Floquet insulators and lattice fermions beyond naive time discretization

Iadecola, Thomas; Sen, Srimoyee; Sivertsen, Lars

doi:10.1103/PhysRevResearch.6.013098

Title: Floquet insulators and lattice fermions beyond naive time discretization

Journal Article · 25 January 2024 · Physical Review Research

DOI: https://doi.org/10.1103/PhysRevResearch.6.013098 · OSTI ID:2282918

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Periodically driven quantum systems known as Floquet insulators can host topologically protected bound states known as “ $π$ modes” that exhibit response at half the frequency of the drive. Such states can also appear in undriven lattice field theories when time is discretized as a result of fermion doubling, raising the question of whether these two phenomena could be connected. Recently we demonstrated such a connection at the level of an explicit mapping between the spectra of a continuous-time Floquet model and a discrete-time undriven lattice fermion model. However, this mapping relied on a symmetry of the single-particle spectrum that is not present for generic drive parameters. Inspired by the example of the temporal Wilson term in lattice field theory, in this paper we extend this mapping to the full drive parameter space by allowing the parameters of the discrete-time model to be frequency-dependent. The spectra of the resulting lattice fermion models exactly match the quasienergy spectrum of the Floquet model in the thermodynamic limit. Our results demonstrate that spectral features characteristic of beyond-equilibrium physics in Floquet systems can be replicated in static systems with appropriate time discretization. Published by the American Physical Society 2024

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Research Organization:: Iowa State Univ., Ames, IA (United States)

Sponsoring Organization:: USDOE; USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: SC0021892

OSTI ID:: 2282918

Journal Information:: Physical Review Research, Journal Name: Physical Review Research Journal Issue: 1 Vol. 6; ISSN PPRHAI; ISSN 2643-1564

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

References (48)

