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1. Many-Body Resonances in the Avalanche Instability of Many-Body Localization

   https://doi.org/10.1103/PhysRevLett.130.250405  

   Ha, Hyunsoo; Morningstar, Alan; Huse, David A. (June 2023, Physical Review Letters)

   Many-body localized (MBL) systems fail to reach thermal equilibrium under their own dynamics, even though they are interacting, nonintegrable, and in an extensively excited state. One instability toward thermalization of MBL systems is the so-called “avalanche,” where a locally thermalizing rare region is able to spread thermalization through the full system. The spreading of the avalanche may be modeled and numerically studied in finite one-dimensional MBL systems by weakly coupling an infinite-temperature bath to one end of the system. We find that the avalanche spreads primarily via strong many-body resonances between rare near-resonant eigenstates of the closed system. Thus we find and explore a detailed connection between many-body resonances and avalanches in MBL systems. 

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2. Anomalous localization in a kicked quasicrystal

   https://doi.org/10.1038/s41567-023-02329-4  

   Shimasaki, Toshihiko; Prichard, Max; Kondakci, H. Esat; Pagett, Jared E.; Bai, Yifei; Dotti, Peter; Cao, Alec; Dardia, Anna R.; Lu, Tsung-Cheng; Grover, Tarun; et al (January 2024, Nature Physics)

   Abstract Quantum transport can distinguish between dynamical phases of matter. For instance, ballistic propagation characterizes the absence of disorder, whereas in many-body localized phases, particles do not propagate for exponentially long times. Additional possibilities include states of matter exhibiting anomalous transport in which particles propagate with a non-trivial exponent. Here we report the experimental observation of anomalous transport across a broad range of the phase diagram of a kicked quasicrystal. The Hamiltonian of our system has been predicted to exhibit a rich phase diagram, including not only fully localized and fully delocalized phases but also an extended region comprising a nested pattern of localized, delocalized and multifractal states, which gives rise to anomalous transport. Our cold-atom realization is enabled by new Floquet engineering techniques, which expand the accessible phase diagram by five orders of magnitude. Mapping transport properties throughout the phase diagram, we observe disorder-driven re-entrant delocalization and sub-ballistic transport, and we present a theoretical explanation of these phenomena based on eigenstate multifractality. 

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3. Screening the Coulomb interaction leads to a prethermal regime in two-dimensional bad conductors

   https://doi.org/10.1038/s41467-023-42778-2  

   Stanley, L. J.; Lin, Ping V.; Jaroszyński, J.; Popović, Dragana (November 2023, Nature Communications)

   Abstract The absence of thermalization in certain isolated many-body systems is of great fundamental interest. Many-body localization (MBL) is a widely studied mechanism for thermalization to fail in strongly disordered quantum systems, but it is still not understood precisely how the range of interactions affects the dynamical behavior and the existence of MBL, especially in dimensionsD > 1. By investigating nonequilibrium dynamics in strongly disorderedD = 2 electron systems with power-law interactions ∝ 1/r^αand poor coupling to a thermal bath, here we observe MBL-like, prethermal dynamics forα = 3. In contrast, forα = 1, the system thermalizes, although the dynamics is glassy. Our results provide important insights for theory, especially since we obtained them on systems that are much closer to the thermodynamic limit than synthetic quantum systems employed in previous studies of MBL. Thus, our work is a key step towards further studies of ergodicity breaking and quantum entanglement in real materials. 

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4. Partons as unique ground states of quantum Hall parent Hamiltonians: The case of Fibonacci anyons

   https://doi.org/10.21468/SciPostPhys.15.2.043  

   Tanhayi Ahari, Mostafa; Bandyopadhyay, Sumanta; Nussinov, Zohar; Seidel, Alexander; Ortiz, Gerardo (January 2023, SciPost Physics)

   We present microscopic, multiple Landau level, (frustration-free and positive semi-definite) parent Hamiltonians whose ground states, realizing different quantum Hall fluids, are parton-like and whose excitations display either Abelian or non-Abelian braiding statistics. We prove ground state energy monotonicity theorems for systems with different particle numbers in multiple Landau levels, demonstrate S-duality in the case of toroidal geometry, and establish complete sets of zero modes of special Hamiltonians stabilizing parton-like states, specifically at filling factor\nu=2/3 $\nu =2/3$. The emergent Entangled Pauli Principle (EPP), introduced in [Phys. Rev. B 98, 161118(R) (2018)] and which defines the “DNA” of the quantum Hall fluid, is behind the exact determination of the topological characteristics of the fluid, including charge and braiding statistics of excitations, and effective edge theory descriptions. When the closed-shell condition is satisfied, the densest (i.e., the highest density and lowest total angular momentum) zero-energy mode is a unique parton state. We conjecture that parton-like states generally span the subspace of many-body wave functions with the two-bodyM $M$-clustering property within any given number of Landau levels, that is, wave functions withM $M$th-order coincidence plane zeroes and both holomorphic and anti-holomorphic dependence on variables. General arguments are supplemented by rigorous considerations for theM=3 $M=3$case of fermions in four Landau levels. For this case, we establish that the zero mode counting can be done by enumerating certain patterns consistent with an underlying EPP. We apply the coherent state approach of [Phys. Rev. X 1, 021015 (2011)] to show that the elementary (localized) bulk excitations are Fibonacci anyons. This demonstrates that the DNA associated with fractional quantum Hall states encodes all universal properties. Specifically, for parton-like states, we establish a link with tensor network structures of finite bond dimension that emerge via root level entanglement. 

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5. Many-body localized hidden generative models

   https://doi.org/10.1103/PhysRevResearch.6.043041  

   Zhong, Weishun; Gao, Xun; Yelin, Susanne F; Najafi, Khadijeh (October 2024, Physical Review Research)

   Quantum generative models hold the promise of accelerating or improving machine learning tasks by leveraging the probabilistic nature of quantum states, but the successful optimization of these models remains a difficult challenge. To tackle this challenge, we present a new architecture for quantum generative modeling that combines insights from classical machine learning and quantum phases of matter. In particular, our model utilizes both many-body localized (MBL) dynamics and hidden units to improve the optimization of the model. We demonstrate the applicability of our model on a diverse set of classical and quantum tasks, including a toy version of MNIST handwritten digits, quantum data obtained from quantum many-body states, and nonlocal parity data. Our architecture and algorithm provide novel strategies of utilizing quantum many-body systems as learning resources and reveal a powerful connection between disorder, interaction, and learning in quantum many-body systems. Published by the American Physical Society2024 

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