Juven Wang (Harvard)

Ultra Quantum Matter and Beyond the Standard Model Physics

Ongoing ideas developed from the quantum matter and quantum field theory frontier may guide us to explore new physics beyond the 4d Standard Model. I will mention a few such ideas. First, new physics for neutrinos: right-handed neutrinos can carry a Z_16 class mixed gauge-gravitational global anomaly index, which could be replaced by 4d or 5d topological quantum field theory, or 4d interacting conformal field theory. These theories provide possible new neutrino mass mechanisms [arXiv:2012.15860]. Proton stability may also be protected by a discrete symmetry [2204.08393]. Second, deconfined quantum criticality between Grand Unified Theories: dictated by a Z_2 class global anomaly, a gapless quantum critical region can happen between Georgi-Glashow and Pati-Salam models as deformation of Standard Model, where Beyond Standard Model physics like deconfined dark photons occur as neighbor phases [arXiv:2106.16248, arXiv:2112.14765, arXiv:2202.13498]. Third, the familiar C, P, and T symmetries together with fermion parity (-1)^F could "fractionalize" to form a non-abelian finite group structure. Examples include the familiar 4d spin-1/2 Dirac fermion [arXiv:2109.15320], and 1d Majorana zero modes [arXiv:2011.12320, arXiv:2011.13921], etc.

This is a Zoom talk. Sign up for the mailing list to get the zoom link. Recording is available per request.

Shreya Vardhan (MIT)

Bound entanglement and information recovery in thermalized states.

For mixed states, a quantity called logarithmic negativity provides a better measure of entanglement than mutual information. I will discuss the behavior of this quantity in various universality classes of mixed states that are in a macroscopic thermal equilibrium. At finite temperature, this quantity reveals a rich entanglement phase diagram with some surprising features. In particular, there are regimes where the logarithmic negativity is much larger than the mutual information, implying that there is a large amount of "bound entanglement," which cannot be distilled into EPR pairs. I will also comment on applications to evaporating black holes and related results for the Hayden-Preskill experiment at finite temperature.

This is a hybrid talk. Recording is available per request.

Ruben Verresen (Harvard)

Topological order and long-range entanglement from measuring SPT phases.

A fundamental distinction between many-body quantum states are those with short- and long-range entanglement (SRE and LRE). The latter, such as cat states, topological order, or critical states cannot be created by finite-depth circuits. Remarkably, examples are known where LRE is obtained by performing single-site measurements on SRE, such as the toric code from measuring a sublattice of a 2D cluster state. In this talk, I will discuss a vast generalization, where LRE appears quite generally by performing single-site measurements on symmetry-protected topological (SPT) phases. As a special case of such measurement-based conversion of SRE into LRE, we can implement the Kramers-Wannier transformation in finite time, which amounts to gauging a symmetry. As an application, I will outline how this is a scalable method to prepare LRE states using existing platforms such as Rydberg atom arrays, where toric code, non-Abelian topological order, and even exotic fracton phases of matter can be prepared with high fidelity. Time permitting, I will also discuss various open questions raised by this new connection between SPT and LRE.

Based on work with Nat Tantivasadakarn, Ryan Thorngren and Ashvin Vishwanath (arXiv:2112.03061 and arXiv:2112.01519)

This is a hybrid AND blackboard talk. Recording is available per request.

Michael Wang (UMass Amherst)

Self-limiting assembly of frustrated puzzlemers: 2D and beyond!

Geometrically frustrated self-assembly, a process by which the local preferred arrangement of self-assembling particles cannot be realized perfectly on scales much larger than the particles themselves, has recently emerged as a paradigm for potentially controlling the growth and ultimately, the size of self-assembled structures (self-limiting assembling). In this talk, I will describe and analyze a model system of trapezoidal-shaped particles (puzzlemers) to understand how particle shape and interactions can generate frustration and affect the morphology and size of the resulting assemblies. By examining the energy landscapes for 2D sheets of puzzlemers, I will show that the assemblies exhibit polymorphism with puzzlemers assembling into either tall, straight or curved, annulus-like structures with finite dimensions, each with unique energetics. In addition, I will identify some key ingredients necessary for assembling these self-limiting structures with well-controlled sizes much larger than the individual particles themselves, but still finite. Finally, I will briefly discuss recent attempts to understand how these 2D sheets of puzzlemers can escape or relieve some frustration by buckling into 3D to form tubes or wrinkled sheets.

