Extracting off-diagonal order from diagonal basis measurements

Xiao, Bo; Moreno, Javier Robledo; Fishman, Matthew; Sels, Dries; Khatami, Ehsan; Scalettar, Richard

doi:10.1103/PhysRevResearch.6.L022064

Title: Extracting off-diagonal order from diagonal basis measurements

Journal Article · 17 June 2024 · Physical Review Research

DOI: https://doi.org/10.1103/PhysRevResearch.6.L022064 · OSTI ID:2373214

;

; Fishman, Matthew; Sels, Dries;

; Scalettar, Richard

Quantum gas microscopy has developed into a powerful tool to explore strongly correlated quantum systems. However, discerning phases with topological or off-diagonal long range order requires the ability to extract these correlations from site-resolved measurements. Here, we show that a multiscale complexity measure can pinpoint the transition to and from the bond ordered wave phase of the one-dimensional extended Hubbard model with an off-diagonal order parameter, sandwiched between diagonal charge and spin density wave phases, using only diagonal descriptors. We study the model directly in the thermodynamic limit using the recently developed variational uniform matrix product states algorithm, and draw our samples from degenerate ground states related by global spin rotations, emulating the projective measurements that are accessible in experiments. Our results will have important implications for the study of exotic phases using optical lattice experiments. Published by the American Physical Society 2024

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Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0022311

OSTI ID:: 2373214

Journal Information:: Physical Review Research, Journal Name: Physical Review Research Journal Issue: 2 Vol. 6; ISSN 2643-1564; ISSN PPRHAI

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

References (77)