Floquet topological insulators Cayssol, Jérôme; Dóra, Balázs; Simon, Ferenc physica status solidi (RRL) - Rapid Research Letters, Vol. 7, Issue 1-2 https://doi.org/10.1002/pssr.201206451	journal	January 2013
Ensemble fermions for electroweak dynamics and the fermion preheating temperature Mou, Zong-Gang; Saffin, Paul M.; Tranberg, Anders Journal of High Energy Physics, Vol. 2013, Issue 11 https://doi.org/10.1007/JHEP11(2013)097	journal	November 2013
A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems Abanin, Dmitry; De Roeck, Wojciech; Ho, Wen Wei Communications in Mathematical Physics, Vol. 354, Issue 3 https://doi.org/10.1007/s00220-017-2930-x	journal	June 2017
A method for simulating chiral fermions on the lattice Kaplan, David B. Physics Letters B, Vol. 288, Issue 3-4 https://doi.org/10.1016/0370-2693(92)91112-M	journal	August 1992
Chern-Simons currents and chiral fermions on the lattice Golterman, Maarten F. L.; Jansen, Karl; Kaplan, David B. Physics Letters B, Vol. 301, Issue 2-3 https://doi.org/10.1016/0370-2693(93)90692-B	journal	March 1993
Absence of neutrinos on a lattice Nielsen, H. B.; Ninomiya, M. Nuclear Physics B, Vol. 185, Issue 1 https://doi.org/10.1016/0550-3213(81)90361-8	journal	July 1981
Absence of neutrinos on a lattice Nielsen, H. B.; Ninomiya, M. Nuclear Physics B, Vol. 193, Issue 1 https://doi.org/10.1016/0550-3213(81)90524-1	journal	December 1981
Absence of neutrinos on a lattice: Proof by homotopy theory Nielsen, H. B.; Ninomiya, M. Nuclear Physics B, Vol. 195, Issue 3, p. 541-542 https://doi.org/10.1016/0550-3213(82)90011-6	journal	February 1982
Sphaleron transitions and baryon asymmetry: A numerical, real-time analysis Ambjørn, J.; Askgaard, T.; Porter, H. Nuclear Physics B, Vol. 353, Issue 2 https://doi.org/10.1016/0550-3213(91)90341-T	journal	April 1991
Chiral fermions from lattice boundaries Shamir, Yigal Nuclear Physics B, Vol. 406, Issue 1-2 https://doi.org/10.1016/0550-3213(93)90162-I	journal	September 1993
Exactly massless quarks on the lattice Neuberger, Herbert Physics Letters B, Vol. 417, Issue 1-2 https://doi.org/10.1016/S0370-2693(97)01368-3	journal	January 1998
More about exactly massless quarks on the lattice Neuberger, Herbert Physics Letters B, Vol. 427, Issue 3-4 https://doi.org/10.1016/S0370-2693(98)00355-4	journal	May 1998
Real-time dynamics with fermions on a lattice Aarts, Gert; Smit, Jan Nuclear Physics B, Vol. 555, Issue 1-2 https://doi.org/10.1016/S0550-3213(99)00320-X	journal	August 1999
Floquet approach to ℤ2 lattice gauge theories with ultracold atoms in optical lattices Schweizer, Christian; Grusdt, Fabian; Berngruber, Moritz Nature Physics, Vol. 15, Issue 11 https://doi.org/10.1038/s41567-019-0649-7	journal	September 2019
Realization of an anomalous Floquet topological system with ultracold atoms Wintersperger, Karen; Braun, Christoph; Ünal, F. Nur Nature Physics, Vol. 16, Issue 10 https://doi.org/10.1038/s41567-020-0949-y	journal	June 2020
Floquet engineering of topological metal states and hybridization of edge states with bulk states in dimerized two-leg ladders Jangjan, Milad; Hosseini, Mir Vahid Scientific Reports, Vol. 10, Issue 1 https://doi.org/10.1038/s41598-020-71196-3	journal	August 2020
Topological phase transition between a normal insulator and a topological metal state in a quasi-one-dimensional system Jangjan, Milad; Hosseini, Mir Vahid Scientific Reports, Vol. 11, Issue 1 https://doi.org/10.1038/s41598-021-92390-x	journal	June 2021
Band structure engineering and non-equilibrium dynamics in Floquet topological insulators Rudner, Mark S.; Lindner, Netanel H. Nature Reviews Physics, Vol. 2, Issue 5 https://doi.org/10.1038/s42254-020-0170-z	journal	May 2020
Universal high-frequency behavior of periodically driven systems: from dynamical stabilization to Floquet engineering Bukov, Marin; D'Alessio, Luca; Polkovnikov, Anatoli Advances in Physics, Vol. 64, Issue 2 https://doi.org/10.1080/00018732.2015.1055918	journal	March 2015
Time crystals: a review Sacha, Krzysztof; Zakrzewski, Jakub Reports on Progress in Physics, Vol. 81, Issue 1 https://doi.org/10.1088/1361-6633/aa8b38	journal	November 2017
Topological singularities and the general classification of Floquet–Bloch systems Nathan, Frederik; Rudner, Mark S. New Journal of Physics, Vol. 17, Issue 12 https://doi.org/10.1088/1367-2630/17/12/125014	journal	December 2015
Microwave Engineering of Programmable XXZ Hamiltonians in Arrays of Rydberg Atoms Scholl, P.; Williams, H. J.; Bornet, G. PRX Quantum, Vol. 3, Issue 2 https://doi.org/10.1103/PRXQuantum.3.020303	journal	April 2022
Simulating Heisenberg interactions in the Ising model with strong drive fields Ciavarella, Anthony N.; Caspar, Stephan; Singh, Hersh Physical Review A, Vol. 108, Issue 4 https://doi.org/10.1103/PhysRevA.108.042216	journal	October 2023
Floquet topological phase transitions in a periodically quenched dimer Jangjan, Milad; Foa Torres, Luis E. F.; Hosseini, Mir Vahid Physical Review B, Vol. 106, Issue 22 https://doi.org/10.1103/PhysRevB.106.224306	journal	December 2022