This is a hybrid talk. Recording is available per request (contact Grace).

Nishad Maskara (Harvard)

Amplifying topological order parameters with local quantum error correction.

In this talk, I will discuss ongoing work to develop a technique for amplifying Wilson loops in a Z2 topologically ordered phase by applying local quantum error correction (QEC). Extending the QCNN framework for phase classification of Cong et al (2018), we interpret the application of local QEC as generating a real space RG flow towards the topological fixed point. In the Heisenberg picture, local QEC coarse-grains the bare Wilson loops, with the width of the new Wilson loops dependent on the range of the local QEC procedure. We present theoretical arguments that in the thermodynamic limit, if the coarse-grained Wilson loops to go one then this provides a sufficient condition for certification of topological order. We demonstrate the technique with numerical simulations of the canonical toric code model as well as the recently proposed and observed dimer model on a ruby lattice [Verresen et al. (2020) and Semeghini et al. (2021)]. Further, local error correction can also catch and correct local incoherent errors, suggesting the technique also can be applied to mixed states. We show this using a classical bit-flip error model as well. Finally, we present some preliminary results on experimental data from Semeghini et al.

This is a hybrid talk. Recording is available per request.

Wen Wei Ho (Stanford)

Emergent quantum state designs from quantum chaotic dynamics: a new random matrix universality and applications for quantum information science.

In this talk I will introduce the idea of a novel kind of emergent random matrix universality that quantum many-body systems can exhibit. Specifically, I will consider quench dynamics of systems which are believed to be quantum chaotic, occuring at infinite temperatures. I will show that the distribution of pure states supported on a small subsystem, generated from projective measurements of the remainder of the system in a local basis, generically approaches a universal form: it becomes uniformly distributed in Hilbert space. This goes beyond the standard paradigm of quantum thermalization, which only dictates that the subsystem at late times relaxes to an ensemble of states that reproduces the expectation values of local observables in a thermal state. Instead, our results imply more generally that the distribution of quantum states themselves is indistinguishable from random states, i.e. the ensemble forms a "quantum state design" in the parlance of quantum information theory. I will show how this phenomenology can be demonstrated in an exactly-solvable toy model, the kicked Ising model, leveraging the dual unitary nature of its dynamics. Lastly, I will briefly sketch how such universal randomness can be harnessed to design algorithms for quantum state learning, i.e. the learning of important physical features of a system, which are implementable in existing quantum simulator platforms despite their limited controls.

This is a hybrid talk. Recording is NOT available for this talk.

Ruihua Fan (Harvard)

Floquet conformal field theory with spatially deformed Hamiltonians.

In this talk, I will introduce a class of exactly solvable Floquet many-body systems: 1+1D conformal field theories driven by spatially deformed Hamiltonians. It supports both heating and non-heating phases distinguished by the pattern of energy and entanglement growth. I will introduce a quasi-particle picture to explain the dynamics and why the heating phase can be used for cooling. If time permits, I will also explain what happens if the driving is quasi-periodic or random.

This is an online talk. Recording is available per request.

Asja Radja (Harvard)

Deciphering the physical rules of biological patterns: how marine glass skeletons form from biological foams.

Silica (glass) skeletons of radiolarians and phaeodarians, single-celled protists found in all oceans on earth, produce striking geometric structures that have inspired scientists, artists, and architects for decades. While several attempts have been made to rationalize the formation of these intricate structures, little clarity has emerged as to whether it is more appropriate to consider the patterned skeletons as developing from directly encoded, active cellular processes, or as an energetically passive result of material equilibration. Here I provide the first mathematical model of skeletal patterning based on liquid-gas phase separation, a physicochemical process dictated purely by organic constituents of these cells. I show how silica deposition in some radiolarians and phaeodarians across the evolutionary tree may be templated by biological foams and quantify how the dynamics of spherically-bound foams resemble many final forms of radiolarian and phaeodarian skeletons seen in nature.

This is a Zoom talk. Recording is available per request (contact Grace).

Xueyang Song (MIT)

Doping a chiral spin liquid towards topological superconductivity and duality of critical theories.

