 2020
Entanglement entropy and quantum field theory Calabrese, Pasquale; Cardy, John Journal of Statistical Mechanics: Theory and Experiment, Vol. 2004, Issue 06 https://doi.org/10.1088/1742-5468/2004/06/P06002	journal	June 2004
Evolution of entanglement entropy in one-dimensional systems Calabrese, Pasquale; Cardy, John Journal of Statistical Mechanics: Theory and Experiment, Vol. 2005, Issue 04 https://doi.org/10.1088/1742-5468/2005/04/P04010	journal	April 2005
Entanglement and correlation functions following a local quench: a conformal field theory approach Calabrese, Pasquale; Cardy, John Journal of Statistical Mechanics: Theory and Experiment, Vol. 2007, Issue 10 https://doi.org/10.1088/1742-5468/2007/10/P10004	journal	October 2007
Entanglement entropy and conformal field theory Calabrese, Pasquale; Cardy, John Journal of Physics A: Mathematical and Theoretical, Vol. 42, Issue 50 https://doi.org/10.1088/1751-8113/42/50/504005	journal	December 2009
Entanglement scaling of operators: a conformal field theory approach, with a glimpse of simulability of long-time dynamics in 1 + 1d Dubail, J. Journal of Physics A: Mathematical and Theoretical, Vol. 50, Issue 23 https://doi.org/10.1088/1751-8121/aa6f38	journal	May 2017
Scattering of surface plasmons on graphene by a discontinuity in surface conductivity Rejaei, Behzad; Khavasi, Amin Journal of Optics, Vol. 17, Issue 7 https://doi.org/10.1088/2040-8978/17/7/075002	journal	June 2015
Entanglement of quantum evolutions Zanardi, Paolo Physical Review A, Vol. 63, Issue 4 https://doi.org/10.1103/PhysRevA.63.040304	journal	March 2001
Operator space entanglement entropy in a transverse Ising chain Prosen, Tomaž; Pižorn, Iztok Physical Review A, Vol. 76, Issue 3 https://doi.org/10.1103/PhysRevA.76.032316	journal	September 2007
Validity of Machine Learning in the Quantitative Analysis of Complex Scanning Near-Field Optical Microscopy Signals Using Simulated Data Chen, Xinzhong; Ren, Richard; Liu, Mengkun Physical Review Applied, Vol. 15, Issue 1 https://doi.org/10.1103/PhysRevApplied.15.014001	journal	January 2021
Diffusion and operator entanglement spreading Alba, Vincenzo Physical Review B, Vol. 104, Issue 9 https://doi.org/10.1103/PhysRevB.104.094410	journal	September 2021
Power-law decay of standing waves on the surface of topological insulators Wang, Jing; Li, Wei; Cheng, Peng Physical Review B, Vol. 84, Issue 23 https://doi.org/10.1103/PhysRevB.84.235447	journal	December 2011
Nano-optical imaging of WS e 2 waveguide modes revealing light-exciton interactions Fei, Z.; Scott, M. E.; Gosztola, D. J. Physical Review B, Vol. 94, Issue 8 https://doi.org/10.1103/PhysRevB.94.081402	journal	August 2016
Deep inelastic scattering as a probe of entanglement: Confronting experimental data Kharzeev, Dmitri E.; Levin, Eugene Physical Review D, Vol. 104, Issue 3 https://doi.org/10.1103/PhysRevD.104.L031503	journal	August 2021
F 2 and F L at small x using a collinearly improved BFKL resummation Hentschinski, Martin; Sabio Vera, Agustín; Salas, Clara Physical Review D, Vol. 87, Issue 7 https://doi.org/10.1103/PhysRevD.87.076005	journal	April 2013
Deep inelastic scattering as a probe of entanglement Kharzeev, Dmitri E.; Levin, Eugene M. Physical Review D, Vol. 95, Issue 11 https://doi.org/10.1103/PhysRevD.95.114008	journal	June 2017
Thermal radiation and entanglement in proton-proton collisions at energies available at the CERN Large Hadron Collider Baker, O. K.; Kharzeev, D. E. Physical Review D, Vol. 98, Issue 5 https://doi.org/10.1103/PhysRevD.98.054007	journal	September 2018
Is the efficiency of classical simulations of quantum dynamics related to integrability? Prosen, Tomaž; Žnidarič, Marko Physical Review E, Vol. 75, Issue 1 https://doi.org/10.1103/PhysRevE.75.015202	journal	January 2007
