**Host** Ehud Altman**Time/Venue** Wednesday, October 21, 10:15 am Pacific Time via Zoom **Talk Title**: Many-body quantum chaos and the local pairing of Feynman histories**Abstract** I will discuss many-body quantum dynamics under random Floquet circuits, simple examples of systems with local interactions that support ergodic phases. Quite generally, physical properties can be expressed in terms of multiple sums over Feynman histories, which for these models are paths or many-body orbits in Fock space. A natural simplification of such sums is the diagonal approximation, where the only terms that are retained are ones in which each path is paired with a partner that carries the complex conjugate weight. Our central result is to show how the diagonal approximation must be extended in many-body systems with local interactions. This leads to deviations of spectral statistics from random matrix theory, and of matrix element correlations from the eigenstate thermalisation hypothesis. Strikingly, both kinds of deviation diverge with system size. If there is time, I will also discuss the connection to the entanglement membrane, known to characterise the scrambling of quantum information.

## Special QM Seminar Speaker Sam Garratt (Oxford) Wednesday, October 21, 10:15 am

## Special QM/AMO Joint Seminar Speakers Kaoru Mizuta & Yoshihiro Michishita (Kyoto University) Monday, March 9, 4:15 pm in 325 LeConte

**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)

## QM Seminar Speaker Daniil Antonenko (Landau Institute / Skoltech) Wednesday, March 4 pm in Le Conte 402

**Host** Vlad Kozii/Joel Moore**Time/Venue** Tomorrow, Wednesday, March 4 pm in Le Conte 402**Title** Mesoscopic conductance fluctuations in topological superconducting wires**Abstract** We study quasiparticle transport in the bulk of disordered topological superconducting wires (length L) of symmetry class D, which can have a pair of edge Majorana states. Our focus is the critical regime between topological and critical phases, in which average conductance <g> scales as 1/\sqrt{L} at large L. We calculate conductance variance var g with the help of n = 2 (two-replica) nonlinear supersymmetric sigma-model, which boils down to the Fourier analysis on the sigma-model supermanifold. Eigenfunctions of the corresponding Laplace-Beltrami operator were constructed with the help of Iwasawa parametrisation. We obtained explicit expression for var g at arbitrary L in the diffusive regime, which describes the crossover from the regime of Drude conductivity at small lengths to the regime of a broad conductance distribution at large lengths. Also we analyse the case of left/right channels imbalance, which is described by a sigma-model with Wess-Zumino-Witten topological term.

## QM Seminar Speaker Kamran Behnia (ESPCI Paris) Wednesday, April 15, 2 pm in 402 LeConte

**Time/Venue **Wednesday, April 15, 2 pm in 402 LeConte**Host **James Analytis**Title** tba**Abstract** tba

## Special QM Seminar Speaker Bart Andrews (University of Zurich) Friday, February 21, 11 am in 3 LeConte (please note this room change from 325 LeConte)

**Time/Venue **Friday, February 21, 11 am in 3 LeConte (please note this room change from 325 LeConte)**Host **Mike Zaletel

**Fractional quantum Hall states for Moiré superstructures in the**

Title

Title

Hofstadter regime

**Abstract**We present evidence for fractional quantum Hall states in a

recently-proposed Moiré superlattice Hamiltonian, inspired by the

low-energy physics of twisted bilayer graphene at the first magic angle

[Koshino et al., PRX 8, 031087 (2018)]. We apply a perpendicular

magnetic field to the minimal effective two-orbital Fermi-Hubbard model,

through the use a Peierls substitution, so that the system is in the

Hofstadter regime. Subsequently, we determine the Landau level splitting

and study the structure of the Chern bands for a range of magnetic flux

per plaquette. In doing so, we identify topological flat minibands in

the spectrum at low energies, and show that, with the inclusion of a

density-density interaction, fractional quantum Hall states can be

realized solely within these flat bands. We characterize the primary

fractional state through the use of charge pumping, spectral flow,

entanglement scaling, and CFT edge state counting; and comment on its

breakdown transition. Ultimately, we discuss the implications of these

results for experiment, as well as other effective Moiré Hamiltonians.

## Special QM/AMO Seminar Speaker Pedram Roushan (Google Inc.) Friday, February 14, 2 pm in LeConte 3

**Time/Venue** 2 pm in LeConte 3**Host** Norman Yao**Title** Entanglement dynamics in ergodic and many-body localized phase; A look under the hood of quantum supremacy**Abstract** When various parts of a quantum system interact information is distributed between them. This process leads to growth of correlations and spread of entanglement. In physical platforms, proper measurement of spread of information and distilling it from noise is challenging. Here, we devise a protocol and measure scrambling in random quantum circuits, known to generate ergodic dynamics. We measure out-of-time-order correlations (OTOC) and visualize quantum scrambling in 1D and 2D arrays. We observe a diffusive propagation of wave front and are able to control it by changing the integrability of the hamiltonian of the system.