This talk will discuss a novel route to obtain a topological superconducting state with d-wave pairing symmetry. This is achieved by doping an exotic quantum spin state - chiral spin liquid(CSL) which breaks time reversal. I'll first introduce the parton formalism used in the study of strongly correlated systems, where the electrons are decomposed into two slave particles. Applied in the CSL, one species of slave particles, called spinons, form a chern insulator. If upon doping the CSL, another slave particle species carrying charge, enters the bosonic integer quantum hall state, then the physical state has vanishing resistivity, i.e. becomes superconducting. In this way a wavefunction is projected from a product of two quantum hall states and describes a d+id superconductor. The gauge flux nucleates electron cooper pairs.

At the quantum critical point between the CSL and d+id superconductors, quantum electrodynamics(QED) with gapless Dirac fermions emerges. Through a conventional mechanism where one slave particle condenses to obtain a superconductor, one derives a different formulation of the critical theory w/ bosonic fields and either U(1)_2 or SU(2)_1 terms. Interestingly, a charge-density-wave order parameter also becomes critical at the transition. I'll show that the QED, U(1)_2 and SU(2)_1 theories are dual to each other, as partly proposed by Benini, Hsin and Seiberg (2017). This CSL-SC transition is applicable on square, triangular and kagome lattices, with slight differences in global symmetries.

This is a hybrid talk. Recording is available per request.

Gregory Kahanamoku-Meyer (Berkeley)

Classical verification of quantum advantage.

An important milestone on the path to application-ready quantum computing is the demonstration of quantum computational advantage: solving some problem faster on a quantum computer than would be possible on any classical computer. Excitingly, several experiments have already performed sampling problems which are believed to be intractable for even the world's top supercomputers. But a challenge arises in the verification of these experiments: checking the quantum computer's output requires exponential classical resources, so correctness cannot be explicitly verified at classically intractable system sizes. Here we present protocols for efficiently-verifiable quantum advantage, through cryptographic "proofs of quantumness." These protocols have the combined advantages of polynomial-time classical verification, and security against even adversarial classical impostors via well-studied cryptographic hardness assumptions. After discussion of the protocols we present progress toward their implementation on near-term quantum devices.

This is a hybrid talk. Recording is available per request.

Dries Sels (NYU - Flatiron institute)

Taking arms against a sea of troubles, a critical discussion on many-body localization.

Understanding the properties of far from equilibrium quantum many-body systems has been at the forefront of quantum condensed matter research for the past decade. In particular, understanding when and how systems can avoid thermalizing under their own dynamics has captivated many of us. Current wisdom dictates that 1D systems with a local Hamiltonian can evade thermalization when subject to sufficiently strong disorder, a phenomenon called many-body localization (MBL).

In this talk I will give an overview of the works that have led to that belief, and contrast that them with new findings that challenge the current dogma. I will show that in a large regime of disorder strengths, thus far believed to be rather deep in the MBL phase, the system is undoubtably ergodic. I’ll argue that the simplest picture for understanding these results is one in which there is no MBL phase.

This is a Zoom talk. Recording is available per request.

Alexander Mietke (MIT)

Defect braiding and spontaneous chiral symmetry breaking in dihedral liquid crystals.

Dihedral (“k-atic”) liquid crystals (DLCs) are assemblies of microscopic constituent particles that exhibit k-fold discrete rotational and reflection symmetries. Generalizing the half-integer defects in nematic liquid crystals, two-dimensional k-atic DLCs can host point defects of fractional topological charge ±m/k. Starting from a generic microscopic model, we derive a unified hydrodynamic description of DLCs with aligning or antialigning short-range interactions in terms of Ginzburg-Landau and Landau-Brazovskii-Swift-Hohenberg theories for a universal complex order-parameter field. Building on this framework, we demonstrate in particle simulations how adiabatic braiding protocols, implemented through suitable boundary conditions, enable defect-pairs to carve out subdomains with an emerging anyonic exchange symmetry: Every braiding-exchange of the defect-pair shifts the subdomain orientation by a fractional angle 2π/k and k consecutive braids restore the initial configuration of the DLC. Analytic solutions and simulations of the mean-field theory further predict a novel spontaneous chiral symmetry-breaking transition in anti-aligning DLCs, in quantitative agreement with the patterns observed in particle simulations.

This is a Zoom talk. Recording is available per request.

Iris Cong (Harvard)

Recognizing Topological Phases of Matter with Quantum Convolutional Neural Networks.