Dynamical Simulation of Integrable and Nonintegrable Models in the Heisenberg Picture Muth, Dominik; Unanyan, Razmik G.; Fleischhauer, Michael Physical Review Letters, Vol. 106, Issue 7 https://doi.org/10.1103/PhysRevLett.106.077202	journal	February 2011
Long-Wavelength Local Density of States Oscillations Near Graphene Step Edges Xue, Jiamin; Sanchez-Yamagishi, Javier; Watanabe, K. Physical Review Letters, Vol. 108, Issue 1 https://doi.org/10.1103/PhysRevLett.108.016801	journal	January 2012
Phase-Resolved Surface Plasmon Interferometry of Graphene Gerber, Justin A.; Berweger, Samuel; O’Callahan, Brian T. Physical Review Letters, Vol. 113, Issue 5 https://doi.org/10.1103/PhysRevLett.113.055502	journal	July 2014
Operator Entanglement in Interacting Integrable Quantum Systems: The Case of the Rule 54 Chain Alba, V.; Dubail, J.; Medenjak, M. Physical Review Letters, Vol. 122, Issue 25 https://doi.org/10.1103/PhysRevLett.122.250603	journal	June 2019
Discovering Physical Concepts with Neural Networks Iten, Raban; Metger, Tony; Wilming, Henrik Physical Review Letters, Vol. 124, Issue 1 https://doi.org/10.1103/PhysRevLett.124.010508	journal	January 2020
Einstein-Podolsky-Rosen Paradox and Quantum Entanglement at Subnucleonic Scales Tu, Zhoudunming; Kharzeev, Dmitri E.; Ullrich, Thomas Physical Review Letters, Vol. 124, Issue 6 https://doi.org/10.1103/PhysRevLett.124.062001	journal	February 2020
Ab Initio Mismatched Interface Theory of Graphene on α − RuCl 3 : Doping and Magnetism Gerber, Eli; Yao, Yuan; Arias, Tomas A. Physical Review Letters, Vol. 124, Issue 10 https://doi.org/10.1103/PhysRevLett.124.106804	journal	March 2020
Entangling Power and Quantum Circuit Complexity Eisert, J. Physical Review Letters, Vol. 127, Issue 2 https://doi.org/10.1103/PhysRevLett.127.020501	journal	July 2021
Complex Optical Constants on a Subwavelength Scale Hillenbrand, R.; Keilmann, F. Physical Review Letters, Vol. 85, Issue 14 https://doi.org/10.1103/PhysRevLett.85.3029	journal	October 2000
Universality of Entropy Scaling in One Dimensional Gapless Models Korepin, V. E. Physical Review Letters, Vol. 92, Issue 9 https://doi.org/10.1103/PhysRevLett.92.096402	journal	March 2004
Machine learning and the physical sciences Carleo, Giuseppe; Cirac, Ignacio; Cranmer, Kyle Reviews of Modern Physics, Vol. 91, Issue 4 https://doi.org/10.1103/RevModPhys.91.045002	journal	December 2019
DeepFace: Closing the Gap to Human-Level Performance in Face Verification Taigman, Yaniv; Yang, Ming; Ranzato, Marc'Aurelio 2014 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) https://doi.org/10.1109/CVPR.2014.220	conference	June 2014
SeNet: Structured Edge Network for Sea–Land Segmentation Cheng, Dongcai; Meng, Gaofeng; Cheng, Guangliang IEEE Geoscience and Remote Sensing Letters, Vol. 14, Issue 2 https://doi.org/10.1109/LGRS.2016.2637439	journal	February 2017
Recent Trends in Deep Learning Based Natural Language Processing [Review Article] Young, Tom; Hazarika, Devamanyu; Poria, Soujanya IEEE Computational Intelligence Magazine, Vol. 13, Issue 3 https://doi.org/10.1109/MCI.2018.2840738	journal	August 2018
Transient exciton-polariton dynamics in WSe ₂ by ultrafast near-field imaging Mrejen, M.; Yadgarov, L.; Levanon, A. Science Advances, Vol. 5, Issue 2 https://doi.org/10.1126/sciadv.aat9618	journal	February 2019
Imaging Quasiparticle Interference in Bi₂Sr₂CaCu₂O_8+δ Hoffman, J. E.; McElroy, K.; Lee, D.-H. Science, Vol. 297, Issue 5584, p. 1148-1151 https://doi.org/10.1126/science.1072640	journal	July 2002
Mott Transition in VO2 Revealed by Infrared Spectroscopy and Nano-Imaging Qazilbash, M. M.; Brehm, M.; Chae, B. -G. Science, Vol. 318, Issue 5857 https://doi.org/10.1126/science.1150124	journal	December 2007
Tunable Phonon Polaritons in Atomically Thin van der Waals Crystals of Boron Nitride Dai, S.; Fei, Z.; Ma, Q. Science, Vol. 343, Issue 6175 https://doi.org/10.1126/science.1246833	journal	March 2014
