# P4: Non-equilibrium RG methods and Floquet theory

## Project Description

Periodic modulations of dissipative or correlated low-dimensional quantum systems reveal a rich variety of interesting many-body phenomena, in particular, in the case of high-frequency modulations [1]. Most recently, such systems have attracted interest in the quest to realize topologically protected states [2]. In the first funding period of the RTG, the functional renormalization group (FRG) [3] and the real-time renormalization group method (RTRG) [4] were combined with Floquet theory and applied to the interacting resonant level model (IRLM) in the presence of an external high-frequency field [5,6]. Whereas the FRG was applied in this project to its full extent, the RTRG was still only used in the perturbative sense. However, the “RG version” of this method was already fully combined with Floquet theory.

In the first part of the present project, based on previous works for the IRLM with the RTRG method [7,8,9], we will analytically solve the complete set of RTRG equations for the IRLM with high-frequency fields and improve the understanding already obtained within FRG.

Secondly, based on a previous work for the non-equilibrium Kondo model in strong coupling [10,11], we will use the RTRG method to study the Kondo model in the presence of a harmonically modulated bias voltage and analyze whether the nonlinear conductance in the strong coupling regime exhibits side resonances shifted by the external frequency or not. This issue is still not clarified, either from the theoretical [12,13] or from the experimental side [14].

Finally, we will study a topological 2-band quantum wire coupled to a strongly correlated quantum dot by using two complementary methods: the RTRG, by expanding in the tunneling coupling of the wire to the dot, and the FRG, by expanding in the Coulomb interaction on the quantum dot. According to a recent proposal [15], the topological states in the quantum wire are induced by spin-orbit interaction, Zeeman fields and a periodically driven external electric field. The aim of this part of the project is to study the manipulation of the topological states at the end of the quantum wire by the gate voltage on the dot and to study the influence of further fermionic and bosonic baths coupled to the quantum wire. The latter is important since the heat produced by the high-frequency fields has to be absorbed by a phonon bath and the populations of the topological states have to be fixed by a tunneling coupling to an additional fermionic reservoir. These issues have already been studied for Floquet-driven topological quantum wires via equation-of-motion methods [16], but need a more thorough analysis with Keldysh formalism and RG methods.

The present project is complementary to P13.

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[2] F. Nathan and M.S. Rudner, New. J. Phys. **17**, 125014 (2015); T. Kitagawa, E. Berg, M. Rudner, and E. Demler, Phys. Rev. B **82**, 235114 (2010)

[3] W. Metzner, M. Salmhofer, C. Honerkamp, V. Meden, and K. Schönhammer, Rev. Mod. Phys. **84**, 299 (2012)

[4] H. Schoeller, Eur. Phys. J. Special Topics **168**, 179 (2009)

[5] A.K. Eissing, V. Meden, and D.M. Kennes, Phys. Rev. Lett. **116**, 026801 (2016)

[6] A.K. Eissing, V. Meden, and D.M. Kennes, Phys. Rev. B **94**, 245116 (2016)

[7] C. Karrasch, S. Andergassen, M. Pletyukhov, D. Schuricht, L. Borda, V. Meden, and H. Schoeller, Europhys. Lett. **90**, 30003 (2010)

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[9] D. M. Kennes, O. Kashuba, M. Pletyukhov, H. Schoeller, and V. Meden, Phys. Rev. Lett. **110**, 100405 (2013)

[10] M. Pletyukhov and H. Schoeller, Phys. Rev. Lett. **108**, 260601 (2012)

[11] F. Reininghaus, M. Pletyukhov, and H. Schoeller, Phys. Rev. B **90**, 085121 (2014)

[12] M. Hettler and H. Schoeller, Phys. Rev. Lett. **74**, 4907 (1995)

[13] A. Kaminski, Y.V. Nazarov, and L.I. Glazman, Phys. Rev. Lett. **83**, 384 (1999); ibid. Phys. Rev. B **62**, 8154 (2000)

[14] J.M. Elzerman, S. De Franceschi, D. Goldhaber-Gordon, W.G. van der Wiel, and L.P. Kouwenhoven, J. of Low Temperature Physics **118**, 375 (2000); A. Kogan, S. Amasha, and M.A. Kastner, Science **304**, 1293 (2004)

[15] M. Thakurathi, D. Loss, and J. Klinovaja, Phys. Rev. B **95**, 155407 (2017)

[16] K.I. Seetharam, C. Bardyn, N.H. Lindner, M.S. Rudner, and G. Refael, Phys. Rev. X **5**, 041050 (2015)