In this talk, I introduce our recently developed quantum machine learning model called the quantum convolutional neural network (QCNN), which is inspired by the widely successful convolutional neural network (CNN) used for image recognition. Our quantum convolutional neural network (QCNN) makes use of only O(log(N)) variational parameters for input sizes of N qubits, allowing for its efficient training and implementation on realistic, near-term quantum devices. To explicitly illustrate its capabilities, I show that QCNNs can accurately recognize quantum states associated with a one-dimensional symmetry-protected topological phase, with performance surpassing existing approaches. Finally, motivated by recent experimental breakthroughs in the realization of two-dimensional topological phases, I then present our latest work on constructing a generic QCNN framework for recognizing two-dimensional phases of matter and demonstrating its potential through two examples involving the toric code topological order.

This is a Zoom talk. Recording is available per request.

Botond Tyukodi (Brandeis)

Size-control and escape mechanisms in self-limiting assemblies with open boundaries.

Self-limiting assembly refers to a self-assembly process which autonomously terminates at a large, but well-defined finite-sized structures. Such self-limited assembly underlies crucial functions in many biological systems; examples include viral protein capsids, bacterial microcompartments, and other protein-shelled organelles. Achieving similar capabilities in synthetic systems is of great interest for nanotechnology, and recently human-engineered programmable subunits have been developed that form similar self-limited capsid structures. In these biological and synthetic examples, self-limitation is driven by a preferred curvature of the subunits, which causes the structure to close upon itself and thus eliminate boundaries at which additional subunits could assemble. However, mechanisms to achieve self-limited structures with open boundaries have yet to be realized.

In this talk we use computational and theoretical modeling to investigate self-limited assembly of structures with open boundaries through the mechanism of ‘geometric frustration’, in which the preferred local packing of subunits is incompatible with the preferred-large scale assembly geometry. This incompatibility can, in principle, lead to a strain energy that is super-extensive as a function of assembly size and thereby causes assembly to terminate at a finite size. However, despite important continuum theory studies, it remains unclear how robust geometric frustration limited assembly is to finite temperatures and the formation of defects that release strain.

Motivated by ongoing DNA origami experiments, we study triangular subunits whose shape favors assembly into a hexagonal array, but whose interaction geometry favors a negative Gaussian curvature that leads to geometric frustration. The resulting structures are catenoids which self-close in one dimension, but are self-limited with open boundaries in the other one. We perform dynamic Monte Carlo simulations and free energy calculations to determine parameter regimes in which the structures are self-limited, and the key control parameters that enable tuning their self-limited size. We also identify two primary mechanisms by which the assembly escapes self-limitation: i) screening of the long-range elastic strain field, and ii) proliferation of crack defects that release frustration.

This is a hybrid talk. Sign up for the mailing list to get the zoom link.

Ethan Lake (MIT)

Dipole conservation and the Bose-Hubbard model.

I will discuss a simple model of interacting bosons whose dynamics conserves both boson charge and boson dipole moment. This model, the ``dipolar Bose-Hubbard model'', provides a simple framework in which the consequences of dipolar conservation laws can be explored. I will discuss the phase diagram of this model in various dimensions, and show how it realizes several rather unusual phases of matter (including an ``insulating superfluid''). This talk is based on joint work with M. Hermele and T. Senthil.

This is a hybrid talk. Sign up for the mailing list to get the zoom link.

Luyi Qiu (Harvard University)

Bacterial shape: instabilities of rod-shaped cells and formation of helices.

Bacteria are diverse in shape, and their shape is dictated by a rigid, mesh-like cell wall. I will first discuss how rod-shaped bacteria, modeled as cylindrical shells, can experience an instability upon bending. The study of such instabilities was pioneered by Brazier nearly a century ago, for open tubes (e.g., a common drinking straw). For the case of highly pressurized closed shells - relevant for bacteria such as E. coli - we find that this instability is significantly postponed by its internal pressure, while the cell wall bending stiffness has little influence. This suggests a novel experimental method to infer internal pressure in rod-shaped bacteria. Next, I will discuss how rod-shaped bacteria may transform into helices due to the combination of inner pressure and heterogeneity in the cell wall elastic modulus, motivated by recent experiments on the helical shaped bacterium H. pylori. We hope these results will shed light on the biological significance of bacteria mechanical structure as well as novel design of transformable materials inspired by biology.

