Emergent Replica Conformal Symmetry in Non-Hermitian SYK$_2$ Chains

Pengfei Zhang; Shao-Kai Jian; Chunxiao Liu; Xiao Chen

doi:10.22331/q-2021-11-16-579

Emergent Replica Conformal Symmetry in Non-Hermitian SYK$_2$ Chains

Pengfei Zhang¹, Shao-Kai Jian², Chunxiao Liu³, and Xiao Chen⁴

¹Institute for Quantum Information and Matter and Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA 91125, USA
²Condensed Matter Theory Center and Joint Quantum Institute, Department of Physics, University of Maryland, College Park, MD 20742, USA
³Department of Physics, University of California Santa Barbara, Santa Barbara, CA 93106, USA
⁴Department of Physics, Boston College, Chestnut Hill, MA 02467, USA

Published:	2021-11-16, volume 5, page 579
Eprint:	arXiv:2104.04088v2
Doi:	https://doi.org/10.22331/q-2021-11-16-579
Citation:	Quantum 5, 579 (2021).

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Abstract

Recently, the steady states of non-unitary free fermion dynamics are found to exhibit novel critical phases with power-law squared correlations and a logarithmic subsystem entanglement. In this work, we theoretically understand the underlying physics by constructing solvable static/Brownian quadratic Sachdev-Ye-Kitaev chains with non-Hermitian dynamics. We find the action of the replicated system generally shows (one or infinite copies of) ${O(2)\times O(2)}$ symmetries, which is broken to ${O(2)}$ by the saddle-point solution. This leads to an emergent conformal field theory of the Goldstone modes. We derive the effective action and obtain the universal critical behaviors of squared correlators. Furthermore, the entanglement entropy of a subsystem ${A}$ with length ${L_A}$ corresponds to the energy of the half-vortex pair ${S\sim \rho_s \log L_A}$, where ${\rho_s}$ is the total stiffness of the Goldstone modes. We also discuss special limits with more than one branch of Goldstone modes and comment on interaction effects.

Featured image: (a) Schematics of the non-Hermitian free fermion chains. (b) The path-integral contour for the purity calculation. (c) The effective theory is an XY model on a half-infinite plane, with twisted boundary condition on the boundary t=T. The second Rényi entropy corresponds to the energy of the half-vortex pair.

Popular summary

Quantum system, subject to repeated measurements, is undergoing non-unitary dynamics. For many-body free fermions, this gives rise to critical steady states with a logarithmic subsystem entanglement and power law decay of correlation functions. We use solvable large N models to reveal the underlying mechanism: the emergence of criticality due to Goldstone modes in the replicated Hilbert space. We can then map the calculation of the entanglement entropy to the energy of a half-vortex pair, which shows the logarithmic scaling.

► BibTeX data

@article{Zhang2021emergentreplica,
  doi = {10.22331/q-2021-11-16-579},
  url = {https://doi.org/10.22331/q-2021-11-16-579},
  title = {Emergent {R}eplica {C}onformal {S}ymmetry in {N}on-{H}ermitian {SYK}{$_2$} {C}hains},
  author = {Zhang, Pengfei and Jian, Shao-Kai and Liu, Chunxiao and Chen, Xiao},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {5},
  pages = {579},
  month = nov,
  year = {2021}
}

► References

[1] Mark Srednicki. Chaos and quantum thermalization. Phys. Rev. E, 50: 888–901, Aug 1994. 10.1103/PhysRevE.50.888.
https://doi.org/10.1103/PhysRevE.50.888

[2] J. M. Deutsch. Quantum statistical mechanics in a closed system. Phys. Rev. A, 43: 2046–2049, Feb 1991. 10.1103/PhysRevA.43.2046.
https://doi.org/10.1103/PhysRevA.43.2046

[3] Rahul Nandkishore and David A. Huse. Many-body localization and thermalization in quantum statistical mechanics. Annual Review of Condensed Matter Physics, 6 (1): 15–38, 2015. 10.1146/annurev-conmatphys-031214-014726.
https://doi.org/10.1146/annurev-conmatphys-031214-014726