Organic Superconductors Ishiguro, Takehiko; Yamaji, Kunihiko Springer Series in Solid-State Sciences https://doi.org/10.1007/978-3-642-97190-7	book	January 1990
A practical introduction to tensor networks: Matrix product states and projected entangled pair states Orús, Román Annals of Physics, Vol. 349 https://doi.org/10.1016/j.aop.2014.06.013	journal	October 2014
A perspective on machine learning and data science for strongly correlated electron problems Johnston, Steven; Khatami, Ehsan; Scalettar, Richard Carbon Trends, Vol. 9 https://doi.org/10.1016/j.cartre.2022.100231	journal	October 2022
A high-bias, low-variance introduction to Machine Learning for physicists Mehta, Pankaj; Bukov, Marin; Wang, Ching-Hao Physics Reports, Vol. 810 https://doi.org/10.1016/j.physrep.2019.03.001	journal	May 2019
The One-Dimensional Hubbard Model Essler, Fabian H. L.; Frahm, Holger; Göhmann, Frank Cambridge University Press https://doi.org/10.1017/CBO9780511534843	book	January 2009
Chemistry and Physics in One Dimension: Synthesis and Properties of Nanowires and Nanotubes Hu, Jiangtao; Odom, Teri Wang; Lieber, Charles M. Accounts of Chemical Research, Vol. 32, Issue 5, p. 435-445 https://doi.org/10.1021/ar9700365	journal	February 1999
Direct observation of Tomonaga–Luttinger-liquid state in carbon nanotubes at low temperatures Ishii, Hiroyoshi; Kataura, Hiromichi; Shiozawa, Hidetsugu Nature, Vol. 426, Issue 6966 https://doi.org/10.1038/nature02074	journal	December 2003
Single-atom-resolved fluorescence imaging of an atomic Mott insulator Sherson, Jacob F.; Weitenberg, Christof; Endres, Manuel Nature, Vol. 467, Issue 7311 https://doi.org/10.1038/nature09378	journal	August 2010
Observation of spatially ordered structures in a two-dimensional Rydberg gas Schauß, Peter; Cheneau, Marc; Endres, Manuel Nature, Vol. 491, Issue 7422 https://doi.org/10.1038/nature11596	journal	October 2012
Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models Labuhn, Henning; Barredo, Daniel; Ravets, Sylvain Nature, Vol. 534, Issue 7609 https://doi.org/10.1038/nature18274	journal	June 2016
A cold-atom Fermi–Hubbard antiferromagnet Mazurenko, Anton; Chiu, Christie S.; Ji, Geoffrey Nature, Vol. 545, Issue 7655 https://doi.org/10.1038/nature22362	journal	May 2017
Probing many-body dynamics on a 51-atom quantum simulator Bernien, Hannes; Schwartz, Sylvain; Keesling, Alexander Nature, Vol. 551, Issue 7682 https://doi.org/10.1038/nature24622	journal	November 2017
Machine learning phases of matter Carrasquilla, Juan; Melko, Roger G. Nature Physics, Vol. 13, Issue 5 https://doi.org/10.1038/nphys4035	journal	February 2017
Learning phase transitions by confusion van Nieuwenburg, Evert P. L.; Liu, Ye-Hua; Huber, Sebastian D. Nature Physics, Vol. 13, Issue 5 https://doi.org/10.1038/nphys4037	journal	February 2017
Correlator convolutional neural networks as an interpretable architecture for image-like quantum matter data Miles, Cole; Bohrdt, Annabelle; Wu, Ruihan Nature Communications, Vol. 12, Issue 1 https://doi.org/10.1038/s41467-021-23952-w	journal	June 2021
Certification of quantum states with hidden structure of their bitstrings Sotnikov, O. M.; Iakovlev, I. A.; Iliasov, A. A. npj Quantum Information, Vol. 8, Issue 1 https://doi.org/10.1038/s41534-022-00559-7	journal	April 2022
Identifying topological order through unsupervised machine learning Rodriguez-Nieva, Joaquin F.; Scheurer, Mathias S. Nature Physics, Vol. 15, Issue 8 https://doi.org/10.1038/s41567-019-0512-x	journal	May 2019
Identifying quantum phase transitions using artificial neural networks on experimental data Rem, Benno S.; Käming, Niklas; Tarnowski, Matthias Nature Physics, Vol. 15, Issue 9 https://doi.org/10.1038/s41567-019-0554-0	journal	July 2019
Classifying snapshots of the doped Hubbard model with machine learning Bohrdt, Annabelle; Chiu, Christie S.; Ji, Geoffrey Nature Physics, Vol. 15, Issue 9 https://doi.org/10.1038/s41567-019-0565-x	journal	July 2019
Many-body physics with individually controlled Rydberg atoms Browaeys, Antoine; Lahaye, Thierry Nature Physics, Vol. 16, Issue 2 https://doi.org/10.1038/s41567-019-0733-z	journal	January 2020
