**Host** Joel Moore**Time/Venue** Monday, March 9, 4:15 – 5:15 pm in 325 LeConte**Kaoru Mizuta Talk Title **Floquet engineering with emergent symmetries: Control of symmetry protected topological phases

**Recently periodically driven (Floquet) systems have attracted much interested, and Floquet engineering, control of phases by a periodic drive, is one of the most vigorous fields in Floquet systems. However, in conventional Floquet engineering, only high-frequency drives (=drives whose energy scale is much smaller than the frequency) are mainly utilized since it is based on**

**Kaoru Mizuta Abstract***high-frequency expansion theory*, only applicable to Floquet systems under high-frequency drives.

Therefore, we extend the conventional high-frequency expansion theory to the cases in the presence of resonant drives (= drives whose local energy scale is comparable to the frequency) and propose a new scheme of Floquet engineering done by high-frequency and resonant drives [1]. We clarify that the effective Hamiltonian describing long-time dynamics acquires an emergent Z_N symmetry, and hence our scheme enables us to simultaneously control phases and add a symmetry to the system. With our Floquet engineering, we also propose a way to realize/control topological phases protected by a Z_2×Z_2 symmetry only in the presence of a Z_2 symmetry [2].

[References]

[1] K. Mizuta, K. Takasan, and Norio Kawakami, Phys. Rev. B 100, 020301(R) (2019)

[2] K. Mizuta, K. Takasan, and Norio Kawakami, Phys. Rev. A 100, 0521009 (2019)

**Property as open quantum systems and the nonhermiticity in strongly-correlated electron systems**

**Yoshihiro Michishita Talk Title**The phenomena described by the non-hermitian Hamiltonian has been intensively studied especially in the context of artificial quantum systems[1-4]. Effective non-hermitian Hamiltonian induces novel topological phases[1,2], unusual critical phenomena[3], enhanced sensitivity[4] , and so on.

**Yoshihiro Michishita Abstract**The phenomena described by the non-hermitian Hamiltonian has been intensively studied especially in the context of artificial quantum systems[1-4]. Effective non-hermitian Hamiltonian induces novel topological phases[1,2], unusual critical phenomena[3], enhanced sensitivity[4] , and so on.

In the open quantum systems(OQS), such as cold atomic systems, it is possible to deribe an effective non-hermitian Hamiltonian under certain conditions even though the Hamiltonian describing the total system is hermitian. However, as the system becomes larger, it becomes difficult to experimentally realize these conditions, such as postselection or a PT-symmetric setup. Thus, experiments about nonhermitian phenomena in artificial quantum systems are particularly done in one-dimensional or small systems.

On the other hand, in strongly-correlated electron systems(SCES), it is also possible to derive the effective non-hermitian Hamiltonian determining the spectral function[5]. In this case, the non-hermiticity comes from the scattering by interaction and the certain setup, such as post selection or PT-symmetric setup, is not necessary. Thus, it seems to be easier to observe the bulk 2D or 3D non-hermitian phenomena in SCES than in OQS. The non-hermitian physics in SCES also hold the potential to explain the pseudo-gap in curate superconductors or quantum oscillation[6] in the topological Kondo insulator SmB6 and YbB12. Therefore the non-hermitian physics in SCES is also studied intensively today[7].

One problem is that the way to introduce the effective non-hermitian Hamiltonian in each context is quite different and it is not clear their relation, especially whether they are the same or not.

We close this gap and demonstrate that the non-hermitian Hamiltonians emerging in both fields are identical, and we clarify the why postselection is not necessary to derive a non-hermitian Hamiltonian in strongly correlated materials[8]. Using this knowledge, we propose a method to analyze non-hermitian properties without the necessity of postselection by studying specific response functions of open quantum systems and strongly-correlated systems. We have also shown that non-markovness of the dynamics of the single particles in strongly-correlated electron systems is relevant.

In this seminar, I will shortly explain about the difference between the non-hermitian Hamiltonian in SCES and that in OQS and talk about our recent work[7,8]. I look forward to your participation.

References:

[1] H. Shen, B. Zhen, and L. Fu, Phys. Rev. Lett. 120, 146402 (2018)

[2] Z. Gong, Y. Ashida, K. Kawabata, K. Takasan, S. Higashikawa, and M. Ueda, Phys. Rev. X 8, 031079 (2018)

[3] Y. Ashida, S. Furukawa, and M. Ueda, Nature communications 8, 15791 (2017)

[4] W. Chen, S ̧. K. Özdemir, G. Zhao, J. Wiersig, and L. Yang, Nature 548, 192 (2017)

[5]V. Kozii and L. Fu, arXiv:1708.05841 (2017)

[6]H. Shen and L. Fu, Phys. Rev. Lett. 121, 026403 (2018)

[7]Y. Michishita, T. Yoshida and R. Peters PRB: 101(8),085122(2020)

[8]Y. Michishita, and R. Peters arXiv: 2001.09045(2020)