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Tensor product states are powerful tools for simulating area-law entangled states of many-body systems. The applicability of such methods to the non-equilibrium dynamics of many-body systems is less clear due to the presence of large amounts of entanglement. New methods seek to reduce the numerical cost by selectively discarding those parts of the many-body wavefunction, which are thought to have relatively litte effect on dynamical quantities of interest. We present a theory for the sizes of “backflow corrections”, i.e., systematic errors due to these truncation effects and introduce the dissipation-assisted operator evolution (DAOE) method for calculating transport properties of strongly interacting lattice systems in the high temperature regime. In the DAOE method, we represent the observable as a matrix product operator, and show that the dissipation leads to a decay of operator entanglement, allowing us to capture the dynamics to long times. We benchmark this scheme by calculating spin and energy diffusion constants in a variety of physical models and compare to other existing methods.

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The interplay between spontaneous symmetry breaking and topology can result in exotic quantum states of matter. A celebrated example is the quantum anomalous Hall (QAH) effect, which exhibits an integer quantum Hall effect at zero magnetic field due to topologically nontrivial bands and intrinsic magnetism. In the presence of strong electron-electron interactions, fractional-QAH (FQAH) effect at zero magnetic field can emerge, which is a lattice analog of fractional quantum Hall effect without Landau level formation. In this talk, I will present experimental observation of FQAH effect in twisted MoTe 2 bilayer, using combined magneto- optical and -transport measurements. In addition, we find an anomalous Hall state near the filling factor -1/2, whose behavior resembles that of the composite Fermi liquid phase in the half-filled lowest Landau level of a two-dimensional electron gas at high magnetic field. Direct observation of the FQAH and associated effects paves the way for researching charge fractionalization and anyonic statistics at zero magnetic field.

Reference 1. Observation of Fractionally Quantized Anomalous Hall Effect, Heonjoon Park et al., Nature, https://www.nature.com/articles/s41586-023-06536-0 (2023);
2. Signatures of Fractional Quantum Anomalous Hall States in Twisted MoTe2 Bilayer, Jiaqi Cai et al., Nature, https://www.nature.com/articles/s41586-023-06289-w (2023);
3. Programming Correlated Magnetic States via Gate Controlled Moiré Geometry, Eric Anderson et al., Science, https://www.science.org/doi/full/10.1126/science.adg4268 (2023)

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here are two notions of a symmetry of a group G on a 3d topological order (TO): an "algebraic" symmetry, where G acts by automorphisms on the tensor category defining the (TO), and a "field-theoretic" symmetry, where the TFT corresponding to the TO is extended to manifolds with a principal G-bundle. The "field-theoretic" notion is stronger than the "algebraic" one, and the obstruction is sometimes referred to as the anomaly of the TO. The goal of this talk is to discuss a project joint with Weicheng Ye and Matthew Yu on computing these anomalies for fermionic TOs/spin TFTs: we develop a general framework employing Gaiotto-Kapustin's bosonic shadow construction. I will discuss both the mathematical conjectures our framework rests on as well as its use in examples. The Smith long exact sequence appears in our computations.