Quantum gas microscopy for single atom and spin detection Gross, Christian; Bakr, Waseem S. Nature Physics, Vol. 17, Issue 12 https://doi.org/10.1038/s41567-021-01370-5	journal	November 2021
Quantum phases of matter on a 256-atom programmable quantum simulator Ebadi, Sepehr; Wang, Tout T.; Levine, Harry Nature, Vol. 595, Issue 7866 https://doi.org/10.1038/s41586-021-03582-4	journal	July 2021
Quantum simulation of 2D antiferromagnets with hundreds of Rydberg atoms Scholl, Pascal; Schuler, Michael; Williams, Hannah J. Nature, Vol. 595, Issue 7866 https://doi.org/10.1038/s41586-021-03585-1	journal	July 2021
Machine learning quantum phases of matter beyond the fermion sign problem Broecker, Peter; Carrasquilla, Juan; Melko, Roger G. Scientific Reports, Vol. 7, Issue 1 https://doi.org/10.1038/s41598-017-09098-0	journal	August 2017
Multiscale structural complexity of natural patterns Bagrov, Andrey A.; Iakovlev, Ilia A.; Iliasov, Askar A. Proceedings of the National Academy of Sciences, Vol. 117, Issue 48 https://doi.org/10.1073/pnas.2004976117	journal	November 2020
Minimally entangled typical thermal state algorithms Stoudenmire, E. M.; White, Steven R. New Journal of Physics, Vol. 12, Issue 5 https://doi.org/10.1088/1367-2630/12/5/055026	journal	May 2010
Principal component analysis of the magnetic transition in the three-dimensional Fermi-Hubbard model Khatami, Ehsan Journal of Physics: Conference Series, Vol. 1290, Issue 1 https://doi.org/10.1088/1742-6596/1290/1/012006	journal	October 2019
Unsupervised machine learning of topological phase transitions from experimental data Käming, Niklas; Dawid, Anna; Kottmann, Korbinian Machine Learning: Science and Technology, Vol. 2, Issue 3 https://doi.org/10.1088/2632-2153/abffe7	journal	July 2021
Visualizing strange metallic correlations in the two-dimensional Fermi-Hubbard model with artificial intelligence Khatami, Ehsan; Guardado-Sanchez, Elmer; Spar, Benjamin M. Physical Review A, Vol. 102, Issue 3 https://doi.org/10.1103/PhysRevA.102.033326	journal	September 2020
Machine learning detection of Berezinskii-Kosterlitz-Thouless transitions in q -state clock models Miyajima, Yusuke; Murata, Yusuke; Tanaka, Yasuhiro Physical Review B, Vol. 104, Issue 7 https://doi.org/10.1103/PhysRevB.104.075114	journal	August 2021
Magnetic Susceptibility at Zero Temperature for the One-Dimensional Hubbard Model Shiba, H. Physical Review B, Vol. 6, Issue 3 https://doi.org/10.1103/PhysRevB.6.930	journal	August 1972
Tricritical behavior in the extended Hubbard chains Nakamura, Masaaki Physical Review B, Vol. 61, Issue 24 https://doi.org/10.1103/PhysRevB.61.16377	journal	June 2000
Bond-order-wave phase and quantum phase transitions in the one-dimensional extended Hubbard model Sengupta, Pinaki; Sandvik, Anders W.; Campbell, David K. Physical Review B, Vol. 65, Issue 15 https://doi.org/10.1103/PhysRevB.65.155113	journal	April 2002
Pattern of charge ordering in quasi-one-dimensional organic charge-transfer solids Clay, R. T.; Mazumdar, S.; Campbell, D. K. Physical Review B, Vol. 67, Issue 11 https://doi.org/10.1103/PhysRevB.67.115121	journal	March 2003
Scaling of entanglement support for matrix product states Tagliacozzo, L.; de Oliveira, Thiago. R.; Iblisdir, S. Physical Review B, Vol. 78, Issue 2 https://doi.org/10.1103/PhysRevB.78.024410	journal	July 2008
Matrix product states for critical spin chains: Finite-size versus finite-entanglement scaling Pirvu, B.; Vidal, G.; Verstraete, F. Physical Review B, Vol. 86, Issue 7 https://doi.org/10.1103/PhysRevB.86.075117	journal	August 2012
Gap scaling at Berezinskii-Kosterlitz-Thouless quantum critical points in one-dimensional Hubbard and Heisenberg models Dalmonte, M.; Carrasquilla, J.; Taddia, L. Physical Review B, Vol. 91, Issue 16 https://doi.org/10.1103/PhysRevB.91.165136	journal	April 2015
Ising tricriticality in the extended Hubbard model with bond dimerization Ejima, Satoshi; Essler, Fabian H. L.; Lange, Florian Physical Review B, Vol. 93, Issue 23 https://doi.org/10.1103/PhysRevB.93.235118	journal	June 2016
Unifying time evolution and optimization with matrix product states Haegeman, Jutho; Lubich, Christian; Oseledets, Ivan Physical Review B, Vol. 94, Issue 16 https://doi.org/10.1103/PhysRevB.94.165116	journal	October 2016
