Mini Symposium on Many-Body Localization
March 25, 2021

Thursday March 25, 2021

All times are in the CET timezone. Please note that Europe has not yet switched to daylight saving time unlike other parts of the world.

Therefore you may encounter "unusual" time shifts, so please double check.
 

The meeting will take place in big blue button: https://meet.pks.mpg.de/m/iva-ngt-pqq-gfd.

(only in case of technical problems we will use zoom as fallback option here).

Non-Hermitian Many-Body Localization

Ryusuke Hamazaki

Recent study on isolated quantum many-body systems have revealed two different phases distinguished by their dynamics and spectral statistics. One is an ergodic phase whose spectral statistics exhibit universality of random matrices, and the other is a many-body localized (MBL) phase where dynamics is constrained owing to strong disorder. In this talk, we analyze non-Hermitian quantum many-body systems in the presence of interaction and disorder. We show that MBL induced by strong disorder suppresses imaginary parts of complex eigenenergies for general non-Hermitian Hamiltonians having time-reversal symmetry [1]. Specifically, we demonstrate that a novel real-complex transition occurs upon MBL and profoundly affects the dynamical stability and spectral statistics of non-Hermitian interacting systems with asymmetric hopping. Furthermore, the real-complex transition is shown to be absent in non-Hermitian many-body systems with gain and/or loss that breaks time-reversal symmetry, even though the MBL transition is still captured by its spectral transitions [1,2].

[1] R. Hamazaki, K. Kawabata, and M. Ueda, Phys. Rev. Lett. 123, 090603 (2019).
[2] R. Hamazaki, K. Kawabata, N. Kura and M. Ueda. Phys. Rev. Research, 2 (2), 023286 (2020).

Investigating many-body localization with quantum processors

Cheng Chen

Many-body localization (MBL) describes a quantum phase where an isolated interacting system subject to sufficient disorder displays non-ergodic behavior, evading thermal equilibrium that occurs under its own dynamics. In the past decade, thermalization and MBL have attracted extensive attention and become a new research paradigm in condensed matter physics. However, as a typical nonequilibrium phenomenon in strongly-correlated systems, investigations on MBL suffer from the finite size effect of many-body numerical algorithms. There are still some controversial issues in this field, and these controversies can hardly be solved under the traditional research framework. We noticed the fast development of quantum computing in recent years, and these quantum devices have the potential to tackle real-time dynamics of quantum many-body systems with much larger sizes compared to which can be solved by exact numerical methods. In this talk, we would like to share our cooperative experience with quantum computing experimentalists, by showing how we observed energy-resolved MBL and mobility edge on a quantum superconducting processor with 20 qubits [Nature Physics, 17, 234–239 (2021)]. I will also briefly introduce our recent work on MBL without disorders, dubbed Stark-MBL. This work is done on a processor with 32 qubits [arXiv:2011.13895], which is already beyond what exact diagonalization can do.

POLFED - a new diagonalization approach to study non-equilibrium phenomena

Piotr Sierant

I will introduce a polynomially filtered exact diagonalization (POLFED) method of computing eigenvectors of large sparse matrices at arbitrary energies - a task that often arises when studying non-equilibrium phenomena in quantum many-body systems. The algorithm finds an optimal basis of a subspace spanned by eigenvectors with eigenvalues close to a specified energy target using a high order polynomial of the matrix. The memory requirements scale much better with system size than in the state-of-the-art shift-invert approach, while the total CPU time used by the two methods is similar. The performance of POLFED is not severely impeded when the the number of non-zero elements in the matrix is increased allowing to efficiently study models with long-range
interactions.

I will demonstrate the potential of POLFED by examining many-body localization (MBL) transition in 1D interacting quantum spin-1/2 chains. Non-monotonic system size dependence of bipartite entanglement entropy and of the gap ratio highlights the importance of finite-size effects in the system. Possible scenarios regarding the MBL transition along with estimates for the critical disorder strength will be discussed. I will present results regarding MBL in highly constrained one-dimensional quantum spin chains. The increase of Hilbert space dimension with system size is slower than in the usually considered spin-1/2 chains which allows to investigate considerably larger system sizes. A mechanism of constraints induced delocalization restores ergodicity of the constrained quantum spin chains in the thermodynamic limit.

[1] P. Sierant, M. Lewenstein, J. Zakrzewski, Phys. Rev. Lett. 125, 156601 (2020)
[2] P. Sierant, E. Gonzalez Lazo, M. Dalmonte, A. Scardicchio, J. Zakrzewski, in preparation

Many-body localization in quasiperiodic systems

Sarang Gopalakrishnan

Abstract: We construct local integrals of motion (LIOMs) in quasiperiodic systems in the many-body localized (MBL) phase, and analyze their properties as a function of the quasiperiodic potential strength. We find that LIOMs are unstable at a considerably higher value of the quasiperiodic potential than the conventional MBL transition point for these systems (located via level statistics, entanglement, and related probes). Collapsing the data on LIOMs also yields different critical exponents than the conventional ones. We speculate on the reasons for this discrepancy and what it might be telling us about the nature of the quasiperiodic MBL transition.

Eigenstate susceptibility of small (disordered) spin chains

Dries Sels

In this talk I will discuss how the norm of the adiabatic gauge potential, the generator of adiabatic deformations between eigenstates, serves as a sensitive measure of quantum chaos. 

I will show that the onset of quantum chaos at infinite temperature is characterized by universal behavior in a number of 1D lattice models. Specifically, we show that the onset of quantum chaos is marked by maxima of the typical fidelity susceptibilities that scale with the square of the inverse average level spacing, saturating their upper bound.