Dissipative Floquet Dynamics: from Steady State to Measurement Induced Criticality in Trapped-ion Chains

Piotr Sierant1,2, Giuliano Chiriacò1,3, Federica M. Surace1,3, Shraddha Sharma1, Xhek Turkeshi1,3, Marcello Dalmonte1,3, Rosario Fazio1,4, and Guido Pagano5

1The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
2Institute of Theoretical Physics, Jagiellonian University in Krakow, Łojasiewicza 11, 30-348 Kraków, Poland
3SISSA — International School of Advanced Studies, via Bonomea 265, 34136 Trieste, Italy
4Dipartimento di Fisica, Università di Napoli ``Federico II'', Monte S. Angelo, I-80126 Napoli, Italy
5Department of Physics and Astronomy, Rice University, 6100 Main Street, Houston, TX 77005, USA

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Abstract

Quantum systems evolving unitarily and subject to quantum measurements exhibit various types of non-equilibrium phase transitions, arising from the competition between unitary evolution and measurements. Dissipative phase transitions in steady states of time-independent Liouvillians and measurement induced phase transitions at the level of quantum trajectories are two primary examples of such transitions. Investigating a many-body spin system subject to periodic resetting measurements, we argue that many-body dissipative Floquet dynamics provides a natural framework to analyze both types of transitions. We show that a dissipative phase transition between a ferromagnetic ordered phase and a paramagnetic disordered phase emerges for long-range systems as a function of measurement probabilities. A measurement induced transition of the entanglement entropy between volume law scaling and sub-volume law scaling is also present, and is distinct from the ordering transition. The two phases correspond to an error-correcting and a quantum-Zeno regimes, respectively. The ferromagnetic phase is lost for short range interactions, while the volume law phase of the entanglement is enhanced. An analysis of multifractal properties of wave function in Hilbert space provides a common perspective on both types of transitions in the system. Our findings are immediately relevant to trapped ion experiments, for which we detail a blueprint proposal based on currently available platforms.

Entanglement among many particles is a fundamental feature that allows quantum processors to tackle specific tasks faster than their classical counterparts. The main challenge in creating and protecting entanglement is posed by another puzzling feature of quantum mechanics, namely decoherence: a quantum system “measured” by the environment loses its quantum correlations and is projected into classical states. Errors caused by environmental noise can be modelled as non-unitary operations acting on the qubits. Hence, understanding how correlations propagates in quantum systems in presence of controlled local non-unitary operations, and which tools can be employed to govern its dynamics, are not only fundamental questions, but represent crucial steps towards building reliable and scalable quantum processors where entanglement can be tailored and protected.
In this work we study quantum systems subjected to the interplay between unitary coherent evolution and the interaction with the outside environment. We develop a unified framework to study a prototypical quantum many-body system, one-dimensional long-range interacting spin chains, and investigate two different but related phenomena: A symmetry breaking phase transition that separates an ordered and disordered phase, and a “measurement induced” phase transition that separates two regimes in which entanglement behaves in dramatically different ways. Moreover, we examine the requirements and challenges for an experimental realization of both phenomena with trapped atomic ions.
Our results suggest that the two phenomena are fundamentally related and that induced entanglement phase transitions may be observed in a much broader class of systems than what has been considered so far.

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► References

[1] L. M. Sieberer, M. Buchhold, and S. Diehl, Reports on Progress in Physics 79, 096001 (2016).
https:/​/​doi.org/​10.1088/​0034-4885/​79/​9/​096001

[2] T. E. Lee, S. Gopalakrishnan, and M. D. Lukin, Phys. Rev. Lett. 110, 257204 (2013).
https:/​/​doi.org/​10.1103/​PhysRevLett.110.257204

[3] J. Jin, A. Biella, O. Viyuela, L. Mazza, J. Keeling, R. Fazio, and D. Rossini, Phys. Rev. X 6, 031011 (2016).
https:/​/​doi.org/​10.1103/​PhysRevX.6.031011

[4] M. F. Maghrebi and A. V. Gorshkov, Physical Review B 93, 014307 (2016).
https:/​/​doi.org/​10.1103/​PhysRevB.93.014307

[5] V. R. Overbeck, M. F. Maghrebi, A. V. Gorshkov, and H. Weimer, Phys. Rev. A 95, 042133 (2017).
https:/​/​doi.org/​10.1103/​PhysRevA.95.042133

[6] M. Foss-Feig, J. T. Young, V. V. Albert, A. V. Gorshkov, and M. F. Maghrebi, Phys. Rev. Lett. 119, 190402 (2017).
https:/​/​doi.org/​10.1103/​PhysRevLett.119.190402

[7] J. Jin, A. Biella, O. Viyuela, C. Ciuti, R. Fazio, and D. Rossini, Phys. Rev. B 98, 241108 (2018).
https:/​/​doi.org/​10.1103/​PhysRevB.98.241108

[8] J. M. Fink, A. Dombi, A. Vukics, A. Wallraff, and P. Domokos, Phys. Rev. X 7, 011012 (2017).
https:/​/​doi.org/​10.1103/​PhysRevX.7.011012

[9] M. Fitzpatrick, N. M. Sundaresan, A. C. Y. Li, J. Koch, and A. A. Houck, Phys. Rev. X 7, 011016 (2017).
https:/​/​doi.org/​10.1103/​PhysRevX.7.011016

[10] N. Fläschner, D. Vogel, M. Tarnowski, M. Tarnowski, B. S. Rem, D.-S. Lühmann, M. Heyl, J. C. Budich, L. Mathey, K. Sengstock, and C. Weitenberg, Nature Physics 14, 265 (2018).
https:/​/​doi.org/​10.1038/​s41567-017-0013-8