This is a hybrid talk. Sign up for the mailing list to get the zoom link.

David Long (Boston University)

Boosting the Quantum State of a Cavity with Floquet Driving.

The striking nonlinear effects exhibited by cavity QED systems make them a powerful tool in modern condensed matter and atomic physics. A recently discovered example is the quantized pumping of energy into a cavity by a strongly coupled, periodically driven spin. I will uncover a remarkable feature of these energy pumps: they coherently translate, or boost, a quantum state of the cavity in the Fock basis. Furthermore, I will argue that the required ultra-strong coupling may be achieved in a rotating frame. Boosting thus enables the preparation of highly excited nonclassical cavity states in near term optical cavity and circuit QED experiments. One need only boost low occupation states.

This is a hybrid talk. Sign up for the mailing list to get the zoom link.

Brian Swingle (Brandeis)

Quantum Chaos in Adamantane.

In the context of chaotic quantum many-body systems, we show that operator growth, as diagnosed by out-of-time-order correlators of local operators, also leaves a sharp imprint in out-of-time-order correlators of global operators. In particular, the characteristic spacetime shape of growing local operators can be accessed using global measurements without any local control or readout. Building on an earlier conjectured phase diagram for operator growth in chaotic systems with power-law interactions, we show that existing nuclear spin data for out-of-time-order correlators of global operators in adamantane is consistent with our theory. We also predict super-polynomial operator growth in dipolar systems in 3d and discuss the potential observation of this physics in future experiments with nuclear spins and ultra-cold polar molecules. Forthcoming work with Tianci Zhou.

This is a hybrid talk. Sign up for the mailing list to get the zoom link.

Anna Golubeva (MIT)

The efficiency of machine-learning quantum states.

Machine learning has provided a variety of new computational tools for physics that have proven successful for many problems. An important application of ML in quantum many-body physics is the use of generative modeling for wavefunction reconstruction. Since the number of classical parameters needed to encode a quantum wavefunction scales rapidly with the number of qubits, the ability to learn efficient representations is of critical importance. In this talk, I will present the results from two empirical studies that systematically evaluate the scaling of computational resources for reconstructing positive-real wavefunctions with Restricted Boltzmann Machines (RBMs) and investigate pruning as a way to compress the RBM wavefunction representation.

This is a hybrid talk. Sign up for the mailing list to get the zoom link.

Anne Meeussen (Harvard University)

Shape-morphing matter.

Thin sheets show unusual behaviour, from crumpling to stiffening when curved. These phenomena arise from a geometry-mediated competition between stretching and bending energies, which produces rich emergent effects. Here, we harness a thin sheet with a simple geometry-a "groovy sheet" with parallel undulations-to create a multistable structure with minimal preprogramming. We show that our groovy sheets exhibit rapid, easy-to-actuate, and reversible shape-switching between a large array of out-of-plane states via snap-through instabilities. Our work opens up new vistas for the design of shape-shifting materials, leveraging thin sheets' potential for large elastic deflections.

This is an online talk. We still encourage you to come to Lyman 425 and listen to it from there. Food will be provided. For a zoom link please sign up for the mailing list.

Pavel (Pasha) Dolgirev (Harvard University)

Coherent terahertz emission in photoexcited striped superconductors.

In this talk, I will first present our experimental finding that impulsive photoexcitation of striped superconductor LBCO results in a coherent terahertz emission at the Josephson Plasma frequency. This phenomenon is unexpected because no external magnetic field or electric bias has been applied. This effect appears to be correlated with the strength and coherence length of the charge order. I will then argue that behind the observed terahertz emission is the nonlinear optical effect called shift current, which encodes the downconversion of the high-frequency electric field into low-frequency charge current. In the rest of the talk, I aim to address two questions: 1) given the generation of the shift currents, how do we get sharp coherent emission? and 2) what is the origin of the shift current in the first place? The likely answer to the first question is that the shift currents drive the Surface Josephson Plasmons, which can radiate out because their dispersion is backfolded onto the light cone due to the stripes. For the second question, I will discuss lattice symmetries of various stripes patterns and their implications on the probable origin.

This is a hybrid talk. Sign up for the mailing list to get the zoom link.

Dominic Else (Harvard University)

Critical drag as a mechanism for resistivity, with application to strange metals.