[4] Fabien Alet and Nicolas Laflorencie. Many-body localization: An introduction and selected topics. Comptes Rendus Physique, 19 (6): 498–525, 2018. 10.1016/j.crhy.2018.03.003.
https://doi.org/10.1016/j.crhy.2018.03.003

[5] Dmitry Abanin, Wojciech De Roeck, Wen Wei Ho, and François Huveneers. A rigorous theory of many-body prethermalization for periodically driven and closed quantum systems. Communications in Mathematical Physics, 354 (3): 809–827, 2017. 10.1007/s00220-017-2930-x.
https://doi.org/10.1007/s00220-017-2930-x

[6] Tomotaka Kuwahara, Takashi Mori, and Keiji Saito. Floquet–magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Annals of Physics, 367: 96–124, 2016. 10.1016/j.aop.2016.01.012.
https://doi.org/10.1016/j.aop.2016.01.012

[7] Subhashish Banerjee. Open quantum systems. Springer, 2018. 10.1007/978-981-13-3182-4.
https://doi.org/10.1007/978-981-13-3182-4

[8] Yaodong Li, Xiao Chen, and Matthew P. A. Fisher. Quantum zeno effect and the many-body entanglement transition. Phys. Rev. B, 98: 205136, Nov 2018. 10.1103/PhysRevB.98.205136.
https://doi.org/10.1103/PhysRevB.98.205136

[9] Xiangyu Cao, Antoine Tilloy, and Andrea De Luca. Entanglement in a fermion chain under continuous monitoring. SciPost Phys., 7: 24, 2019. 10.21468/SciPostPhys.7.2.024.
https://doi.org/10.21468/SciPostPhys.7.2.024

[10] Yaodong Li, Xiao Chen, and Matthew P. A. Fisher. Measurement-driven entanglement transition in hybrid quantum circuits. Phys. Rev. B, 100: 134306, Oct 2019. 10.1103/PhysRevB.100.134306.
https://doi.org/10.1103/PhysRevB.100.134306

[11] Brian Skinner, Jonathan Ruhman, and Adam Nahum. Measurement-induced phase transitions in the dynamics of entanglement. Phys. Rev. X, 9: 031009, Jul 2019. 10.1103/PhysRevX.9.031009.
https://doi.org/10.1103/PhysRevX.9.031009

[12] Amos Chan, Rahul M. Nandkishore, Michael Pretko, and Graeme Smith. Unitary-projective entanglement dynamics. Phys. Rev. B, 99: 224307, Jun 2019. 10.1103/PhysRevB.99.224307.
https://doi.org/10.1103/PhysRevB.99.224307

[13] Yimu Bao, Soonwon Choi, and Ehud Altman. Theory of the phase transition in random unitary circuits with measurements. Physical Review B, 101 (10), Mar 2020. ISSN 2469-9969. 10.1103/physrevb.101.104301.
https://doi.org/10.1103/physrevb.101.104301

[14] Soonwon Choi, Yimu Bao, Xiao-Liang Qi, and Ehud Altman. Quantum error correction in scrambling dynamics and measurement-induced phase transition. Physical Review Letters, 125 (3), Jul 2020. ISSN 1079-7114. 10.1103/physrevlett.125.030505.
https://doi.org/10.1103/physrevlett.125.030505

[15] Michael J Gullans and David A Huse. Dynamical purification phase transition induced by quantum measurements. Physical Review X, 10 (4): 041020, 2020a. 10.1103/PhysRevX.10.041020.
https://doi.org/10.1103/PhysRevX.10.041020

[16] Michael J. Gullans and David A. Huse. Scalable probes of measurement-induced criticality. Phys. Rev. Lett., 125: 070606, Aug 2020b. 10.1103/PhysRevLett.125.070606.
https://doi.org/10.1103/PhysRevLett.125.070606

[17] Chao-Ming Jian, Yi-Zhuang You, Romain Vasseur, and Andreas W. W. Ludwig. Measurement-induced criticality in random quantum circuits. Phys. Rev. B, 101: 104302, Mar 2020a. 10.1103/PhysRevB.101.104302.
https://doi.org/10.1103/PhysRevB.101.104302