[11] N. Syassen, D. M. Bauer, M. Lettner, T. Volz, D. Dietze, J. J. García-Ripoll, J. I. Cirac, G. Rempe, and S. Dürr, Science 320, 1329 (2008).
https:/​/​doi.org/​10.1126/​science.1155309

[12] T. Tomita, S. Nakajima, I. Danshita, Y. Takasu, and Y. Takahashi, Science Advances 3, e1701513 (2017).
https:/​/​doi.org/​10.1126/​sciadv.1701513

[13] S. Diehl, A. Micheli, A. Kantian, B. Kraus, H. P. Büchler, and P. Zoller, Nature Physics 4, 878 (2008).
https:/​/​doi.org/​10.1038/​nphys1073

[14] D. Poletti, J.-S. Bernier, A. Georges, and C. Kollath, Phys. Rev. Lett. 109, 045302 (2012).
https:/​/​doi.org/​10.1103/​PhysRevLett.109.045302

[15] D. Poletti, P. Barmettler, A. Georges, and C. Kollath, Phys. Rev. Lett. 111, 195301 (2013).
https:/​/​doi.org/​10.1103/​PhysRevLett.111.195301

[16] L. M. Sieberer, S. D. Huber, E. Altman, and S. Diehl, Phys. Rev. Lett. 110, 195301 (2013).
https:/​/​doi.org/​10.1103/​PhysRevLett.110.195301

[17] J. Marino and S. Diehl, Phys. Rev. Lett. 116, 070407 (2016).
https:/​/​doi.org/​10.1103/​PhysRevLett.116.070407

[18] M. Schiró, C. Joshi, M. Bordyuh, R. Fazio, J. Keeling, and H. E. Türeci, Phys. Rev. Lett. 116, 143603 (2016).
https:/​/​doi.org/​10.1103/​PhysRevLett.116.143603

[19] F. Minganti, A. Biella, N. Bartolo, and C. Ciuti, Phys. Rev. A 98, 042118 (2018).
https:/​/​doi.org/​10.1103/​PhysRevA.98.042118

[20] R. Rota, F. Minganti, C. Ciuti, and V. Savona, Phys. Rev. Lett. 122, 110405 (2019).
https:/​/​doi.org/​10.1103/​PhysRevLett.122.110405

[21] J. T. Young, A. V. Gorshkov, M. Foss-Feig, and M. F. Maghrebi, Phys. Rev. X 10, 011039 (2020).
https:/​/​doi.org/​10.1103/​PhysRevX.10.011039

[22] D. A. Paz and M. F. Maghrebi, ``Driven-dissipative ising model: Dynamical crossover at weak dissipation,'' (2021), arXiv:1906.08278.
arXiv:1906.08278

[23] M. Marcuzzi, E. Levi, S. Diehl, J. P. Garrahan, and I. Lesanovsky, Phys. Rev. Lett. 113, 210401 (2014).
https:/​/​doi.org/​10.1103/​PhysRevLett.113.210401

[24] K. Seetharam, A. Lerose, R. Fazio, and J. Marino, ``Correlation engineering via non-local dissipation,'' (2021), arXiv:2101.06445.
arXiv:2101.06445

[25] V. R. Morrison, R. P. Chatelain, K. L. Tiwari, A. Hendaoui, A. Bruhács, M. Chaker, and B. J. Siwick, Science 346, 445 (2014).
https:/​/​doi.org/​10.1126/​science.1253779

[26] D. Fausti, R. I. Tobey, N. Dean, S. Kaiser, A. Dienst, M. C. Hoffmann, S. Pyon, T. Takayama, H. Takagi, and A. Cavalleri, Science 331, 189 (2011).
https:/​/​doi.org/​10.1126/​science.1197294

[27] M. Mitrano, A. Cantaluppi, D. Nicoletti, S. Kaiser, A. Perucchi, S. Lupi, P. Di Pietro, D. Pontiroli, M. Riccò, S. R. Clark, D. Jaksch, and A. Cavalleri, Nature 530, 461 (2016).
https:/​/​doi.org/​10.1038/​nature16522

[28] A. Zong, A. Kogar, Y.-Q. Bie, T. Rohwer, C. Lee, E. Baldini, E. Ergeçen, M. B. Yilmaz, B. Freelon, E. J. Sie, H. Zhou, J. Straquadine, P. Walmsley, P. E. Dolgirev, A. V. Rozhkov, I. R. Fisher, P. Jarillo-Herrero, B. V. Fine, and N. Gedik, Nature Physics 15, 27 (2019).
https:/​/​doi.org/​10.1038/​s41567-018-0311-9

[29] A. Kogar, A. Zong, P. E. Dolgirev, X. Shen, J. Straquadine, Y.-Q. Bie, X. Wang, T. Rohwer, I.-C. Tung, Y. Yang, R. Li, J. Yang, S. Weathersby, S. Park, M. E. Kozina, E. J. Sie, H. Wen, P. Jarillo-Herrero, I. R. Fisher, X. Wang, and N. Gedik, Nature Physics 16, 159 (2020).
https:/​/​doi.org/​10.1038/​s41567-019-0705-3

[30] T. F. Nova, A. S. Disa, M. Fechner, and A. Cavalleri, Science 364, 1075 (2019).
https:/​/​doi.org/​10.1126/​science.aaw4911

[31] A. Disa, M. Fechner, T. Nova, B. Liu, M. Först, D. Prabhakaran, P. Radaelli, and A. Cavalleri, Nature Physics 16, 937 (2020).
https:/​/​doi.org/​10.1038/​s41567-020-0936-3

[32] G. Chiriacò, A. J. Millis, and I. L. Aleiner, Phys. Rev. B 98, 220510(R) (2018).
https:/​/​doi.org/​10.1103/​PhysRevB.98.220510