In this talk, I will discuss very general ways to reason about electrical resistivity in metals, beyond the conventional Fermi liquid theory. This will lead to a proposal for a new mechanism for resistivity that we call "critical drag", where the resistivity originates from critical fluctuations. This is strikingly different to more conventional resistivity mechanisms that involve violation of conservation laws such as momentum conservation. Furthermore, I will argue on general grounds that critical drag is the only resistivity mechanism that is compatible with certain basic experimentally motivated assumptions about the so-called "strange metals" seen in cuprates and other materials.

The arguments of this talk are based on powerful theoretical concepts such as emergent symmetries and anomalies, invoking ideas that originated in the study of topological phases of matter.

This is an online talk. We still encourage you to come to Lyman 425 and listen to it from there. Food will be provided. For a zoom link please sign up for the mailing list.

Soonwon Choi (MIT)

Emergence of universal randomness from chaotic quantum dynamics.

Universality -- the emergence of features independent of precise microscopic details -- allows us to simplify the analysis of complex systems and to establish important general principles. For example, quantum thermalization constitutes a universal behavior emerging from out-of-equilibrium dynamics, as it prescribes that the density matrix of a local subsystem is driven to a Gibbs ensemble under generic dynamics of isolated quantum many-body systems, independent of the details of initial states.

In this talk, we describe a novel kind of universal phenomenon that occurs in strongly interacting many-body quantum dynamics beyond the conventional thermalization. More specifically, we point out that a single many-body wavefunction can encode an ensemble of a large number of pure states defined on a subsystem. Then, for a wide class of many-body wavefunctions, we show that the ensembles encoded in them display universal statistical properties by using a notion in quantum information theory, called quantum state k-designs. The special case (k=1) reduces to the conventional quantum thermalization. Our proposed universality is corroborated by (1) two theorems, (2) exact results from a chaotic Floquet dynamics, (3) extensive numerical simulations of Hamiltonian dynamics, and (4) recent experimental observations based on a Rydberg quantum simulator. Our results offer a new approach for studying quantum chaos and provide a practical method for sampling pseudorandom quantum states. The observed universality leads to the development of a novel benchmarking method applicable for a wide variety of near-term quantum devices. If time permitting , I will explain how our results allow us to develop a novel sample-efficient benchmarking protocol, which has been already demonstrated in an experiment.

Jinghui Liu (MIT)

Topological defects and information flows on the membrane of a living cell.

Topological defects determine the structure and function of physical and biological matter over a wide range of scales, from the turbulent vortices in planetary atmospheres, oceans or quantum fluids to bioelectrical signaling in the heart and brain. While many advances have been made in understanding the defect dynamics in passive non-equilibrium fluids, it remains elusive whether physical laws that govern their statistics and dynamics extend to information flows in biologically active processes. Here, I will discuss several recent studies on a defect-mediated turbulence that underlies the complex wave propagation patterns of Rho-GTP signaling protein on the membrane of starfish egg cells, a process closely relevant to information processing in early developments. Combining direct experimental observations with quantitative analysis and mathematical modeling, we show that the phase velocity field extracted from the Rho-GTP concentration waves exhibits vortical defect motions and annihilation dynamics reminiscent of those seen in quantum fluids and active nematics. Moreover, these spiral wave cores undergo spontaneous braiding dynamics and can be mapped quantitatively to predictions from a generic continuum theory. We hope these results will shed light on designing and controlling biological structures with logical capabilities which feature robust and efficient information-processing units.

Daniel Parker (Harvard University)

Fractional Chern Insulators and Hofstadter Band Geometry in Magic-Angle Graphene

Fractional Chern Insulators (FCIs) generalize the celebrated fractional quantum hall effect to the lattice setting. A number of theoretical proposals have suggested (hBN-aligned) magic-angle graphene (hBN-MATBG) is a prime candidate for realizing FCIs, as its bandstructure and quantum geometry are relatively close to that of the lowest Landau level. Indeed, this was borne out in a recent experiment from the Yacoby group [1], which observed 8 FCIs in hBN-MATBG at magnetic fields as low as 5 Tesla. This talk will examine a constellation of questions surrounding this experiment. Can we understand the appearance of these FCIs? What quantum geometric conditions are necessary to favor FCIs in the minibands of the Hofstadter butterfly? Can MATBG support FCIs without an external field?