Quantum thermalization through entanglement in an isolated many-body system Kaufman, A. M.; Tai, M. E.; Lukin, A. Science, Vol. 353, Issue 6301 https://doi.org/10.1126/science.aaf6725	journal	August 2016
Polaritons in van der Waals materials Basov, D. N.; Fogler, M. M.; Garcia de Abajo, F. J. Science, Vol. 354, Issue 6309 https://doi.org/10.1126/science.aag1992	journal	October 2016
Solving the quantum many-body problem with artificial neural networks Carleo, Giuseppe; Troyer, Matthias Science, Vol. 355, Issue 6325 https://doi.org/10.1126/science.aag2302	journal	February 2017
Programmable hyperbolic polaritons in van der Waals semiconductors Sternbach, A. J.; Chae, S. H.; Latini, S. Science, Vol. 371, Issue 6529 https://doi.org/10.1126/science.abe9163	journal	February 2021
AAMQS: A non-linear QCD analysis of new HERA data at small-x including heavy quarks Albacete, Javier L.; Armesto, Néstor; Milhano, José Guilherme The European Physical Journal C, Vol. 71, Issue 7 https://doi.org/10.1140/epjc/s10052-011-1705-3	journal	July 2011
An analysis of systematic effects in finite size scaling studies using the gradient flow Nada, Alessandro; Ramos, Alberto The European Physical Journal C, Vol. 81, Issue 1 https://doi.org/10.1140/epjc/s10052-020-08759-1	journal	January 2021
Bethe Ansatz for XXX chain with negative spin Hao, Kun; Kharzeev, Dmitri; Korepin, Vladimir International Journal of Modern Physics A, Vol. 34, Issue 31 https://doi.org/10.1142/S0217751X19501975	journal	November 2019
Algebraic Aspects of the Bethe Ansatz Faddeev, L. D. International Journal of Modern Physics A, Vol. 10, Issue 13 https://doi.org/10.1142/S0217751X95000905	journal	May 1995
ImageNet classification with deep convolutional neural networks Krizhevsky, Alex; Sutskever, Ilya; Hinton, Geoffrey E. Communications of the ACM, Vol. 60, Issue 6 https://doi.org/10.1145/3065386	journal	May 2017
Deep Learning--based Text Classification: A Comprehensive Review Minaee, Shervin; Kalchbrenner, Nal; Cambria, Erik ACM Computing Surveys, Vol. 54, Issue 3 https://doi.org/10.1145/3439726	journal	June 2021
The FEniCS Project Version 1.5 Alnæs, Martin; Blechta, Jan; Hake, Johan University Library Heidelberg https://doi.org/10.11588/ans.2015.100.20553	text	January 2015
Substrate-enhanced infrared near-field spectroscopy Aizpurua, Javier; Taubner, Thomas; García de Abajo, F. Javier Optics Express, Vol. 16, Issue 3 https://doi.org/10.1364/OE.16.001529	journal	January 2008
Artifact free time resolved near-field spectroscopy Sternbach, A. J.; Hinton, J.; Slusar, T. Optics Express, Vol. 25, Issue 23 https://doi.org/10.1364/OE.25.028589	journal	January 2017
Polariton panorama Basov, D. N.; Asenjo-Garcia, Ana; Schuck, P. James Nanophotonics, Vol. 10, Issue 1 https://doi.org/10.1515/nanoph-2020-0449	journal	November 2020
Neural Machine Translation: A Review Stahlberg, Felix Journal of Artificial Intelligence Research, Vol. 69 https://doi.org/10.1613/jair.1.12007	journal	September 2020
Measurement of charged particle multiplicity distributions in DIS at HERA and its implication to entanglement entropy of partons Collaboration, H1 HEPData https://doi.org/10.17182/hepdata.102570	collection	January 2021

Similar Records

Entanglement entropy in random quantum spin-S chains

Journal Article · 2007 · Physical Review. A · OSTI ID:20982498

Saguia, A; Boechat, B; Continentino, M A; +1 more

Deep inelastic scattering as a probe of entanglement

Journal Article · 2017 · Physical Review D · OSTI ID:1392245

Kharzeev, Dmitri E.; Levin, Eugene M.

Operator space entanglement entropy in a transverse Ising chain

Journal Article · 2007 · Physical Review. A · OSTI ID:21015947

Prosen, Tomaz; Pizorn, Iztok

Related Subjects

97 MATHEMATICS AND COMPUTING

Title: Entanglement entropy production in deep inelastic scattering

Citation Formats

References (106)

Similar Records

Related Subjects