Discovering phase transitions with unsupervised learning Wang, Lei Physical Review B, Vol. 94, Issue 19 https://doi.org/10.1103/PhysRevB.94.195105	journal	November 2016
Machine learning of explicit order parameters: From the Ising model to SU(2) lattice gauge theory Wetzel, Sebastian J.; Scherzer, Manuel Physical Review B, Vol. 96, Issue 18 https://doi.org/10.1103/PhysRevB.96.184410	journal	November 2017
Variational optimization algorithms for uniform matrix product states Zauner-Stauber, V.; Vanderstraeten, L.; Fishman, M. T. Physical Review B, Vol. 97, Issue 4 https://doi.org/10.1103/PhysRevB.97.045145	journal	January 2018
Machine learning vortices at the Kosterlitz-Thouless transition Beach, Matthew J. S.; Golubeva, Anna; Melko, Roger G. Physical Review B, Vol. 97, Issue 4 https://doi.org/10.1103/PhysRevB.97.045207	journal	January 2018
Topological nature of spinons and holons: Elementary excitations from matrix product states with conserved symmetries Zauner-Stauber, V.; Vanderstraeten, L.; Haegeman, J. Physical Review B, Vol. 97, Issue 23 https://doi.org/10.1103/PhysRevB.97.235155	journal	June 2018
Critical entanglement for the half-filled extended Hubbard model Spalding, Jon; Tsai, Shan-Wen; Campbell, David K. Physical Review B, Vol. 99, Issue 19 https://doi.org/10.1103/PhysRevB.99.195445	journal	May 2019
Discovering phases, phase transitions, and crossovers through unsupervised machine learning: A critical examination Hu, Wenjian; Singh, Rajiv R. P.; Scalettar, Richard T. Physical Review E, Vol. 95, Issue 6 https://doi.org/10.1103/PhysRevE.95.062122	journal	June 2017
Minimally Entangled Typical Quantum States at Finite Temperature White, Steven R. Physical Review Letters, Vol. 102, Issue 19 https://doi.org/10.1103/PhysRevLett.102.190601	journal	May 2009
Theory of Finite-Entanglement Scaling at One-Dimensional Quantum Critical Points Pollmann, Frank; Mukerjee, Subroto; Turner, Ari M. Physical Review Letters, Vol. 102, Issue 25 https://doi.org/10.1103/PhysRevLett.102.255701	journal	June 2009
Time-Dependent Variational Principle for Quantum Lattices Haegeman, Jutho; Cirac, J. Ignacio; Osborne, Tobias J. Physical Review Letters, Vol. 107, Issue 7 https://doi.org/10.1103/PhysRevLett.107.070601	journal	August 2011
Quantum Loop Topography for Machine Learning Zhang, Yi; Kim, Eun-Ah Physical Review Letters, Vol. 118, Issue 21 https://doi.org/10.1103/PhysRevLett.118.216401	journal	May 2017
Complex Density Wave Orders and Quantum Phase Transitions in a Model of Square-Lattice Rydberg Atom Arrays Samajdar, Rhine; Ho, Wen Wei; Pichler, Hannes Physical Review Letters, Vol. 124, Issue 10 https://doi.org/10.1103/PhysRevLett.124.103601	journal	March 2020
Correlation exponents and the metal-insulator transition in the one-dimensional Hubbard model Schulz, H. J. Physical Review Letters, Vol. 64, Issue 23 https://doi.org/10.1103/PhysRevLett.64.2831	journal	June 1990
Density matrix formulation for quantum renormalization groups White, Steven R. Physical Review Letters, Vol. 69, Issue 19 https://doi.org/10.1103/PhysRevLett.69.2863	journal	November 1992
Spin-Peierls Transition in the Heisenberg Chain with Finite-Frequency Phonons Sandvik, Anders W.; Campbell, David K. Physical Review Letters, Vol. 83, Issue 1 https://doi.org/10.1103/PhysRevLett.83.195	journal	July 1999
Phase Diagram of the One-Dimensional Extended Hubbard Model at Half Filling Tsuchiizu, M.; Furusaki, A. Physical Review Letters, Vol. 88, Issue 5 https://doi.org/10.1103/PhysRevLett.88.056402	journal	January 2002
Ground-State Phase Diagram of a Half-Filled One-Dimensional Extended Hubbard Model Jeckelmann, Eric Physical Review Letters, Vol. 89, Issue 23 https://doi.org/10.1103/PhysRevLett.89.236401	journal	November 2002
Ground State Phases of the Half-Filled One-Dimensional Extended Hubbard Model Sandvik, Anders W.; Balents, Leon; Campbell, David K. Physical Review Letters, Vol. 92, Issue 23 https://doi.org/10.1103/PhysRevLett.92.236401	journal	June 2004