The many-body localized (MBL) phase has distinctive signatures such as slow dephasing and logarithmic entanglement growth that result in slow and subtle modification of the dynamics. By implementing phase sensitive techniques, we map out the structure of local integrals of motion in the MBL phase and determine the spatio-temporal entanglement growth between the localized sites. In addition, we study the preservation of entanglement in the MBL phase. The interferometric protocols implemented here measure affirmative correlations and exclude artifacts due to the imperfect isolation of the system.

## QM Seminar Speaker Prof. Keshav Dani (OIST-Okinawa Institute of Science and Technology) Wednesday, January 22, 2 pm in 402 LeConte

**Time/Venue** Wednesday, January 22, 2 pm in LeConte 402**Host** Feng Wang / Joel Moore**Title** Into the dark world of excitons in atomically thin semiconductors**Abstract** About a decade ago, the discovery of monolayers of transition metal dichalcogenides opened a new frontier in the study of optically excited states in semiconductors, and related opto-electronic technologies. These materials exhibit a plethora of robust excitonic states, such as bright excitons at the K & K’ valleys, momentum- and spin-forbidden dark excitons, and hot excitons. Optics-based experiments have revealed much about the bright excitonic states, but they remain largely unable to access their valley character, their scattering channels into other valleys within the Brilloin Zone, and the nature of the dark states in these valleys.

Angle-Resolved Photoemission Spectroscopy (ARPES) based techniques would be ideal to access the valley character, and momentum-resolved scattering channels of photoexcited states in 2D semiconductors. But these are very challenging experiments to perform on the typically-available, micron-scale, 2D semiconductors. In today’s talk, I will discuss the challenges involved, and progress made in my lab to date towards this aim. And – time permitting – we will end with an entertaining peek into the ‘quantum psychology of dark excitons’!

## Special QM Seminar Speaker Luca Delacretaz (University of Chicago) Thursday, January 16, 2 pm in 325 LeConte hall

**Time/Venue **Thursday, January 16, 2 pm in 325 LeConte hall**Host **Ehud Altman

**Absence of Diffusion on the Edge**

Title

Title

**The edge of a FQH droplet supports gapless excitations that are protected by a U(1) anomaly. At small but finite temperature, diffusive spreading is expected to occur around the chiral ballistic front. I will show that this chiral diffusive fixed point is never stable. Hydrodynamic long-time tails give large corrections to dissipative transport on the edge, leading to a breakdown of diffusion and driving the edge to a dissipative fixed point in the KPZ universality class. Translation invariance is not assumed.**

**Abstract****This rather simple setup presents several striking features: (i) a hydrodynamic theory describes a condensed matter system, but the long lived collective excitation is not momentum, and (ii) a quantum anomaly has dramatic consequences, leading to (iii) large hydrodynamic long-time tails.**

## Special QM Seminar Speaker Michael Gullans, (Princeton), Monday, January 13 at 2 pm in Old LeConte 325

**Time/Venue** Monday, January 13 at 2 pm in Old LeConte 325**Host** Ehud Altman**Title **The Measurement-Induced Transition in Open Quantum Systems

**Abstract** Quantum technologies fundamentally rely on quantum control, measurement, and feedback. Measurement-induced transitions are a recently uncovered class of critical phenomena that occur when many-body unitary dynamics are interspersed with measurements at a tunable rate [1,2]. We uncover precise connections between this phase transition and quantum error correction thresholds in the quantum channel capacity of open system dynamics [3,4]. We then show how to define a local order parameter for the transition that measures the ability of the system to store one bit of quantum information for exponentially long times [5]. Using this order parameter, we identify scalable probes of the transition that are immediately applicable to advanced quantum computing platforms such as trapped ions or superconducting qubits. Studying this class of measurement-driven many-body dynamics may potentially lead to more efficient realizations of scalable, fault-tolerant quantum computing, as well as deepen our understanding of the transition from quantum to classical physics in many-body systems.

[1] Y. Li, X. Chen, and M. P. A. Fisher, Phys. Rev B 98, 205136 (2018).

[2] B. Skinner, J. Ruhman, and A. Nahum, Phys. Rev. X 9, 031009 (2019).

[3] S. Choi, Y. Bao, X.-L. Qi, and E. Altman, arXiv:1903.05124

[4] M. J. Gullans and D. A. Huse, arXiv:1905.05195

[5] M. J. Gullans and D. A. Huse, arXiv:1910.00020

## QM Seminar Speaker Professor Giulio Casati, (University of Insubria; Lake Como School of Advanced Studies), Wednesday, January 8 at 2 pm in Old LeConte 402

**Time/Venue** Wednesday, January 8 at 2 pm in Old LeConte 402**Host **Joel Moore**Title/Abstract** Quantum Chaos; From classical diffusion to Anderson localization and beyond