[33] M. A. Sentef, A. Tokuno, A. Georges, and C. Kollath, Phys. Rev. Lett. 118, 087002 (2017).
https:/​/​doi.org/​10.1103/​PhysRevLett.118.087002

[34] Z. Sun and A. J. Millis, Phys. Rev. X 10, 021028 (2020).
https:/​/​doi.org/​10.1103/​PhysRevX.10.021028

[35] S. Dhar and S. Dasgupta, Phys. Rev. A 93, 050103 (2016).
https:/​/​doi.org/​10.1103/​PhysRevA.93.050103

[36] A. Nahum, J. Ruhman, S. Vijay, and J. Haah, Phys. Rev. X 7, 031016 (2017).
https:/​/​doi.org/​10.1103/​PhysRevX.7.031016

[37] Y. Li, X. Chen, and M. P. A. Fisher, Phys. Rev. B 98, 205136 (2018).
https:/​/​doi.org/​10.1103/​PhysRevB.98.205136

[38] Y. Li, X. Chen, and M. P. Fisher, Physical Review B 100, 134306 (2019).
https:/​/​doi.org/​10.1103/​PhysRevB.100.134306

[39] Y. Li, X. Chen, A. W. W. Ludwig, and M. P. A. Fisher, Phys. Rev. B 104, 104305 (2021).
https:/​/​doi.org/​10.1103/​PhysRevB.104.104305

[40] Y. Li and M. P. A. Fisher, Phys. Rev. B 103, 104306 (2021).
https:/​/​doi.org/​10.1103/​PhysRevB.103.104306

[41] A. Chan, R. M. Nandkishore, M. Pretko, and G. Smith, Phys. Rev. B 99, 224307 (2019).
https:/​/​doi.org/​10.1103/​PhysRevB.99.224307

[42] T. Zhou and A. Nahum, Phys. Rev. B 99, 174205 (2019).
https:/​/​doi.org/​10.1103/​PhysRevB.99.174205

[43] B. Skinner, J. Ruhman, and A. Nahum, Phys. Rev. X 9, 031009 (2019).
https:/​/​doi.org/​10.1103/​PhysRevX.9.031009

[44] Y. Bao, S. Choi, and E. Altman, Physical Review B 101, 104301 (2020).
https:/​/​doi.org/​10.1103/​PhysRevB.101.104301

[45] C.-M. Jian, Y.-Z. You, R. Vasseur, and A. W. W. Ludwig, Phys. Rev. B 101, 104302 (2020).
https:/​/​doi.org/​10.1103/​PhysRevB.101.104302

[46] M. J. Gullans and D. A. Huse, Phys. Rev. Lett. 125, 070606 (2020a).
https:/​/​doi.org/​10.1103/​PhysRevLett.125.070606

[47] M. J. Gullans and D. A. Huse, Phys. Rev. X 10, 041020 (2020b).
https:/​/​doi.org/​10.1103/​PhysRevX.10.041020

[48] S. Gopalakrishnan and M. J. Gullans, Phys. Rev. Lett. 126, 170503 (2021).
https:/​/​doi.org/​10.1103/​PhysRevLett.126.170503

[49] X. Turkeshi, R. Fazio, and M. Dalmonte, Phys. Rev. B 102, 014315 (2020).
https:/​/​doi.org/​10.1103/​PhysRevB.102.014315

[50] X. Turkeshi, A. Biella, R. Fazio, M. Dalmonte, and M. Schiró, Phys. Rev. B 103, 224210 (2021).
https:/​/​doi.org/​10.1103/​PhysRevB.103.224210

[51] M. Ippoliti, M. J. Gullans, S. Gopalakrishnan, D. A. Huse, and V. Khemani, Phys. Rev. X 11, 011030 (2021).
https:/​/​doi.org/​10.1103/​PhysRevX.11.011030

[52] M. Buchhold, Y. Minoguchi, A. Altland, and S. Diehl, Phys. Rev. X 11, 041004 (2021).
https:/​/​doi.org/​10.1103/​PhysRevX.11.041004

[53] T. Minato, K. Sugimoto, T. Kuwahara, and K. Saito, Phys. Rev. Lett. 128, 010603 (2022).
https:/​/​doi.org/​10.1103/​PhysRevLett.128.010603

[54] M. Block, Y. Bao, S. Choi, E. Altman, and N. Y. Yao, Phys. Rev. Lett. 128, 010604 (2022).
https:/​/​doi.org/​10.1103/​PhysRevLett.128.010604

[55] S. Sharma, X. Turkeshi, R. Fazio, and M. Dalmonte, ``Measurement-induced criticality in extended and long-range unitary circuits,'' (2021), arXiv:2110.14403.
arXiv:2110.14403

[56] T. Hashizume, G. Bentsen, and A. J. Daley, ``Measurement-induced phase transitions in sparse nonlocal scramblers,'' (2021), arXiv:2109.10944.
arXiv:2109.10944

[57] S. Sahu, S.-K. Jian, G. Bentsen, and B. Swingle, ``Entanglement phases in large-n hybrid brownian circuits with long-range couplings,'' (2021), arXiv:2109.00013.
arXiv:2109.00013

[58] X. Chen, Y. Li, M. P. A. Fisher, and A. Lucas, Phys. Rev. Research 2, 033017 (2020).
https:/​/​doi.org/​10.1103/​PhysRevResearch.2.033017

[59] A. Biella and M. Schiró, Quantum 5, 528 (2021).
https:/​/​doi.org/​10.22331/​q-2021-08-19-528