Topological defects and gapless modes in insulators and superconductors Teo, Jeffrey C. Y.; Kane, C. L. Physical Review B, Vol. 82, Issue 11 https://doi.org/10.1103/PhysRevB.82.115120	journal	September 2010
Topological characterization of periodically driven quantum systems Kitagawa, Takuya; Berg, Erez; Rudner, Mark Physical Review B, Vol. 82, Issue 23 https://doi.org/10.1103/PhysRevB.82.235114	journal	December 2010
Floquet generation of Majorana end modes and topological invariants Thakurathi, Manisha; Patel, Aavishkar A.; Sen, Diptiman Physical Review B, Vol. 88, Issue 15 https://doi.org/10.1103/PhysRevB.88.155133	journal	October 2013
Complex classes of periodically driven topological lattice systems Fruchart, Michel Physical Review B, Vol. 93, Issue 11 https://doi.org/10.1103/PhysRevB.93.115429	journal	March 2016
Classification of topological phases in periodically driven interacting systems Else, Dominic V.; Nayak, Chetan Physical Review B, Vol. 93, Issue 20 https://doi.org/10.1103/PhysRevB.93.201103	journal	May 2016
Phase structure of one-dimensional interacting Floquet systems. I. Abelian symmetry-protected topological phases von Keyserlingk, C. W.; Sondhi, S. L. Physical Review B, Vol. 93, Issue 24 https://doi.org/10.1103/PhysRevB.93.245145	journal	June 2016
Long-range Heisenberg models in quasiperiodically driven crystals of trapped ions Bermudez, A.; Tagliacozzo, L.; Sierra, G. Physical Review B, Vol. 95, Issue 2 https://doi.org/10.1103/PhysRevB.95.024431	journal	January 2017
Hamiltonian formulation of Wilson's lattice gauge theories Kogut, John; Susskind, Leonard Physical Review D, Vol. 11, Issue 2 https://doi.org/10.1103/PhysRevD.11.395	journal	January 1975
Solitons with fermion number ½ Jackiw, R.; Rebbi, C. Physical Review D, Vol. 13, Issue 12 https://doi.org/10.1103/PhysRevD.13.3398	journal	June 1976
A remnant of chiral symmetry on the lattice Ginsparg, Paul H.; Wilson, Kenneth G. Physical Review D, Vol. 25, Issue 10 https://doi.org/10.1103/PhysRevD.25.2649	journal	May 1982
Chern-Simons number diffusion and hard thermal loops on the lattice Bödeker, D.; Moore, Guy D.; Rummukainen, K. Physical Review D, Vol. 61, Issue 5 https://doi.org/10.1103/PhysRevD.61.056003	journal	February 2000
Realization of the Hofstadter Hamiltonian with Ultracold Atoms in Optical Lattices Aidelsburger, M.; Atala, M.; Lohse, M. Physical Review Letters, Vol. 111, Issue 18 https://doi.org/10.1103/PhysRevLett.111.185301	journal	October 2013
Topological Index for Periodically Driven Time-Reversal Invariant 2D Systems Carpentier, David; Delplace, Pierre; Fruchart, Michel Physical Review Letters, Vol. 114, Issue 10 https://doi.org/10.1103/PhysRevLett.114.106806	journal	March 2015
Phase Structure of Driven Quantum Systems Khemani, Vedika; Lazarides, Achilleas; Moessner, Roderich Physical Review Letters, Vol. 116, Issue 25 https://doi.org/10.1103/PhysRevLett.116.250401	journal	June 2016
Floquet Time Crystals Else, Dominic V.; Bauer, Bela; Nayak, Chetan Physical Review Letters, Vol. 117, Issue 9 https://doi.org/10.1103/PhysRevLett.117.090402	journal	August 2016
Solitons in Polyacetylene Su, W. P.; Schrieffer, J. R.; Heeger, A. J. Physical Review Letters, Vol. 42, Issue 25 https://doi.org/10.1103/PhysRevLett.42.1698	journal	June 1979
Robust Dynamic Hamiltonian Engineering of Many-Body Spin Systems Choi, Joonhee; Zhou, Hengyun; Knowles, Helena S. Physical Review X, Vol. 10, Issue 3 https://doi.org/10.1103/PhysRevX.10.031002	journal	July 2020
Anomalous Edge States and the Bulk-Edge Correspondence for Periodically Driven Two-Dimensional Systems Rudner, Mark S.; Lindner, Netanel H.; Berg, Erez Physical Review X, Vol. 3, Issue 3 https://doi.org/10.1103/PhysRevX.3.031005	journal	July 2013
Periodically Driven Quantum Systems: Effective Hamiltonians and Engineered Gauge Fields Goldman, N.; Dalibard, J. Physical Review X, Vol. 4, Issue 3 https://doi.org/10.1103/PhysRevX.4.031027	journal	August 2014
Long-time Behavior of Isolated Periodically Driven Interacting Lattice Systems D’Alessio, Luca; Rigol, Marcos Physical Review X, Vol. 4, Issue 4 https://doi.org/10.1103/PhysRevX.4.041048	journal	December 2014
Classification of Interacting Topological Floquet Phases in One Dimension Potter, Andrew C.; Morimoto, Takahiro; Vishwanath, Ashvin Physical Review X, Vol. 6, Issue 4 https://doi.org/10.1103/PhysRevX.6.041001	journal	October 2016
Colloquium: Topological insulators Hasan, M. Z.; Kane, C. L. Reviews of Modern Physics, Vol. 82, Issue 4, p. 3045-3067 https://doi.org/10.1103/RevModPhys.82.3045	journal	November 2010
Colloquium: Atomic quantum gases in periodically driven optical lattices Eckardt, André Reviews of Modern Physics, Vol. 89, Issue 1 https://doi.org/10.1103/RevModPhys.89.011004	journal	March 2017
Discrete Time Crystals Else, Dominic V.; Monroe, Christopher; Nayak, Chetan Annual Review of Condensed Matter Physics, Vol. 11, Issue 1 https://doi.org/10.1146/annurev-conmatphys-031119-050658	journal	March 2020