[18] Aidan Zabalo, Michael J. Gullans, Justin H. Wilson, Sarang Gopalakrishnan, David A. Huse, and J. H. Pixley. Critical properties of the measurement-induced transition in random quantum circuits. Phys. Rev. B, 101: 060301, Feb 2020. 10.1103/PhysRevB.101.060301.
https://doi.org/10.1103/PhysRevB.101.060301

[19] Qicheng Tang and W. Zhu. Measurement-induced phase transition: A case study in the nonintegrable model by density-matrix renormalization group calculations. Phys. Rev. Research, 2: 013022, Jan 2020. 10.1103/PhysRevResearch.2.013022.
https://doi.org/10.1103/PhysRevResearch.2.013022

[20] M. Szyniszewski, A. Romito, and H. Schomerus. Entanglement transition from variable-strength weak measurements. Phys. Rev. B, 100: 064204, Aug 2019. 10.1103/PhysRevB.100.064204.
https://doi.org/10.1103/PhysRevB.100.064204

[21] Lei Zhang, Justin A. Reyes, Stefanos Kourtis, Claudio Chamon, Eduardo R. Mucciolo, and Andrei E. Ruckenstein. Nonuniversal entanglement level statistics in projection-driven quantum circuits. Physical Review B, 101 (23), Jun 2020a. ISSN 2469-9969. 10.1103/physrevb.101.235104.
https://doi.org/10.1103/physrevb.101.235104

[22] Shimpei Goto and Ippei Danshita. Measurement-Induced Transitions of the Entanglement Scaling Law in Ultracold Gases with Controllable Dissipation. arXiv e-prints, art. arXiv:2001.03400, January 2020. 10.1103/PhysRevA.102.033316.
https://doi.org/10.1103/PhysRevA.102.033316
arXiv:2001.03400

[23] Shao-Kai Jian, Zhi-Cheng Yang, Zhen Bi, and Xiao Chen. Yang-lee edge singularity triggered entanglement transition. arXiv preprint arXiv:2101.04115, 2021a. 10.1103/PhysRevB.104.L161107.
https://doi.org/10.1103/PhysRevB.104.L161107
arXiv:2101.04115

[24] M Buchhold, Y Minoguchi, A Altland, and S Diehl. Effective theory for the measurement-induced phase transition of dirac fermions. arXiv preprint arXiv:2102.08381, 2021. 10.1103/PhysRevX.11.041004.
https://doi.org/10.1103/PhysRevX.11.041004
arXiv:2102.08381

[25] Yimu Bao, Soonwon Choi, and Ehud Altman. Symmetry enriched phases of quantum circuits. arXiv preprint arXiv:2102.09164, 2021. 10.1016/j.aop.2021.168618.
https://doi.org/10.1016/j.aop.2021.168618
arXiv:2102.09164

[26] Shengqi Sang and Timothy H Hsieh. Measurement-protected quantum phases. Physical Review Research, 3 (2): 023200, 2021. 10.1103/PhysRevResearch.3.023200.
https://doi.org/10.1103/PhysRevResearch.3.023200

[27] Ali Lavasani, Yahya Alavirad, and Maissam Barkeshli. Measurement-induced topological entanglement transitions in symmetric random quantum circuits. Nature Physics, 17 (3): 342–347, Jan 2021. ISSN 1745-2481. 10.1038/s41567-020-01112-z.
https://doi.org/10.1038/s41567-020-01112-z

[28] Matteo Ippoliti, Tibor Rakovszky, and Vedika Khemani. Fractal, logarithmic and volume-law entangled non-thermal steady states via spacetime duality. arXiv preprint arXiv:2103.06873, 2021a.
arXiv:2103.06873

[29] Tsung-Cheng Lu and Tarun Grover. Entanglement transitions via space-time rotation of quantum circuits. arXiv preprint arXiv:2103.06356, 2021.
arXiv:2103.06356

[30] Chao-Ming Jian, Bela Bauer, Anna Keselman, and Andreas WW Ludwig. Criticality and entanglement in non-unitary quantum circuits and tensor networks of non-interacting fermions. arXiv preprint arXiv:2012.04666, 2020b.
arXiv:2012.04666