[60] Q. Tang, X. Chen, and W. Zhu, Phys. Rev. B 103, 174303 (2021).
https:/​/​doi.org/​10.1103/​PhysRevB.103.174303

[61] P. Zhang, C. Liu, S.-K. Jian, and X. Chen, ``Universal entanglement transitions of free fermions with long-range non-unitary dynamics,'' (2021a), arXiv:2105.08895.
arXiv:2105.08895

[62] S.-K. Jian, C. Liu, X. Chen, B. Swingle, and P. Zhang, Phys. Rev. Lett. 127, 140601 (2021).
https:/​/​doi.org/​10.1103/​PhysRevLett.127.140601

[63] P. Zhang, S.-K. Jian, C. Liu, and X. Chen, Quantum 5, 579 (2021b).
https:/​/​doi.org/​10.22331/​q-2021-11-16-579

[64] T. Müller, S. Diehl, and M. Buchhold, Phys. Rev. Lett. 128, 010605 (2022).
https:/​/​doi.org/​10.1103/​PhysRevLett.128.010605

[65] O. Lunt, M. Szyniszewski, and A. Pal, Phys. Rev. B 104, 155111 (2021).
https:/​/​doi.org/​10.1103/​PhysRevB.104.155111

[66] O. Alberton, M. Buchhold, and S. Diehl, Phys. Rev. Lett. 126, 170602 (2021).
https:/​/​doi.org/​10.1103/​PhysRevLett.126.170602

[67] L. Zhang, J. A. Reyes, S. Kourtis, C. Chamon, E. R. Mucciolo, and A. E. Ruckenstein, Phys. Rev. B 101, 235104 (2020).
https:/​/​doi.org/​10.1103/​PhysRevB.101.235104

[68] R. Vasseur, A. C. Potter, Y.-Z. You, and A. W. W. Ludwig, Phys. Rev. B 100, 134203 (2019).
https:/​/​doi.org/​10.1103/​PhysRevB.100.134203

[69] J. Lopez-Piqueres, B. Ware, and R. Vasseur, Phys. Rev. B 102, 064202 (2020).
https:/​/​doi.org/​10.1103/​PhysRevB.102.064202

[70] A. Nahum, S. Roy, B. Skinner, and J. Ruhman, PRX Quantum 2, 010352 (2021).
https:/​/​doi.org/​10.1103/​PRXQuantum.2.010352

[71] X. Cao, A. Tilloy, and A. D. Luca, SciPost Phys. 7, 24 (2019).
https:/​/​doi.org/​10.21468/​SciPostPhys.7.2.024

[72] S. Maity, S. Bandyopadhyay, S. Bhattacharjee, and A. Dutta, Phys. Rev. B 101, 180301 (2020).
https:/​/​doi.org/​10.1103/​PhysRevB.101.180301

[73] Y. Fuji and Y. Ashida, Phys. Rev. B 102, 054302 (2020).
https:/​/​doi.org/​10.1103/​PhysRevB.102.054302

[74] M. Szyniszewski, A. Romito, and H. Schomerus, Phys. Rev. Lett. 125, 210602 (2020).
https:/​/​doi.org/​10.1103/​PhysRevLett.125.210602

[75] N. Lang and H. P. Büchler, Phys. Rev. A 92, 012128 (2015).
https:/​/​doi.org/​10.1103/​PhysRevA.92.012128

[76] S. Vijay, ``Measurement-driven phase transition within a volume-law entangled phase,'' (2020), arXiv:2005.03052.
arXiv:2005.03052

[77] J. Iaconis, A. Lucas, and X. Chen, Phys. Rev. B 102, 224311 (2020).
https:/​/​doi.org/​10.1103/​PhysRevB.102.224311

[78] G. S. Bentsen, S. Sahu, and B. Swingle, Phys. Rev. B 104, 094304 (2021).
https:/​/​doi.org/​10.1103/​PhysRevB.104.094304

[79] T. Botzung, S. Diehl, and M. Müller, Phys. Rev. B 104, 184422 (2021).
https:/​/​doi.org/​10.1103/​PhysRevB.104.184422

[80] J. Zhang, G. Pagano, P. W. Hess, A. Kyprianidis, P. Becker, H. Kaplan, A. V. Gorshkov, Z.-X. Gong, and C. Monroe, Nature 551, 601 (2017).
https:/​/​doi.org/​10.1038/​nature24654

[81] C. Monroe, W. C. Campbell, L.-M. Duan, Z.-X. Gong, A. V. Gorshkov, P. W. Hess, R. Islam, K. Kim, N. M. Linke, G. Pagano, P. Richerme, C. Senko, and N. Y. Yao, Rev. Mod. Phys. 93, 025001 (2021).
https:/​/​doi.org/​10.1103/​RevModPhys.93.025001

[82] W. L. Tan, P. Becker, F. Liu, G. Pagano, K. S. Collins, A. De, L. Feng, H. B. Kaplan, A. Kyprianidis, R. Lundgren, W. Morong, S. Whitsitt, A. V. Gorshkov, and C. Monroe, Nature Physics 17, 742 (2021).
https:/​/​doi.org/​10.1038/​s41567-021-01194-3

[83] A. Kyprianidis, F. Machado, W. Morong, P. Becker, K. S. Collins, D. V. Else, L. Feng, P. W. Hess, C. Nayak, G. Pagano, N. Y. Yao, and C. Monroe, Science 372, 1192 (2021).
https:/​/​doi.org/​10.1126/​science.abg8102

[84] W. Happer, Rev. Mod. Phys. 44, 169 (1972).

