Macroproperties vs. microstates in the classical simulation of critical phenomena in quench dynamics of 1D Ising models
We study the tractability of classically simulating critical phenomena in the quench dynamics of one-dimensional transverse field Ising models (TFIMs) using highly truncated matrix product states (MPSs). We focus on two paradigmatic examples: a dynamical quantum phase transition (DQPT) that occurs i...
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IOP Publishing
2025-01-01
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| Series: | New Journal of Physics |
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| Online Access: | https://doi.org/10.1088/1367-2630/ada84f |
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| author | Anupam Mitra Tameem Albash Philip Daniel Blocher Jun Takahashi Akimasa Miyake Grant Biedermann Ivan H Deutsch |
| author_facet | Anupam Mitra Tameem Albash Philip Daniel Blocher Jun Takahashi Akimasa Miyake Grant Biedermann Ivan H Deutsch |
| author_sort | Anupam Mitra |
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| description | We study the tractability of classically simulating critical phenomena in the quench dynamics of one-dimensional transverse field Ising models (TFIMs) using highly truncated matrix product states (MPSs). We focus on two paradigmatic examples: a dynamical quantum phase transition (DQPT) that occurs in nonintegrable long-range TFIMs, and the infinite-time correlation length of the integrable nearest-neighbor TFIM when quenched to the critical point, where the quantities of interest involve equal time one- and two- point correlation functions, which we associate with macroproperties. For the DQPT, we show that the order parameters can be efficiently simulated with heavy truncation of the MPS bond dimension. This can be used to reliably extract critical properties of the phase transition, including critical exponents, even when the full many-body state is not simulated with high fidelity. The long-time correlation length near the critical point is more sensitive to the full many-body state fidelity, and generally requires a large bond dimension MPS. Nonetheless, this can still be efficiently simulated with strongly truncated MPS because it can be extracted from the short-time behavior of the dynamics where entanglement is low. Our results provide illustrations of scenarios where accurate calculation of the full many-body state (microstate) is intractable due to the volume-law growth of entanglement, yet a precise specification of an exact microstate may not be required when simulating macroproperties that play a role in phases of matter of many-body systems. We also study the tractability of simulation using truncated MPS based on quantum chaos and equilibration in the models. We find a counterintuitive inverse relationship, whereby local expectation values are most easily approximated for chaotic systems whose exact many-body state is most intractable. |
| format | Article |
| id | doaj-art-117a40a6f76e453e971972a52db435dd |
| institution | Kabale University |
| issn | 1367-2630 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj-art-117a40a6f76e453e971972a52db435dd2025-01-30T13:19:08ZengIOP PublishingNew Journal of Physics1367-26302025-01-0127101302610.1088/1367-2630/ada84fMacroproperties vs. microstates in the classical simulation of critical phenomena in quench dynamics of 1D Ising modelsAnupam Mitra0https://orcid.org/0009-0004-6711-2477Tameem Albash1https://orcid.org/0000-0003-3916-3985Philip Daniel Blocher2Jun Takahashi3Akimasa Miyake4Grant Biedermann5https://orcid.org/0009-0001-7550-0224Ivan H Deutsch6https://orcid.org/0000-0002-1733-5750Center for Quantum Information and Control, Department of Physics and Astronomy, University of New Mexico , Albuquerque, NM 87131, United States of AmericaCenter for Quantum Information and Control, Department of Physics and Astronomy, University of New Mexico , Albuquerque, NM 87131, United States of America; Department of Electrical and Computer Engineering, University of New Mexico , Albuquerque, NM 87131, United States of AmericaCenter for Quantum Information and Control, Department of Physics and Astronomy, University of New Mexico , Albuquerque, NM 87131, United States of AmericaCenter for Quantum Information and Control, Department of Physics and Astronomy, University of New Mexico , Albuquerque, NM 87131, United States of AmericaCenter for Quantum Information and Control, Department of Physics and Astronomy, University of New Mexico , Albuquerque, NM 87131, United States of AmericaCenter for Quantum Research and Technology, Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma , Norman, OK 73019, United States of AmericaCenter for Quantum Information and Control, Department of Physics and Astronomy, University of New Mexico , Albuquerque, NM 87131, United States of AmericaWe study the tractability of classically simulating critical phenomena in the quench dynamics of one-dimensional transverse field Ising models (TFIMs) using highly truncated matrix product states (MPSs). We focus on two paradigmatic examples: a dynamical quantum phase transition (DQPT) that occurs in nonintegrable long-range TFIMs, and the infinite-time correlation length of the integrable nearest-neighbor TFIM when quenched to the critical point, where the quantities of interest involve equal time one- and two- point correlation functions, which we associate with macroproperties. For the DQPT, we show that the order parameters can be efficiently simulated with heavy truncation of the MPS bond dimension. This can be used to reliably extract critical properties of the phase transition, including critical exponents, even when the full many-body state is not simulated with high fidelity. The long-time correlation length near the critical point is more sensitive to the full many-body state fidelity, and generally requires a large bond dimension MPS. Nonetheless, this can still be efficiently simulated with strongly truncated MPS because it can be extracted from the short-time behavior of the dynamics where entanglement is low. Our results provide illustrations of scenarios where accurate calculation of the full many-body state (microstate) is intractable due to the volume-law growth of entanglement, yet a precise specification of an exact microstate may not be required when simulating macroproperties that play a role in phases of matter of many-body systems. We also study the tractability of simulation using truncated MPS based on quantum chaos and equilibration in the models. We find a counterintuitive inverse relationship, whereby local expectation values are most easily approximated for chaotic systems whose exact many-body state is most intractable.https://doi.org/10.1088/1367-2630/ada84fquantum simulationdynamical phase transitionsquantum criticalityquantum quenchapproximation methods for many-body systemstensor network methods |
| spellingShingle | Anupam Mitra Tameem Albash Philip Daniel Blocher Jun Takahashi Akimasa Miyake Grant Biedermann Ivan H Deutsch Macroproperties vs. microstates in the classical simulation of critical phenomena in quench dynamics of 1D Ising models New Journal of Physics quantum simulation dynamical phase transitions quantum criticality quantum quench approximation methods for many-body systems tensor network methods |
| title | Macroproperties vs. microstates in the classical simulation of critical phenomena in quench dynamics of 1D Ising models |
| title_full | Macroproperties vs. microstates in the classical simulation of critical phenomena in quench dynamics of 1D Ising models |
| title_fullStr | Macroproperties vs. microstates in the classical simulation of critical phenomena in quench dynamics of 1D Ising models |
| title_full_unstemmed | Macroproperties vs. microstates in the classical simulation of critical phenomena in quench dynamics of 1D Ising models |
| title_short | Macroproperties vs. microstates in the classical simulation of critical phenomena in quench dynamics of 1D Ising models |
| title_sort | macroproperties vs microstates in the classical simulation of critical phenomena in quench dynamics of 1d ising models |
| topic | quantum simulation dynamical phase transitions quantum criticality quantum quench approximation methods for many-body systems tensor network methods |
| url | https://doi.org/10.1088/1367-2630/ada84f |
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