[31] Matteo Ippoliti, Michael J. Gullans, Sarang Gopalakrishnan, David A. Huse, and Vedika Khemani. Entanglement phase transitions in measurement-only dynamics. Physical Review X, 11 (1), Feb 2021b. ISSN 2160-3308. 10.1103/physrevx.11.011030.
https://doi.org/10.1103/physrevx.11.011030

[32] Federico Carollo and Vincenzo Alba. Emergent dissipative quasi-particle picture in noninteracting markovian open quantum systems. arXiv preprint arXiv:2106.11997, 2021.
arXiv:2106.11997

[33] Xiao Chen, Yaodong Li, Matthew P. A. Fisher, and Andrew Lucas. Emergent conformal symmetry in nonunitary random dynamics of free fermions. Physical Review Research, 2 (3): 033017, Jul 2020a. ISSN 2643-1564. 10.1103/physrevresearch.2.033017.
https://doi.org/10.1103/physrevresearch.2.033017

[34] Ori Alberton, Michael Buchhold, and Sebastian Diehl. Entanglement transition in a monitored free-fermion chain: From extended criticality to area law. Physical Review Letters, 126 (17): 170602, 2021. 10.1103/PhysRevLett.126.170602.
https://doi.org/10.1103/PhysRevLett.126.170602

[35] Chunxiao Liu, Pengfei Zhang, and Xiao Chen. Non-unitary dynamics of sachdev-ye-kitaev chain. SciPost Physics, 10 (2): Art–No, 2021. 10.21468/SciPostPhys.10.2.048.
https://doi.org/10.21468/SciPostPhys.10.2.048

[36] Alexei Kitaev. A simple model of quantum holography, talk given at the kitp program: entanglement in strongly-correlated quantum matter. talk given at the KITP Program: entanglement in strongly-correlated quantum matter, 2015.

[37] Juan Maldacena and Douglas Stanford. Remarks on the sachdev-ye-kitaev model. Phys. Rev. D, 94: 106002, Nov 2016. 10.1103/PhysRevD.94.106002.
https://doi.org/10.1103/PhysRevD.94.106002

[38] Subir Sachdev and Jinwu Ye. Gapless spin-fluid ground state in a random quantum heisenberg magnet. Phys. Rev. Lett., 70: 3339–3342, May 1993. 10.1103/PhysRevLett.70.3339.
https://doi.org/10.1103/PhysRevLett.70.3339

[39] Chunxiao Liu, Xiao Chen, and Leon Balents. Quantum entanglement of the sachdev-ye-kitaev models. Phys. Rev. B, 97: 245126, Jun 2018. 10.1103/PhysRevB.97.245126.
https://doi.org/10.1103/PhysRevB.97.245126

[40] Yingfei Gu, Andrew Lucas, and Xiao-Liang Qi. Spread of entanglement in a Sachdev-Ye-Kitaev chain. Journal of High Energy Physics, 2017 (9): 120, September 2017a. 10.1007/JHEP09(2017)120.
https://doi.org/10.1007/JHEP09(2017)120

[41] Yichen Huang and Yingfei Gu. Eigenstate entanglement in the sachdev-ye-kitaev model. Phys. Rev. D, 100: 041901, Aug 2019. 10.1103/PhysRevD.100.041901.
https://doi.org/10.1103/PhysRevD.100.041901

[42] Pengfei Zhang, Chunxiao Liu, and Xiao Chen. Subsystem Rényi Entropy of Thermal Ensembles for SYK-like models. SciPost Phys., 8: 94, 2020b. 10.21468/SciPostPhys.8.6.094.
https://doi.org/10.21468/SciPostPhys.8.6.094

[43] Arijit Haldar, Surajit Bera, and Sumilan Banerjee. Rényi entanglement entropy of fermi and non-fermi liquids: Sachdev-ye-kitaev model and dynamical mean field theories. Phys. Rev. Research, 2: 033505, Sep 2020. 10.1103/PhysRevResearch.2.033505.
https://doi.org/10.1103/PhysRevResearch.2.033505

[44] Pengfei Zhang. Entanglement entropy and its quench dynamics for pure states of the sachdev-ye-kitaev model. Journal of High Energy Physics, (6): 143. 10.1007/JHEP06(2020)143.
https://doi.org/10.1007/JHEP06(2020)143