[85] R. Noek, G. Vrijsen, D. Gaultney, E. Mount, T. Kim, P. Maunz, and J. Kim, Opt. Lett. 38, 4735 (2013a).
https:/​/​doi.org/​10.1364/​OL.38.004735

[86] J. E. Christensen, D. Hucul, W. C. Campbell, and E. R. Hudson, npj Quantum Information 6, 35 (2020).
https:/​/​doi.org/​10.1038/​s41534-020-0265-5

[87] S. Sang and T. H. Hsieh, Phys. Rev. Research 3, 023200 (2021).
https:/​/​doi.org/​10.1103/​PhysRevResearch.3.023200

[88] Y. Bao, S. Choi, and E. Altman, Annals of Physics 435, 168618 (2021).
https:/​/​doi.org/​10.1016/​j.aop.2021.168618

[89] A. Schnell, A. Eckardt, and S. Denisov, Phys. Rev. B 101, 100301 (2020).
https:/​/​doi.org/​10.1103/​PhysRevB.101.100301

[90] M. Bukov, L. D'Alessio, and A. Polkovnikov, Advances in Physics 64, 139 (2015).
https:/​/​doi.org/​10.1080/​00018732.2015.1055918

[91] B. Žunkovič, M. Heyl, M. Knap, and A. Silva, Phys. Rev. Lett. 120, 130601 (2018).
https:/​/​doi.org/​10.1103/​PhysRevLett.120.130601

[92] P. Hauke and L. Tagliacozzo, Phys. Rev. Lett. 111, 207202 (2013).
https:/​/​doi.org/​10.1103/​PhysRevLett.111.207202

[93] J. Schachenmayer, B. P. Lanyon, C. F. Roos, and A. J. Daley, Phys. Rev. X 3, 031015 (2013).
https:/​/​doi.org/​10.1103/​PhysRevX.3.031015

[94] A. Lerose and S. Pappalardi, Phys. Rev. Research 2, 012041 (2020a).
https:/​/​doi.org/​10.1103/​PhysRevResearch.2.012041

[95] S. Pappalardi, A. Russomanno, B. Žunkovič, F. Iemini, A. Silva, and R. Fazio, Phys. Rev. B 98, 134303 (2018).
https:/​/​doi.org/​10.1103/​PhysRevB.98.134303

[96] A. Lerose and S. Pappalardi, Phys. Rev. A 102, 032404 (2020b).
https:/​/​doi.org/​10.1103/​PhysRevA.102.032404

[97] M. B. Plenio and P. L. Knight, Rev. Mod. Phys. 70, 101 (1998).
https:/​/​doi.org/​10.1103/​RevModPhys.70.101

[98] H. Carmichael, An open systems approach to quantum optics: lectures presented at the Université Libre de Bruxelles, October 28 to November 4, 1991, Vol. 18 (Springer Science & Business Media, 2009).

[99] A. J. Daley, Advances in Physics 63, 77 (2014).
https:/​/​doi.org/​10.1080/​00018732.2014.933502

[100] A. Sørensen and K. Mølmer, Phys. Rev. Lett. 82, 1971 (1999).
https:/​/​doi.org/​10.1103/​PhysRevLett.82.1971

[101] A. Das, K. Sengupta, D. Sen, and B. K. Chakrabarti, Phys. Rev. B 74, 144423 (2006).
https:/​/​doi.org/​10.1103/​PhysRevB.74.144423

[102] B. Sciolla and G. Biroli, Phys. Rev. Lett. 105, 220401 (2010).
https:/​/​doi.org/​10.1103/​PhysRevLett.105.220401

[103] M. Snoek, EuroPhys. Lett. 95, 30006 (2011).
https:/​/​doi.org/​10.1209/​0295-5075/​95/​30006

[104] B. Sciolla and G. Biroli, Journal of Statistical Mechanics: Theory and Experiment 2011, P11003 (2011).
https:/​/​doi.org/​10.1088/​1742-5468/​2011/​11/​p11003

[105] Fino and Algazi, IEEE Transactions on Computers C-25, 1142 (1976).
https:/​/​doi.org/​10.1109/​TC.1976.1674569

[106] J. Arndt, Matters Computational – Ideas, Algorithms, Source Code (Springer-Verlag, Berlin Heidelberg, 2011).

[107] T. Prosen, Phys. Rev. Lett. 80, 1808 (1998).
https:/​/​doi.org/​10.1103/​PhysRevLett.80.1808

[108] T. Prosen, Phys. Rev. E 60, 3949 (1999).
https:/​/​doi.org/​10.1103/​PhysRevE.60.3949

[109] T. L. M. Lezama, S. Bera, and J. H. Bardarson, Phys. Rev. B 99, 161106 (2019).
https:/​/​doi.org/​10.1103/​PhysRevB.99.161106

[110] S. Sarkar and J. S. Satchell, Journal of Physics A: Mathematical and General 20, 2147 (1987).
https:/​/​doi.org/​10.1088/​0305-4470/​20/​8/​028

[111] B. A. Chase and J. M. Geremia, Phys. Rev. A 78, 052101 (2008).
https:/​/​doi.org/​10.1103/​PhysRevA.78.052101

[112] B. Q. Baragiola, B. A. Chase, and J. Geremia, Phys. Rev. A 81, 032104 (2010).
https:/​/​doi.org/​10.1103/​PhysRevA.81.032104

[113] T. E. Lee, H. Häffner, and M. C. Cross, Phys. Rev. Lett. 108, 023602 (2012).
https:/​/​doi.org/​10.1103/​PhysRevLett.108.023602

[114] M. Xu, D. A. Tieri, and M. J. Holland, Phys. Rev. A 87, 062101 (2013).
https:/​/​doi.org/​10.1103/​PhysRevA.87.062101

[115] M. Bolaños and P. Barberis-Blostein, Journal of Physics A: Mathematical and Theoretical 48, 445301 (2015).
https:/​/​doi.org/​10.1088/​1751-8113/​48/​44/​445301

