Simultaneous fermion and exciton condensations from a model Hamiltonian

Sager, LeeAnn M.; Mazziotti, David A.

doi:10.1103/physrevb.105.035143

Simultaneous fermion and exciton condensations from a model Hamiltonian

Journal Article · Tue Jan 25 23:00:00 EST 2022 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.105.035143· OSTI ID:1871629

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Univ. of Chicago, IL (United States); Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, IL (United States)
Univ. of Chicago, IL (United States)

Fermion-exciton condensation in which both fermion-pair (i.e., superconductivity) and exciton condensations occur simultaneously in a single coherent quantum state has recently been conjectured to exist. Here, we capture the fermion-exciton condensation through a model Hamiltonian that can recreate the physics of this new class of highly correlated condensation phenomena. We demonstrate that the Hamiltonian generates the large-eigenvalue signatures of fermion-pair and exciton condensations for a series of states with increasing particle numbers. The results confirm that the dual-condensate wave function arises from the entanglement of fermion-pair and exciton wave functions, which we previously predicted in the thermodynamic limit. Furthermore, this model Hamiltonian—generalizing well-known model Hamiltonians for either superconductivity or exciton condensation—can explore a wide variety of condensation behavior. It provides significant insights into the required forces for generating a fermion-exciton condensate, which will likely be invaluable for realizing such condensations in realistic materials with applications from superconductors to excitonic materials.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Chicago, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES); U.S. National Science Foundation; NSF GRFP

Grant/Contract Number:: SC0019215

OSTI ID:: 1871629

Journal Information:: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 3 Vol. 105; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (68)

