2000 character limit reached
Localization of Lindbladian Fermions (2401.14006v1)
Published 25 Jan 2024 in cond-mat.dis-nn
Abstract: We study a Lindbladian generalization of the Anderson model of localization that describes disordered free fermions coupled to a disordered environment. From finite size scaling of both eigenvalue statistics and participation ratio, we identify localization transitions in both the non-Hermitian Lindbladian spectrum, which governs transient relaxation dynamics, and in the Hermitian stationary state density matrix. These localization transitions occur at different critical values of Hamiltonian and dissipative disorder strength, implying the existence of atypical phases with a mixture of localized and delocalized features. We find this phenomenon is robust to changes to the value of the dissipative spectral gap.
- P. W. Anderson, Phys. Rev. 109, 1492 (1958).
- P. W. Anderson, Proceedings of the National Academy of Sciences 69, 1097 (1972), https://www.pnas.org/doi/pdf/10.1073/pnas.69.5.1097 .
- I. Bloch, Nature Physics 1, 23 (2005).
- L. J. LeBlanc and J. H. Thywissen, Phys. Rev. A 75, 053612 (2007).
- I. Bloch, J. Dalibard, and W. Zwerger, Rev. Mod. Phys. 80, 885 (2008).
- M. A. Cazalilla and A. M. Rey, Reports on Progress in Physics 77, 124401 (2014).
- H. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press) (2002).
- C. W. Gardiner and P. Zoller, Quantum Noise (Springer-Verlag Berlin Heidelberg) (2004).
- T. Can, Journal of Physics A: Mathematical and Theoretical 52, 485302 (2019).
- L. Sá, P. Ribeiro, and T. Prosen, Journal of Physics A: Mathematical and Theoretical 53, 305303 (2020).
- S. Lange and C. Timm, Chaos: An Interdisciplinary Journal of Nonlinear Science 31, 10.1063/5.0033486 (2021), 023101, https://pubs.aip.org/aip/cha/article-pdf/doi/10.1063/5.0033486/14629411/023101_1_online.pdf .
- L. Sá, P. Ribeiro, and T. c. v. Prosen, Phys. Rev. X 10, 021019 (2020).
- J. Li, T. c. v. Prosen, and A. Chan, Phys. Rev. Lett. 127, 170602 (2021).
- A. Kulkarni, T. Numasawa, and S. Ryu, Phys. Rev. B 106, 075138 (2022).
- L. Sá, P. Ribeiro, and T. Prosen, Phys. Rev. Res. 4, L022068 (2022).
- F. Thompson and A. Kamenev, Annals of Physics 455, 169385 (2023).
- A. Beck and M. Goldstein, Phys. Rev. B 103, L241401 (2021).
- A. C. C. de Albornoz, D. C. Rose, and A. Pal, Entanglement and localization in long-range quadratic lindbladians (2023).
- D. S. Wiersma, Nat. Phys. , 359– (2008).
- D. S. Wiersma, Nat. Photon. , 188– (2013).
- A. F. Tzortzakakis, K. G. Makris, and E. N. Economou, Phys. Rev. B 101, 014202 (2020).
- Y. Huang and B. I. Shklovskii, Phys. Rev. B 101, 014204 (2020a).
- Y. Huang and B. I. Shklovskii, Phys. Rev. B 102, 064212 (2020b).
- X. Luo, T. Ohtsuki, and R. Shindou, Phys. Rev. B 104, 104203 (2021a).
- X. Luo, T. Ohtsuki, and R. Shindou, Phys. Rev. Lett. 126, 090402 (2021b).
- T. Prosen, New Journal of Physics 10, 043026 (2008).
- A. Kamenev, Field theory of non-equilibrium systems (Cambridge University Press, 2023).
- L. M. Sieberer, M. Buchhold, and S. Diehl, Reports on Progress in Physics 79, 096001 (2016).
- A. MacKinnon and B. Kramer, Phys. Rev. Lett. 47, 1546 (1981).
- R. J. Bell and P. Dean, Discuss. Faraday Soc. 50, 55 (1970).
- R. J. Bell, Reports on Progress in Physics 35, 1315 (1972).
- A. D. Mirlin and F. Evers, Phys. Rev. B 62, 7920 (2000).
- F. Evers and A. D. Mirlin, Phys. Rev. Lett. 84, 3690 (2000).
- J. Brndiar and P. Markoš, Phys. Rev. B 74, 153103 (2006).
- V. Oganesyan and D. A. Huse, Phys. Rev. B 75, 155111 (2007).
- K. Slevin and T. Ohtsuki, Journal of the Physical Society of Japan 85, 104712 (2016).
- T. Wang, T. Ohtsuki, and R. Shindou, Phys. Rev. B 104, 014206 (2021).