[116] M. Gegg and M. Richter, New Journal of Physics 18, 043037 (2016).
https:/​/​doi.org/​10.1088/​1367-2630/​18/​4/​043037

[117] M. Gegg and M. Richter, Scientific Reports 7, 16304 (2017).
https:/​/​doi.org/​10.1038/​s41598-017-16178-8

[118] M. Gegg, A. Carmele, A. Knorr, and M. Richter, New Journal of Physics 20, 013006 (2018).
https:/​/​doi.org/​10.1088/​1367-2630/​aa9cdd

[119] N. Shammah, S. Ahmed, N. Lambert, S. De Liberato, and F. Nori, Phys. Rev. A 98, 063815 (2018).
https:/​/​doi.org/​10.1103/​PhysRevA.98.063815

[120] F. Iemini, A. Russomanno, J. Keeling, M. Schirò, M. Dalmonte, and R. Fazio, Phys. Rev. Lett. 121, 035301 (2018).
https:/​/​doi.org/​10.1103/​PhysRevLett.121.035301

[121] Y. Hama, W. J. Munro, and K. Nemoto, Phys. Rev. Lett. 120, 060403 (2018).
https:/​/​doi.org/​10.1103/​PhysRevLett.120.060403

[122] S. Sachdev, Quantum Phase Transitions, 2nd ed. (Cambridge University Press, 2011).
https:/​/​doi.org/​10.1017/​CBO9780511973765

[123] D. Rossini and E. Vicari, Phys. Rev. B 102, 035119 (2020).
https:/​/​doi.org/​10.1103/​PhysRevB.102.035119

[124] K. Binder, Phys. Rev. Lett. 47, 693 (1981a).
https:/​/​doi.org/​10.1103/​PhysRevLett.47.693

[125] K. Binder, Zeitschrift für Physik B Condensed Matter 43, 119 (1981b).
https:/​/​doi.org/​10.1007/​BF01293604

[126] Q. Tang and W. Zhu, Phys. Rev. Research 2, 013022 (2020).
https:/​/​doi.org/​10.1103/​PhysRevResearch.2.013022

[127] S. Goto and I. Danshita, Phys. Rev. A 102, 033316 (2020).
https:/​/​doi.org/​10.1103/​PhysRevA.102.033316

[128] O. Lunt and A. Pal, Phys. Rev. Research 2, 043072 (2020).
https:/​/​doi.org/​10.1103/​PhysRevResearch.2.043072

[129] T.-C. Lu and T. Grover, PRX Quantum 2, 040319 (2021).
https:/​/​doi.org/​10.1103/​PRXQuantum.2.040319

[130] M. Szyniszewski, A. Romito, and H. Schomerus, Phys. Rev. B 100, 064204 (2019).
https:/​/​doi.org/​10.1103/​PhysRevB.100.064204

[131] A. Zabalo, M. J. Gullans, J. H. Wilson, S. Gopalakrishnan, D. A. Huse, and J. H. Pixley, Phys. Rev. B 101, 060301 (2020).
https:/​/​doi.org/​10.1103/​PhysRevB.101.060301

[132] B. Groisman, S. Popescu, and A. Winter, Phys. Rev. A 72, 032317 (2005).
https:/​/​doi.org/​10.1103/​PhysRevA.72.032317

[133] R. Fan, S. Vijay, A. Vishwanath, and Y.-Z. You, Phys. Rev. B 103, 174309 (2021).
https:/​/​doi.org/​10.1103/​PhysRevB.103.174309

[134] P. Calabrese and J. Cardy, Journal of Physics A: Mathematical and Theoretical 42, 504005 (2009).
https:/​/​doi.org/​10.1088/​1751-8113/​42/​50/​504005

[135] P. Zoller, M. Marte, and D. F. Walls, Phys. Rev. A 35, 198 (1987).
https:/​/​doi.org/​10.1103/​PhysRevA.35.198

[136] S. Choi, Y. Bao, X.-L. Qi, and E. Altman, Phys. Rev. Lett. 125, 030505 (2020).
https:/​/​doi.org/​10.1103/​PhysRevLett.125.030505

[137] N. Macé, F. Alet, and N. Laflorencie, Phys. Rev. Lett. 123, 180601 (2019).
https:/​/​doi.org/​10.1103/​PhysRevLett.123.180601

[138] A. Rodriguez, L. J. Vasquez, K. Slevin, and R. A. Römer, Phys. Rev. Lett. 105, 046403 (2010).
https:/​/​doi.org/​10.1103/​PhysRevLett.105.046403

[139] W. Beugeling, A. Andreanov, and M. Haque, Journal of Statistical Mechanics: Theory and Experiment 2015, P02002 (2015).
https:/​/​doi.org/​10.1088/​1742-5468/​2015/​02/​p02002

[140] D. J. Luitz, I. Khaymovich, and Y. Bar Lev, SciPost Physics Core 2 (2020).
https:/​/​doi.org/​10.21468/​SciPostPhysCore.2.2.006

[141] T. Brydges, A. Elben, P. Jurcevic, B. Vermersch, C. Maier, B. P. Lanyon, P. Zoller, R. Blatt, and C. F. Roos, Science 364, 260 (2019).
https:/​/​doi.org/​10.1126/​science.aau4963

[142] S. de Léséleuc, V. Lienhard, P. Scholl, D. Barredo, S. Weber, N. Lang, H. P. Büchler, T. Lahaye, and A. Browaeys, Science 365, 775 (2019).
https:/​/​doi.org/​10.1126/​science.aav9105