[45] Yiming Chen, Xiao-Liang Qi, and Pengfei Zhang. Replica wormhole and information retrieval in the syk model coupled to majorana chains. Journal of High Energy Physics, 2020 (6): 121, 2020b. 10.1007/JHEP06(2020)121.
https://doi.org/10.1007/JHEP06(2020)121

[46] Jian Shao-Kai and Brian Swingle. Note on entropy dynamics in the brownian syk model. Journal of High Energy Physics, 2021 (3), 2021. 10.1007/JHEP03(2021)042.
https://doi.org/10.1007/JHEP03(2021)042

[47] Yingfei Gu, Xiao-Liang Qi, and Douglas Stanford. Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models. Journal of High Energy Physics, 2017 (5): 125, May 2017b. 10.1007/JHEP05(2017)125.
https://doi.org/10.1007/JHEP05(2017)125

[48] Richard A. Davison, Wenbo Fu, Antoine Georges, Yingfei Gu, Kristan Jensen, and Subir Sachdev. Thermoelectric transport in disordered metals without quasiparticles: The sachdev-ye-kitaev models and holography. Phys. Rev. B, 95: 155131, Apr 2017. 10.1103/PhysRevB.95.155131.
https://doi.org/10.1103/PhysRevB.95.155131

[49] Xin Chen, Ruihua Fan, Yiming Chen, Hui Zhai, and Pengfei Zhang. Competition between chaotic and nonchaotic phases in a quadratically coupled sachdev-ye-kitaev model. Phys. Rev. Lett., 119: 207603, Nov 2017. 10.1103/PhysRevLett.119.207603.
https://doi.org/10.1103/PhysRevLett.119.207603

[50] Xue-Yang Song, Chao-Ming Jian, and Leon Balents. Strongly correlated metal built from sachdev-ye-kitaev models. Phys. Rev. Lett., 119: 216601, Nov 2017. 10.1103/PhysRevLett.119.216601.
https://doi.org/10.1103/PhysRevLett.119.216601

[51] Pengfei Zhang. Dispersive sachdev-ye-kitaev model: Band structure and quantum chaos. Phys. Rev. B, 96: 205138, Nov 2017. 10.1103/PhysRevB.96.205138.
https://doi.org/10.1103/PhysRevB.96.205138

[52] Chao-Ming Jian, Zhen Bi, and Cenke Xu. Model for continuous thermal metal to insulator transition. Phys. Rev. B, 96: 115122, Sep 2017. 10.1103/PhysRevB.96.115122.
https://doi.org/10.1103/PhysRevB.96.115122

[53] Yiming Chen, Hui Zhai, and Pengfei Zhang. Tunable quantum chaos in the Sachdev-Ye-Kitaev model coupled to a thermal bath. Journal of High Energy Physics, 2017 (7): 150, July 2017. 10.1007/JHEP07(2017)150.
https://doi.org/10.1007/JHEP07(2017)150

[54] Phil Saad, Stephen H Shenker, and Douglas Stanford. A semiclassical ramp in syk and in gravity. arXiv preprint arXiv:1806.06840, 2018.
arXiv:1806.06840

[55] Christoph Sünderhauf, Lorenzo Piroli, Xiao-Liang Qi, Norbert Schuch, and J. Ignacio Cirac. Quantum chaos in the Brownian SYK model with large finite N : OTOCs and tripartite information. Journal of High Energy Physics, 2019 (11): 38, November 2019. 10.1007/JHEP11(2019)038.
https://doi.org/10.1007/JHEP11(2019)038

[56] Nima Lashkari, Douglas Stanford, Matthew Hastings, Tobias Osborne, and Patrick Hayden. Towards the fast scrambling conjecture. Journal of High Energy Physics, 2013 (4), Apr 2013. ISSN 1029-8479. 10.1007/jhep04(2013)022.
https://doi.org/10.1007/jhep04(2013)022

[57] Tianci Zhou and Xiao Chen. Operator dynamics in a brownian quantum circuit. Physical Review E, 99 (5), May 2019. ISSN 2470-0053. 10.1103/physreve.99.052212.
https://doi.org/10.1103/physreve.99.052212

