Exceptional spectral phase in a dissipative collective spin model

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Rubio García, Álvaro
Corps, Angel L.
Molina, Rafael A.
Pérez Bernal, Francisco
Enrique García Ramos, José
Dukelsky, Jorge
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Amer Physical Soc
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We study a model of a quantum collective spin weakly coupled to a spin-polarized Markovian environment and find that the spectrum is divided into two regions that we name normal and exceptional Liouvillian spectral phases. In the thermodynamic limit, the exceptional spectral phase displays the unique property of being made up exclusively of second-order exceptional points. As a consequence, the evolution of any initial density matrix populating this region is slowed down and cannot be described by a linear combination of exponential decays. This phase is separated from the normal one by a critical line in which the density of Liouvillian eigenvalues diverges, a phenomenon analogous to that of excited-state quantum phase transitions observed in some closed quantum systems. In the limit of no bath polarization, this criticality is transferred onto the steady state, implying a dissipative quantum phase transition and the formation of a boundary time crystal.
©2022 American Physical Society. Acknowledgments. This work was partially supported by Grants No. PGC2018-094180-B-I00 and No. PID2019-104002GB-C21 funded by MCIN/AEI/10.13039/501100011033 and FEDER ?A way of making Europe.? It has been also supported by the CAM/FEDER Project No. S2018/TCS-4342 (QUITEMAD-CM) and by the Consejería de Economía, Conocimiento, Empresas y Universidad de la Junta de Andalucía, under Projects No. UHU-1262561 and No. P20-00764. This research has also been supported by the CSIC Research Platform on Quantum Technologies PTI-001. A.L.C. acknowledges financial support from the ?la Caixa? Foundation (ID 100010434) through Fellowship No. LCF/BQ/DR21/11880024. A.R.-G. and J.D. conceived the project. A.R.-G., J.D., and A.L.C. performed the analytical calculations. A.L.C., A.R.-G., A.R., and R.A.M. performed the numerical cal-culations, with the collaboration of F.P.-B. and J.E.G.-R. All figures were formatted by A.L.C. and A.R.-G. Finally, R.A.M., A.R., and A.L.C. took the lead in writing the manuscript, with A.R.-G. and J.D. contributing significantly to the final version. All authors contributed to the discussions and have agreed on the final version of the manuscript.
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