[143] B. Chiaro, C. Neill, A. Bohrdt, M. Filippone, F. Arute, K. Arya, R. Babbush, D. Bacon, J. Bardin, R. Barends, S. Boixo, D. Buell, B. Burkett, Y. Chen, Z. Chen, R. Collins, A. Dunsworth, E. Farhi, A. Fowler, B. Foxen, C. Gidney, M. Giustina, M. Harrigan, T. Huang, S. Isakov, E. Jeffrey, Z. Jiang, D. Kafri, K. Kechedzhi, J. Kelly, P. Klimov, A. Korotkov, F. Kostritsa, D. Landhuis, E. Lucero, J. McClean, X. Mi, A. Megrant, M. Mohseni, J. Mutus, M. McEwen, O. Naaman, M. Neeley, M. Niu, A. Petukhov, C. Quintana, N. Rubin, D. Sank, K. Satzinger, A. Vainsencher, T. White, Z. Yao, P. Yeh, A. Zalcman, V. Smelyanskiy, H. Neven, S. Gopalakrishnan, D. Abanin, M. Knap, J. Martinis, and P. Roushan, ``Direct measurement of non-local interactions in the many-body localized phase,'' (2020), arXiv:1910.06024.
arXiv:1910.06024

[144] G. Pagano, A. Bapat, P. Becker, K. S. Collins, A. De, P. W. Hess, H. B. Kaplan, A. Kyprianidis, W. L. Tan, C. Baldwin, L. T. Brady, A. Deshpande, F. Liu, S. Jordan, A. V. Gorshkov, and C. Monroe, Proceedings of the National Academy of Sciences 117, 25396 (2020).
https:/​/​doi.org/​10.1073/​pnas.2006373117

[145] P. Scholl, M. Schuler, H. J. Williams, A. A. Eberharter, D. Barredo, K.-N. Schymik, V. Lienhard, L.-P. Henry, T. C. Lang, T. Lahaye, A. M. Läuchli, and A. Browaeys, Nature 595, 233 (2021).
https:/​/​doi.org/​10.1038/​s41586-021-03585-1

[146] S. Ebadi, T. T. Wang, H. Levine, A. Keesling, G. Semeghini, A. Omran, D. Bluvstein, R. Samajdar, H. Pichler, W. W. Ho, S. Choi, S. Sachdev, M. Greiner, V. Vuletić, and M. D. Lukin, Nature 595, 227 (2021).
https:/​/​doi.org/​10.1038/​s41586-021-03582-4

[147] J. Zeiher, J.-y. Choi, A. Rubio-Abadal, T. Pohl, R. van Bijnen, I. Bloch, and C. Gross, Phys. Rev. X 7, 041063 (2017).
https:/​/​doi.org/​10.1103/​PhysRevX.7.041063

[148] C. Veit, N. Zuber, O. A. Herrera-Sancho, V. S. V. Anasuri, T. Schmid, F. Meinert, R. Löw, and T. Pfau, Phys. Rev. X 11, 011036 (2021).
https:/​/​doi.org/​10.1103/​PhysRevX.11.011036

[149] A. Solórzano, L. F. Santos, and E. J. Torres-Herrera, Phys. Rev. Research 3, L032030 (2021).
https:/​/​doi.org/​10.1103/​PhysRevResearch.3.L032030

[150] C. Schneider, D. Porras, and T. Schaetz, Reports on Progress in Physics 75, 024401 (2012).
https:/​/​doi.org/​10.1088/​0034-4885/​75/​2/​024401

[151] P. Jurcevic, H. Shen, P. Hauke, C. Maier, T. Brydges, C. Hempel, B. P. Lanyon, M. Heyl, R. Blatt, and C. F. Roos, Phys. Rev. Lett. 119, 080501 (2017).
https:/​/​doi.org/​10.1103/​PhysRevLett.119.080501

[152] H. B. Kaplan, L. Guo, W. L. Tan, A. De, F. Marquardt, G. Pagano, and C. Monroe, Phys. Rev. Lett. 125, 120605 (2020).
https:/​/​doi.org/​10.1103/​PhysRevLett.125.120605

[153] M. K. Joshi, F. Kranzl, A. Schuckert, I. Lovas, C. Maier, R. Blatt, M. Knap, and C. F. Roos, ``Observing emergent hydrodynamics in a long-range quantum magnet,'' (2021), arXiv:2107.00033.
arXiv:2107.00033

[154] P. Richerme, Z.-X. Gong, A. Lee, C. Senko, J. Smith, M. Foss-Feig, S. Michalakis, A. V. Gorshkov, and C. Monroe, Nature 511, 198 (2014).
https:/​/​doi.org/​10.1038/​nature13450

[155] R. Islam, C. Senko, W. C. Campbell, S. Korenblit, J. Smith, A. Lee, E. E. Edwards, C.-C. J. Wang, J. K. Freericks, and C. Monroe, Science 340, 583 (2013).
https:/​/​doi.org/​10.1126/​science.1232296

[156] C.-Y. Shih, S. Motlakunta, N. Kotibhaskar, M. Sajjan, R. Hablützel, and R. Islam, npj Quantum Information 7, 57 (2021).
https:/​/​doi.org/​10.1038/​s41534-021-00396-0

[157] T. Mendes-Santos, X. Turkeshi, M. Dalmonte, and A. Rodriguez, Phys. Rev. X 11, 011040 (2021a).
https:/​/​doi.org/​10.1103/​PhysRevX.11.011040

[158] T. Mendes-Santos, A. Angelone, A. Rodriguez, R. Fazio, and M. Dalmonte, PRX Quantum 2, 030332 (2021b).
https:/​/​doi.org/​10.1103/​PRXQuantum.2.030332

[159] X. Turkeshi, ``Measurement-induced criticality as a data-structure transition,'' (2021), arXiv:2101.06245.
arXiv:2101.06245