[58] Shenglong Xu and Brian Swingle. Locality, quantum fluctuations, and scrambling. Physical Review X, 9 (3), Sep 2019. ISSN 2160-3308. 10.1103/physrevx.9.031048.
https://doi.org/10.1103/physrevx.9.031048

[59] Xiao Chen and Tianci Zhou. Quantum chaos dynamics in long-range power law interaction systems. Physical Review B, 100 (6), Aug 2019. ISSN 2469-9969. 10.1103/physrevb.100.064305.
https://doi.org/10.1103/physrevb.100.064305

[60] Andrew Lucas. Quantum many-body dynamics on the star graph. arXiv e-prints, art. arXiv:1903.01468, March 2019.
arXiv:1903.01468

[61] Lorenzo Piroli, Christoph Sünderhauf, and Xiao-Liang Qi. A random unitary circuit model for black hole evaporation. Journal of High Energy Physics, 2020 (4), Apr 2020. ISSN 1029-8479. 10.1007/jhep04(2020)063.
https://doi.org/10.1007/jhep04(2020)063

[62] Different from previous studies for the interplay between Goldstone modes and entanglement entropy in metlitski2011entanglement,alba2021entanglement for systems with conventional symmetry breaking, here the conformal symmetry only appears upon introducing replicas.

[63] C.J. Pethick and H. Smith. Bose–Einstein Condensation in Dilute Gases. Cambridge University Press, 2008. 10.1017/CBO9780511802850.
https://doi.org/10.1017/CBO9780511802850

[64] Hui Zhai. Ultracold Atomic Physics. Cambridge University Press, 2021. 10.1017/9781108595216.
https://doi.org/10.1017/9781108595216

[65] Antonio M García-García, Yiyang Jia, Dario Rosa, and Jacobus JM Verbaarschot. Replica symmetry breaking and phase transitions in a pt symmetric sachdev-ye-kitaev model. arXiv preprint arXiv:2102.06630, 2021.
arXiv:2102.06630

[66] Alexei Kitaev and S. Josephine Suh. The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual. Journal of High Energy Physics, 2018 (5): 183, May 2018. 10.1007/JHEP05(2018)183.
https://doi.org/10.1007/JHEP05(2018)183

[67] Yingfei Gu, Alexei Kitaev, Subir Sachdev, and Grigory Tarnopolsky. Notes on the complex Sachdev-Ye-Kitaev model. Journal of High Energy Physics, 2020 (2): 157, February 2020. 10.1007/JHEP02(2020)157.
https://doi.org/10.1007/JHEP02(2020)157

[68] Michael Winer, Shao-Kai Jian, and Brian Swingle. Exponential ramp in the quadratic sachdev-ye-kitaev model. Physical Review Letters, 125 (25): 250602, 2020. 10.1103/PhysRevLett.125.250602.
https://doi.org/10.1103/PhysRevLett.125.250602

[69] Note that at the level of the Schwinger-Dyson equation, the phase introduced here is unnecessary. The choice is to make the symmetry not broken by the saddle-point solution.

[70] We verify this numerically within the disorder replica diagonal assumption by solving the Schwinger-Dyson equation at large but finite $T$.

[71] The block diagonal form is verified numerically.

[72] This is similar to the Brownian SYK$_2$ chain model.

[73] In the numerics, we take the initial state $|\psi_0\rangle$ to be the maximally entangled state between Majorana fermions with even and odd indices $c_{x}^i|\psi_0\rangle = 0$ where $c_{x}^i = \chi_{x}^{2i-1}+i \chi_{x}^{2i}$. The numerical details have been explained in previous works liu2020non.

[74] Shao-Kai Jian, Chunxiao Liu, Xiao Chen, Brian Swingle, and Pengfei Zhang. Measurement-induced phase transition in the monitored sachdev-ye-kitaev model. Physical Review Letters, 127 (14): 140601, 2021b. 10.1103/PhysRevLett.127.140601.
https://doi.org/10.1103/PhysRevLett.127.140601

[75] Max A Metlitski and Tarun Grover. Entanglement entropy of systems with spontaneously broken continuous symmetry. arXiv preprint arXiv:1112.5166, 2011.
arXiv:1112.5166

[76] Vincenzo Alba. Entanglement gap, corners, and symmetry breaking. SciPost Phys., 10: 56, 2021. 10.21468/SciPostPhys.10.3.056.
https://doi.org/10.21468/SciPostPhys.10.3.056

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[20] Pengfei Zhang, "Quantum entanglement in the Sachdev—Ye—Kitaev model and its generalizations", Frontiers of Physics 17 4, 43201 (2022).