Dimerization in a Half-Filled One-Dimensional Extended Hubbard Model Zhang, Y. Z. Physical Review Letters, Vol. 92, Issue 24 https://doi.org/10.1103/PhysRevLett.92.246404	journal	June 2004
Phase Diagram of the One-Dimensional Half-Filled Extended Hubbard Model Ejima, Satoshi; Nishimoto, Satoshi Physical Review Letters, Vol. 99, Issue 21 https://doi.org/10.1103/PhysRevLett.99.216403	journal	November 2007
Revealing the topological nature of the bond order wave in a strongly correlated quantum system Julià-Farré, Sergi; González-Cuadra, Daniel; Patscheider, Alexander Physical Review Research, Vol. 4, Issue 3 https://doi.org/10.1103/PhysRevResearch.4.L032005	journal	July 2022
Machine learning discovery of new phases in programmable quantum simulator snapshots Miles, Cole; Samajdar, Rhine; Ebadi, Sepehr Physical Review Research, Vol. 5, Issue 1 https://doi.org/10.1103/PhysRevResearch.5.013026	journal	January 2023
Temperature Dependence of Spin and Charge Orders in the Doped Two-Dimensional Hubbard Model Xiao, Bo; He, Yuan-Yao; Georges, Antoine Physical Review X, Vol. 13, Issue 1 https://doi.org/10.1103/PhysRevX.13.011007	journal	January 2023
Pinning the Order: The Nature of Quantum Criticality in the Hubbard Model on Honeycomb Lattice Assaad, Fakher F.; Herbut, Igor F. Physical Review X, Vol. 3, Issue 3 https://doi.org/10.1103/PhysRevX.3.031010	journal	August 2013
Machine Learning Phases of Strongly Correlated Fermions Ch’ng, Kelvin; Carrasquilla, Juan; Melko, Roger G. Physical Review X, Vol. 7, Issue 3 https://doi.org/10.1103/PhysRevX.7.031038	journal	August 2017
Precise Extrapolation of the Correlation Function Asymptotics in Uniform Tensor Network States with Application to the Bose-Hubbard and XXZ Models Rams, Marek M.; Czarnik, Piotr; Cincio, Lukasz Physical Review X, Vol. 8, Issue 4 https://doi.org/10.1103/PhysRevX.8.041033	journal	November 2018
The density-matrix renormalization group Schollwöck, U. Reviews of Modern Physics, Vol. 77, Issue 1 https://doi.org/10.1103/RevModPhys.77.259	journal	April 2005
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
Probing the Superfluid-to-Mott Insulator Transition at the Single-Atom Level Bakr, W. S.; Peng, A.; Tai, M. E. Science, Vol. 329, Issue 5991 https://doi.org/10.1126/science.1192368	journal	June 2010
Surprises on the Way from One- to Two-Dimensional Quantum Magnets: The Ladder Materials Dagotto, E.; Rice, T. M. Science, Vol. 271, Issue 5249 https://doi.org/10.1126/science.271.5249.618	journal	February 1996
Extended Bose-Hubbard models with ultracold magnetic atoms Baier, S.; Mark, M. J.; Petter, D. Science, Vol. 352, Issue 6282 https://doi.org/10.1126/science.aac9812	journal	April 2016
Site-resolved measurement of the spin-correlation function in the Fermi-Hubbard model Parsons, M. F.; Mazurenko, A.; Chiu, C. S. Science, Vol. 353, Issue 6305 https://doi.org/10.1126/science.aag1430	journal	September 2016
Observation of spatial charge and spin correlations in the 2D Fermi-Hubbard model Cheuk, L. W.; Nichols, M. A.; Lawrence, K. R. Science, Vol. 353, Issue 6305 https://doi.org/10.1126/science.aag3349	journal	September 2016
Spin-imbalance in a 2D Fermi-Hubbard system Brown, Peter T.; Mitra, Debayan; Guardado-Sanchez, Elmer Science, Vol. 357, Issue 6358 https://doi.org/10.1126/science.aam7838	journal	September 2017
Direct observation of nonlocal fermion pairing in an attractive Fermi-Hubbard gas Hartke, Thomas; Oreg, Botond; Turnbaugh, Carter Science, Vol. 381, Issue 6653 https://doi.org/10.1126/science.ade4245	journal	July 2023
Numerical Studies on the Hubbard Model and the t - J Model in One- and Two-Dimensions Imada, Masatoshi; Hatsugai, Yasuhiro Journal of the Physical Society of Japan, Vol. 58, Issue 10 https://doi.org/10.1143/JPSJ.58.3752	journal	October 1989
The ITensor Software Library for Tensor Network Calculations Fishman, Matthew; White, Steven; Stoudenmire, Edwin SciPost Physics Codebases https://doi.org/10.21468/SciPostPhysCodeb.4	journal	August 2022
Tangent-space methods for uniform matrix product states Vanderstraeten, Laurens; Haegeman, Jutho; Verstraete, Frank SciPost Physics Lecture Notes https://doi.org/10.21468/SciPostPhysLectNotes.7	journal	January 2019

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