[160] E. Facco, M. d'Errico, A. Rodriguez, and A. Laio, Scientific Reports 7, 12140 (2017).
https:/​/​doi.org/​10.1038/​s41598-017-11873-y

[161] A. J. Daley, H. Pichler, J. Schachenmayer, and P. Zoller, Phys. Rev. Lett. 109, 020505 (2012).
https:/​/​doi.org/​10.1103/​PhysRevLett.109.020505

[162] D. A. Abanin and E. Demler, Phys. Rev. Lett. 109, 020504 (2012).
https:/​/​doi.org/​10.1103/​PhysRevLett.109.020504

[163] S. J. van Enk and C. W. J. Beenakker, Phys. Rev. Lett. 108, 110503 (2012).
https:/​/​doi.org/​10.1103/​PhysRevLett.108.110503

[164] A. Elben, B. Vermersch, M. Dalmonte, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 120, 050406 (2018).
https:/​/​doi.org/​10.1103/​PhysRevLett.120.050406

[165] H.-Y. Huang, R. Kueng, and J. Preskill, Nature Physics 16, 1050 (2020).
https:/​/​doi.org/​10.1038/​s41567-020-0932-7

[166] R. Noek, G. Vrijsen, D. Gaultney, E. Mount, T. Kim, P. Maunz, and J. Kim, Opt. Lett. 38, 4735 (2013b).
https:/​/​doi.org/​10.1364/​OL.38.004735

[167] M. Schacht, J. R. Danielson, S. Rahaman, J. R. Torgerson, J. Zhang, and M. M. Schauer, Journal of Physics B: Atomic, Molecular and Optical Physics 48, 065003 (2015).
https:/​/​doi.org/​10.1088/​0953-4075/​48/​6/​065003

[168] A. Mohanty, E. A. Dijck, M. N. Portela, N. Valappol, A. T. Grier, T. Meijknecht, L. Willmann, and K. Jungmann, Hyperfine Interactions 233, 113 (2015).
https:/​/​doi.org/​10.1007/​s10751-015-1161-9

[169] M. Roberts, P. Taylor, G. P. Barwood, P. Gill, H. A. Klein, and W. R. C. Rowley, Phys. Rev. Lett. 78, 1876 (1997).
https:/​/​doi.org/​10.1103/​PhysRevLett.78.1876

[170] H. X. Yang, J. Y. Ma, Y. K. Wu, Y. Wang, M. M. Cao, W. X. Guo, Y. Y. Huang, L. Feng, Z. C. Zhou, and L. M. Duan, ``Realizing coherently convertible dual-type qubits with the same ion species,'' (2021), arXiv:2106.14906.
arXiv:2106.14906

[171] A. Erhard, H. Poulsen Nautrup, M. Meth, L. Postler, R. Stricker, M. Stadler, V. Negnevitsky, M. Ringbauer, P. Schindler, H. J. Briegel, R. Blatt, N. Friis, and T. Monz, Nature 589, 220 (2021).
https:/​/​doi.org/​10.1038/​s41586-020-03079-6

[172] S. Debnath, N. M. Linke, C. Figgatt, K. A. Landsman, K. Wright, and C. Monroe, Nature 536, 63 (2016).
https:/​/​doi.org/​10.1038/​nature18648

[173] N. D. Mermin and H. Wagner, Phys. Rev. Lett. 17, 1133 (1966).
https:/​/​doi.org/​10.1103/​PhysRevLett.17.1133

[174] P. C. Hohenberg, Phys. Rev. 158, 383 (1967).
https:/​/​doi.org/​10.1103/​PhysRev.158.383

[175] F. J. Dyson, Communications in Mathematical Physics 12, 91 (1969).
https:/​/​doi.org/​10.1007/​BF01645907

[176] R. D. Averitt and A. J. Taylor, Journal of Physics: Condensed Matter 14, R1357 (2002).
https:/​/​doi.org/​10.1088/​0953-8984/​14/​50/​203
http:/​/​stacks.iop.org/​0953-8984/​14/​i=50/​a=203

[177] D. N. Basov, R. D. Averitt, D. van der Marel, M. Dressel, and K. Haule, Rev. Mod. Phys. 83, 471 (2011).
https:/​/​doi.org/​10.1103/​RevModPhys.83.471

[178] A. Lavasani, Y. Alavirad, and M. Barkeshli, Nature Physics 17, 342 (2021).
https:/​/​doi.org/​10.1038/​s41567-020-01112-z

[179] S. Bravyi, M. B. Hastings, and F. Verstraete, Phys. Rev. Lett. 97, 050401 (2006).
https:/​/​doi.org/​10.1103/​PhysRevLett.97.050401

[180] S. Czischek, G. Torlai, S. Ray, R. Islam, and R. G. Melko, Phys. Rev. A 104, 062405 (2021).
https:/​/​doi.org/​10.1103/​PhysRevA.104.062405

[181] C. Noel, P. Niroula, D. Zhu, A. Risinger, L. Egan, D. Biswas, M. Cetina, A. V. Gorshkov, M. J. Gullans, D. A. Huse, and C. Monroe, ``Observation of measurement-induced quantum phases in a trapped-ion quantum computer,'' (2021), arXiv:2106.05881.
arXiv:2106.05881

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[55] Oliver Lunt, Jonas Richter, and Arijeet Pal, "Quantum simulation using noisy unitary circuits and measurements", arXiv:2112.06682, (2021).

[56] Minjae Jo, Bukyoung Jhun, and B. Kahng, "Resolving mean-field solutions of dissipative phase transitions using permutational symmetry", Chaos Solitons and Fractals 173, 113705 (2023).

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