[21] Xhek Turkeshi, "Measurement-induced criticality as a data-structure transition", Physical Review B 106 14, 144313 (2022).

[22] Lucas Sá, Pedro Ribeiro, and Tomaž Prosen, "Lindbladian dissipation of strongly-correlated quantum matter", Physical Review Research 4 2, L022068 (2022).

[23] Antonio M. García-García, Lucas Sá, Jacobus J. M. Verbaarschot, and Jie Ping Zheng, "Keldysh wormholes and anomalous relaxation in the dissipative Sachdev-Ye-Kitaev model", Physical Review D 107 10, 106006 (2023).

[24] Yi-Neng Zhou, Tian-Gang Zhou, and Pengfei Zhang, "General properties of the spectral form factor in open quantum systems", Frontiers of Physics 19 3, 31202 (2024).

[25] Antonio M. García-García, Lucas Sá, and Jacobus J. M. Verbaarschot, "Universality and its limits in non-Hermitian many-body quantum chaos using the Sachdev-Ye-Kitaev model", Physical Review D 107 6, 066007 (2023).

[26] Pengfei Zhang, "Information scrambling and entanglement dynamics of complex Brownian Sachdev-Ye-Kitaev models", Journal of High Energy Physics 2023 4, 105 (2023).

[27] Liang Mao, Yajiang Hao, and Lei Pan, "Non-Hermitian skin effect in a one-dimensional interacting Bose gas", Physical Review A 107 4, 043315 (2023).

[28] Kohei Kawabata, Anish Kulkarni, Jiachen Li, Tokiro Numasawa, and Shinsei Ryu, "Dynamical quantum phase transitions in Sachdev-Ye-Kitaev Lindbladians", Physical Review B 108 7, 075110 (2023).

[29] Marcin Szyniszewski, Oliver Lunt, and Arijeet Pal, "Disordered monitored free fermions", Physical Review B 108 16, 165126 (2023).

[30] Hanteng Wang, Chang Liu, Pengfei Zhang, and Antonio M. García-García, "Entanglement transition and replica wormholes in the dissipative Sachdev-Ye-Kitaev model", Physical Review D 109 4, 046005 (2024).

[31] Etienne Granet, Carolyn Zhang, and Henrik Dreyer, "Volume-Law to Area-Law Entanglement Transition in a Nonunitary Periodic Gaussian Circuit", Physical Review Letters 130 23, 230401 (2023).

[32] Hugo Lóio, Andrea De Luca, Jacopo De Nardis, and Xhek Turkeshi, "Purification timescales in monitored fermions", Physical Review B 108 2, L020306 (2023).

[33] T. Müller, S. Diehl, and M. Buchhold, "Measurement-Induced Dark State Phase Transitions in Long-Ranged Fermion Systems", Physical Review Letters 128 1, 010605 (2022).

[34] M. Buchhold, Y. Minoguchi, A. Altland, and S. Diehl, "Effective Theory for the Measurement-Induced Phase Transition of Dirac Fermions", Physical Review X 11 4, 041004 (2021).

[35] Shao-Kai Jian, Chunxiao Liu, Xiao Chen, Brian Swingle, and Pengfei Zhang, "Measurement-Induced Phase Transition in the Monitored Sachdev-Ye-Kitaev Model", Physical Review Letters 127 14, 140601 (2021).

[36] Shao-Kai Jian, Chunxiao Liu, Xiao Chen, Brian Swingle, and Pengfei Zhang, "Quantum error as an emergent magnetic field", arXiv:2106.09635, (2021).

[37] Chang-Yan Wang, Tian-Gang Zhou, Yi-Neng Zhou, and Pengfei Zhang, "Distinguishing Quantum Phases through Cusps in Full Counting Statistics", arXiv:2312.11191, (2023).

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