Plancks Gesetz und Lichtquantenhypothese No authors listed Zeitschrift f�r Physik, Vol. 26, Issue 1 https://doi.org/10.1007/BF01327326	journal	December 1924
Quasi spin pairing and the structure of the Lipkin Model Cambiaggio, M. C.; Piastino, A. Zeitschrift f�r Physik A Atoms and Nuclei, Vol. 288, Issue 2 https://doi.org/10.1007/BF01408644	journal	June 1978
Non-coplanar Model States in Quantum Magnetism Applications of the High-Order Coupled Cluster Method Farnell, D. J. J.; Bishop, R. F.; Richter, J. Journal of Statistical Physics, Vol. 176, Issue 1 https://doi.org/10.1007/s10955-019-02297-1	journal	May 2019
Exact eigenstates of the pairing-force Hamiltonian Richardson, R. W.; Sherman, N. Nuclear Physics, Vol. 52 https://doi.org/10.1016/0029-5582(64)90687-X	journal	March 1964
Validity of many-body approximation methods for a solvable model Lipkin, H. J.; Meshkov, N.; Glick, A. J. Nuclear Physics, Vol. 62, Issue 2 https://doi.org/10.1016/0029-5582(65)90862-X	journal	February 1965
A restricted class of exact eigenstates of the pairing-force Hamiltonian Richardson, R. W. Physics Letters, Vol. 3, Issue 6 https://doi.org/10.1016/0031-9163(63)90259-2	journal	February 1963
Integrability of the pairing hamiltonian Cambiaggio, M. C.; Rivas, A. M. F.; Saraceno, M. Nuclear Physics A, Vol. 624, Issue 2 https://doi.org/10.1016/S0375-9474(97)00418-1	journal	October 1997
Application to the exact theory of the pairing model to some even isotopes of lead Richardson, R. W. Physics Letters, Vol. 5, Issue 1 https://doi.org/10.1016/S0375-9601(63)80039-0	journal	June 1963
Complexity and disequilibrium as telltales of superconductivity Pennini, F.; Plastino, A. Physica A: Statistical Mechanics and its Applications, Vol. 506 https://doi.org/10.1016/j.physa.2018.05.003	journal	September 2018
Multiple metastable states in an off-lattice Potts model Farías, Constanza; Davis, Sergio Physica A: Statistical Mechanics and its Applications, Vol. 581 https://doi.org/10.1016/j.physa.2021.126215	journal	November 2021
Comparison of the density-matrix renormalization group method applied to fractional quantum Hall systems in different geometries Hu, Zi-Xiang; Papić, Z.; Johri, S. Physics Letters A, Vol. 376, Issue 30-31 https://doi.org/10.1016/j.physleta.2012.05.031	journal	June 2012
Variational Optimization of the Second-Order Density Matrix Corresponding to a Seniority-Zero Configuration Interaction Wave Function Poelmans, Ward; Van Raemdonck, Mario; Verstichel, Brecht Journal of Chemical Theory and Computation, Vol. 11, Issue 9 https://doi.org/10.1021/acs.jctc.5b00378	journal	August 2015
Electronic Structure Calculations and the Ising Hamiltonian Xia, Rongxin; Bian, Teng; Kais, Sabre The Journal of Physical Chemistry B, Vol. 122, Issue 13 https://doi.org/10.1021/acs.jpcb.7b10371	journal	October 2017
Exciton Condensation in Molecular-Scale van der Waals Stacks Schouten, Anna O.; Sager, LeeAnn M.; Mazziotti, David A. The Journal of Physical Chemistry Letters, Vol. 12, Issue 40 https://doi.org/10.1021/acs.jpclett.1c02368	journal	October 2021
Bose–Einstein condensation of exciton polaritons Kasprzak, J.; Richard, M.; Kundermann, S. Nature, Vol. 443, Issue 7110 https://doi.org/10.1038/nature05131	journal	September 2006
Unconventional superconductivity in magic-angle graphene superlattices Cao, Yuan; Fatemi, Valla; Fang, Shiang Nature, Vol. 556, Issue 7699 https://doi.org/10.1038/nature26160	journal	March 2018
High-temperature superfluidity with indirect excitons in van der Waals heterostructures Fogler, M. M.; Butov, L. V.; Novoselov, K. S. Nature Communications, Vol. 5, Issue 1 https://doi.org/10.1038/ncomms5555	journal	July 2014
Quantum Hall drag of exciton condensate in graphene Liu, Xiaomeng; Watanabe, Kenji; Taniguchi, Takashi Nature Physics, Vol. 13, Issue 8 https://doi.org/10.1038/nphys4116	journal	May 2017
Observation of a quantum phase transition in the quantum Rabi model with a single trapped ion Cai, M. -L.; Liu, Z. -D.; Zhao, W. -D. Nature Communications, Vol. 12, Issue 1 https://doi.org/10.1038/s41467-021-21425-8	journal	February 2021
Evidence of high-temperature exciton condensation in two-dimensional atomic double layers Wang, Zefang; Rhodes, Daniel A.; Watanabe, Kenji Nature, Vol. 574, Issue 7776 https://doi.org/10.1038/s41586-019-1591-7	journal	October 2019
A semi exact solution for a metallic phase in a Holstein-Hubbard chain at half filling with Gaussian anharmonic phonons Debnath, Debika; Malik, M. Zahid; Chatterjee, Ashok Scientific Reports, Vol. 11, Issue 1 https://doi.org/10.1038/s41598-021-91604-6	journal	June 2021
Particle‐Hole Matrix: Its Connection with the Symmetries and Collective Features of the Ground State Garrod, Claude; Rosina, Mitja Journal of Mathematical Physics, Vol. 10, Issue 10 https://doi.org/10.1063/1.1664770	journal	October 1969
Exact Eigenstates of the Pairing‐Force Hamiltonian. II Richardson, R. W. Journal of Mathematical Physics, Vol. 6, Issue 7 https://doi.org/10.1063/1.1704367	journal	July 1965
Structure of Fermion Density Matrices. II. Antisymmetrized Geminal Powers Coleman, A. J. Journal of Mathematical Physics, Vol. 6, Issue 9 https://doi.org/10.1063/1.1704794	journal	September 1965
Natural Spin Orbital Analysis of Hydrogen Molecule Wave Functions Shull, Harrison The Journal of Chemical Physics, Vol. 30, Issue 6 https://doi.org/10.1063/1.1730212	journal	June 1959
Convex-set description of quantum phase transitions in the transverse Ising model using reduced-density-matrix theory Schwerdtfeger, Christine A.; Mazziotti, David A. The Journal of Chemical Physics, Vol. 130, Issue 22 https://doi.org/10.1063/1.3143403	journal	June 2009
Pair 2-electron reduced density matrix theory using localized orbitals Head-Marsden, Kade; Mazziotti, David A. The Journal of Chemical Physics, Vol. 147, Issue 8 https://doi.org/10.1063/1.4999423	journal	August 2017
Electron-hole Superconductivity (Review) Fil, D. V.; Shevchenko, S. I. Low Temperature Physics, Vol. 44, Issue 9 https://doi.org/10.1063/1.5052674	journal	September 2018
First-principles model hamiltonians for ferroelectric phase transitions Rabe, K. M.; Waghmare, U. V. Ferroelectrics, Vol. 151, Issue 1 https://doi.org/10.1080/00150199408244723	journal	January 1994
On the exact solutions of the Lipkin-Meshkov-Glick model Debergh, N.; Stancu, Fl Journal of Physics A: Mathematical and General, Vol. 34, Issue 15 https://doi.org/10.1088/0305-4470/34/15/305	journal	April 2001
On the thermodynamic limit of the Lipkin model Heiss, W. D. Journal of Physics A: Mathematical and General, Vol. 39, Issue 32 https://doi.org/10.1088/0305-4470/39/32/S10	journal	July 2006
Quantum simulation of spin models on an arbitrary lattice with trapped ions Korenblit, S.; Kafri, D.; Campbell, W. C. New Journal of Physics, Vol. 14, Issue 9 https://doi.org/10.1088/1367-2630/14/9/095024	journal	September 2012
Symmetry breaking and the geometry of reduced density matrices Zauner, V.; Draxler, D.; Vanderstraeten, L. New Journal of Physics, Vol. 18, Issue 11 https://doi.org/10.1088/1367-2630/18/11/113033	journal	November 2016
The exact ground state for a class of matrix Hamiltonian models: quantum phase transition and universality in the thermodynamic limit Ostilli, Massimo; Presilla, Carlo Journal of Statistical Mechanics: Theory and Experiment, Vol. 2006, Issue 11 https://doi.org/10.1088/1742-5468/2006/11/P11012	journal	November 2006
Twenty-five Years of High-Temperature Superconductivity – A Personal Review Anderson, Philip W. Journal of Physics: Conference Series, Vol. 449 https://doi.org/10.1088/1742-6596/449/1/012001	journal	July 2013
Quantum magnetism in spin-3/2 chains Hernández-Sarria, J. J.; Argüelles, A.; Rodríguez, K. Journal of Physics: Conference Series, Vol. 614 https://doi.org/10.1088/1742-6596/614/1/012005	journal	July 2015
Correlating AGP on a quantum computer Khamoshi, Armin; Evangelista, Francesco A.; Scuseria, Gustavo E. Quantum Science and Technology, Vol. 6, Issue 1 https://doi.org/10.1088/2058-9565/abc1bb	journal	November 2020
Theory of Superconductivity Bardeen, J.; Cooper, L. N.; Schrieffer, J. R. Physical Review, Vol. 108, Issue 5 https://doi.org/10.1103/PhysRev.108.1175	journal	December 1957
Eigenvalues of Fermion Density Matrices Sasaki, Fukashi Physical Review, Vol. 138, Issue 5B https://doi.org/10.1103/PhysRev.138.B1338	journal	June 1965
On the Bose-Einstein Condensation London, F. Physical Review, Vol. 54, Issue 11 https://doi.org/10.1103/PhysRev.54.947	journal	December 1938
The Theory of Liquid Helium Tisza, Laszlo Physical Review, Vol. 72, Issue 9 https://doi.org/10.1103/PhysRev.72.838	journal	November 1947
Contracted Schrödinger equation: Determining quantum energies and two-particle density matrices without wave functions Mazziotti, David A. Physical Review A, Vol. 57, Issue 6 https://doi.org/10.1103/PhysRevA.57.4219	journal	June 1998
Exactness of wave functions from two-body exponential transformations in many-body quantum theory Mazziotti, David A. Physical Review A, Vol. 69, Issue 1 https://doi.org/10.1103/PhysRevA.69.012507	journal	January 2004
Computation of quantum phase transitions by reduced-density-matrix mechanics Gidofalvi, Gergely; Mazziotti, David A. Physical Review A, Vol. 74, Issue 1 https://doi.org/10.1103/PhysRevA.74.012501	journal	July 2006
Large eigenvalue of the cumulant part of the two-electron reduced density matrix as a measure of off-diagonal long-range order Raeber, Alexandra; Mazziotti, David A. Physical Review A, Vol. 92, Issue 5 https://doi.org/10.1103/PhysRevA.92.052502	journal	November 2015
Potential coexistence of exciton and fermion-pair condensations Sager, LeeAnn M.; Safaei, Shiva; Mazziotti, David A. Physical Review B, Vol. 101, Issue 8 https://doi.org/10.1103/PhysRevB.101.081107	journal	February 2020
Quantum magnetism of iron-based ladders: Blocks, spirals, and spin flux Środa, Maksymilian; Dagotto, Elbio; Herbrych, Jacek Physical Review B, Vol. 104, Issue 4 https://doi.org/10.1103/PhysRevB.104.045128	journal	July 2021
Classical and quantum phase transitions in the Lipkin-Meshkov-Glick model Castaños, Octavio; López-Peña, Ramón; Hirsch, Jorge G. Physical Review B, Vol. 74, Issue 10 https://doi.org/10.1103/PhysRevB.74.104118	journal	September 2006
Room-temperature superfluidity in graphene bilayers Min, Hongki; Bistritzer, Rafi; Su, Jung-Jung Physical Review B, Vol. 78, Issue 12 https://doi.org/10.1103/PhysRevB.78.121401	journal	September 2008
Polynomial similarity transformation theory: A smooth interpolation between coupled cluster doubles and projected BCS applied to the reduced BCS Hamiltonian Degroote, Matthias; Henderson, Thomas M.; Zhao, Jinmo Physical Review B, Vol. 93, Issue 12 https://doi.org/10.1103/PhysRevB.93.125124	journal	March 2016
Quantum signature of exciton condensation Safaei, Shiva; Mazziotti, David A. Physical Review B, Vol. 98, Issue 4 https://doi.org/10.1103/PhysRevB.98.045122	journal	July 2018
t expansion and the Lipkin model Pérez, R.; Cambiaggio, M. C.; Vary, J. P. Physical Review C, Vol. 37, Issue 5 https://doi.org/10.1103/PhysRevC.37.2194	journal	May 1988
Simulation of X X Z Spin Models Using Sideband Transitions in Trapped Bosonic Gases Chu, Anjun; Will, Johannes; Arlt, Jan Physical Review Letters, Vol. 125, Issue 24 https://doi.org/10.1103/PhysRevLett.125.240504	journal	December 2020
Condensation of Indirect Excitons in Coupled AlAs/GaAs Quantum Wells Butov, L. V.; Zrenner, A.; Abstreiter, G. Physical Review Letters, Vol. 73, Issue 2 https://doi.org/10.1103/PhysRevLett.73.304	journal	July 1994
Parity-Affected Superconductivity in Ultrasmall Metallic Grains von Delft, Jan; Zaikin, Andrei D.; Golubev, Dmitrii S. Physical Review Letters, Vol. 77, Issue 15 https://doi.org/10.1103/PhysRevLett.77.3189	journal	October 1996
Signatures of a degenerate many-body state of interlayer excitons in a van der Waals heterostack Sigl, Lukas; Sigger, Florian; Kronowetter, Fabian Physical Review Research, Vol. 2, Issue 4 https://doi.org/10.1103/PhysRevResearch.2.042044	journal	December 2020
Preparation of an exciton condensate of photons on a 53-qubit quantum computer Sager, LeeAnn M.; Smart, Scott E.; Mazziotti, David A. Physical Review Research, Vol. 2, Issue 4 https://doi.org/10.1103/PhysRevResearch.2.043205	journal	November 2020
Chasing the Exciton Condensate Fuhrer, Michael S.; Hamilton, Alex R. Physics, Vol. 9 https://doi.org/10.1103/Physics.9.80	journal	July 2016
Concept of Off-Diagonal Long-Range Order and the Quantum Phases of Liquid He and of Superconductors Yang, C. N. Reviews of Modern Physics, Vol. 34, Issue 4 https://doi.org/10.1103/RevModPhys.34.694	journal	October 1962
Structure of Fermion Density Matrices Coleman, A. J. Reviews of Modern Physics, Vol. 35, Issue 3 https://doi.org/10.1103/RevModPhys.35.668	journal	July 1963
Two Kinds of Bosons and Bose Condensates Kohn, W.; Sherrington, D. Reviews of Modern Physics, Vol. 42, Issue 1 https://doi.org/10.1103/RevModPhys.42.1	journal	January 1970
Signatures of exciton condensation in a transition metal dichalcogenide Kogar, Anshul; Rak, Melinda S.; Vig, Sean Science, Vol. 358, Issue 6368 https://doi.org/10.1126/science.aam6432	journal	December 2017
Bose–Einstein condensation in one-dimensional optical lattices: Bogoliubov’s approximation and beyond Al-Sugheir, Mohamed K.; Awawdeh, Mufeed A.; Ghassib, Humam B. Canadian Journal of Physics, Vol. 94, Issue 7 https://doi.org/10.1139/cjp-2016-0019	journal	July 2016
Analytical and numerical analysis of the complete Lipkin–Meshkov–Glick Hamiltonian Co’, Giampaolo; De Leo, Stefano International Journal of Modern Physics E, Vol. 27, Issue 05 https://doi.org/10.1142/S0218301318500398	journal	May 2018
Coherent states of excitons Keldysh, L. V. Physics-Uspekhi, Vol. 60, Issue 11 https://doi.org/10.3367/ufne.2017.10.038227	journal	November 2017
From Real Materials to Model Hamiltonians With Density Matrix Downfolding Zheng, Huihuo; Changlani, Hitesh J.; Williams, Kiel T. Frontiers in Physics, Vol. 6 https://doi.org/10.3389/fphy.2018.00043	journal	May 2018
Interaction between Different Kinds of Quantum Phase Transitions Plastino, Angel Ricardo; Ferri, Gustavo Luis; Plastino, Angelo Quantum Reports, Vol. 3, Issue 2 https://doi.org/10.3390/quantum3020015	journal	April 2021
Exactly solvable models of nuclei Isacker, Piet; Heyde, Kristiaan Scholarpedia, Vol. 9, Issue 2 https://doi.org/10.4249/scholarpedia.31279	journal	January 2014

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Simultaneous fermion and exciton condensations from a model Hamiltonian

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