@article{14320, abstract = {The development of two-dimensional materials has resulted in a diverse range of novel, high-quality compounds with increasing complexity. A key requirement for a comprehensive quantitative theory is the accurate determination of these materials' band structure parameters. However, this task is challenging due to the intricate band structures and the indirect nature of experimental probes. In this work, we introduce a general framework to derive band structure parameters from experimental data using deep neural networks. We applied our method to the penetration field capacitance measurement of trilayer graphene, an effective probe of its density of states. First, we demonstrate that a trained deep network gives accurate predictions for the penetration field capacitance as a function of tight-binding parameters. Next, we use the fast and accurate predictions from the trained network to automatically determine tight-binding parameters directly from experimental data, with extracted parameters being in a good agreement with values in the literature. We conclude by discussing potential applications of our method to other materials and experimental techniques beyond penetration field capacitance.}, author = {Henderson, Paul M and Ghazaryan, Areg and Zibrov, Alexander A. and Young, Andrea F. and Serbyn, Maksym}, issn = {2469-9969}, journal = {Physical Review B}, number = {12}, publisher = {American Physical Society}, title = {{Deep learning extraction of band structure parameters from density of states: A case study on trilayer graphene}}, doi = {10.1103/physrevb.108.125411}, volume = {108}, year = {2023}, } @article{14406, abstract = {Recently, a concept of generalized multifractality, which characterizes fluctuations and correlations of critical eigenstates, was introduced and explored for all 10 symmetry classes of disordered systems. Here, by using the nonlinear sigma-model ( NL σ M ) field theory, we extend the theory of generalized multifractality to boundaries of systems at criticality. Our numerical simulations on two-dimensional systems of symmetry classes A, C, and AII fully confirm the analytical predictions of pure-scaling observables and Weyl symmetry relations between critical exponents of surface generalized multifractality. This demonstrates the validity of the NL σ M for the description of Anderson-localization critical phenomena, not only in the bulk but also on the boundary. The critical exponents strongly violate generalized parabolicity, in analogy with earlier results for the bulk, corroborating the conclusion that the considered Anderson-localization critical points are not described by conformal field theories. We further derive relations between generalized surface multifractal spectra and linear combinations of Lyapunov exponents of a strip in quasi-one-dimensional geometry, which hold under the assumption of invariance with respect to a logarithmic conformal map. Our numerics demonstrate that these relations hold with an excellent accuracy. Taken together, our results indicate an intriguing situation: the conformal invariance is broken but holds partially at critical points of Anderson localization.}, author = {Babkin, Serafim and Karcher, Jonas F. and Burmistrov, Igor S. and Mirlin, Alexander D.}, issn = {2469-9969}, journal = {Physical Review B}, number = {10}, publisher = {American Physical Society}, title = {{Generalized surface multifractality in two-dimensional disordered systems}}, doi = {10.1103/PhysRevB.108.104205}, volume = {108}, year = {2023}, } @article{14690, abstract = {Generalized multifractality characterizes system size dependence of pure scaling local observables at Anderson transitions in all 10 symmetry classes of disordered systems. Recently, the concept of generalized multifractality has been extended to boundaries of critical disordered noninteracting systems. Here we study the generalized boundary multifractality in the presence of electron-electron interaction, focusing on the spin quantum Hall symmetry class (class C). Employing the two-loop renormalization group analysis within the Finkel'stein nonlinear sigma model, we compute the anomalous dimensions of the pure scaling operators located at the boundary of the system. We find that generalized boundary multifractal exponents are twice larger than their bulk counterparts. Exact symmetry relations between generalized boundary multifractal exponents in the case of noninteracting systems are explicitly broken by the interaction.}, author = {Babkin, Serafim and Burmistrov, I}, issn = {2469-9969}, journal = {Physical Review B}, number = {20}, publisher = {American Physical Society}, title = {{Boundary multifractality in the spin quantum Hall symmetry class with interaction}}, doi = {10.1103/PhysRevB.108.205429}, volume = {108}, year = {2023}, } @article{19803, abstract = {Eu⁢Cd2⁢P2 is notable for its unconventional transport: upon cooling the metallic resistivity changes slope and begins to increase, ultimately 100-fold, before returning to its metallic value. Surprisingly, this giant peak occurs at 18 K, well above the Néel temperature (𝑇𝑁) of 11.5 K. Using a suite of sensitive probes of magnetism, including resonant x-ray scattering and magneto-optical polarimetry, we have discovered that ferromagnetic order onsets above 𝑇𝑁 in the temperature range of the resistivity peak. The observation of inverted hysteresis in this regime shows that ferromagnetism is promoted by coupling of localized spins and itinerant carriers. The resulting carrier localization is confirmed by optical conductivity measurements.}, author = {Sunko, Veronika and Sun, Y. and Vranas, M. and Homes, C. C. and Lee, C. and Donoway, E. and Wang, Z.-C. and Balguri, S. and Mahendru, M. B. and Ruiz, A. and Gunn, B. and Basak, R. and Blanco-Canosa, S. and Schierle, E. and Weschke, E. and Tafti, F. and Frano, A. and Orenstein, J.}, issn = {2469-9969}, journal = {Physical Review B}, number = {14}, publisher = {American Physical Society}, title = {{Spin-carrier coupling induced ferromagnetism and giant resistivity peak in EuCd2P2}}, doi = {10.1103/physrevb.107.144404}, volume = {107}, year = {2023}, } @article{14605, abstract = {The phonon transport mechanisms and ultralow lattice thermal conductivities (κL) in silver halide AgX (X=Cl,Br,I) compounds are not yet well understood. Herein, we study the lattice dynamics and thermal property of AgX under the framework of perturbation theory and the two-channel Wigner thermal transport model based on accurate machine learning potentials. We find that an accurate extraction of the third-order atomic force constants from largely displaced configurations is significant for the calculation of the κL of AgX, and the coherence thermal transport is also non-negligible. In AgI, however, the calculated κL still considerably overestimates the experimental values even including four-phonon scatterings. Molecular dynamics (MD) simulations using machine learning potential suggest an important role of the higher-than-fourth-order lattice anharmonicity in the low-frequency phonon linewidths of AgI at room temperature, which can be related to the simultaneous restrictions of the three- and four-phonon phase spaces. The κL of AgI calculated using MD phonon lifetimes including full-order lattice anharmonicity shows a better agreement with experiments.}, author = {Ouyang, Niuchang and Zeng, Zezhu and Wang, Chen and Wang, Qi and Chen, Yue}, issn = {2469-9969}, journal = {Physical Review B}, number = {17}, publisher = {American Physical Society}, title = {{Role of high-order lattice anharmonicity in the phonon thermal transport of silver halide AgX (X=Cl,Br, I)}}, doi = {10.1103/PhysRevB.108.174302}, volume = {108}, year = {2023}, } @article{13039, abstract = {We calculate reflectivities of dynamically compressed water, water-ethanol mixtures, and ammonia at infrared and optical wavelengths with density functional theory and molecular dynamics simulations. The influence of the exchange-correlation functional on the results is examined in detail. Our findings indicate that the consistent use of the HSE hybrid functional reproduces experimental results much better than the commonly used PBE functional. The HSE functional offers not only a more accurate description of the electronic band gap but also shifts the onset of molecular dissociation in the molecular dynamics simulations to significantly higher pressures. We also highlight the importance of using accurate reference standards in reflectivity experiments and reanalyze infrared and optical reflectivity data from recent experiments. Thus, our combined theoretical and experimental work explains and resolves lingering discrepancies between calculations and measurements for the investigated molecular substances under shock compression.}, author = {French, Martin and Bethkenhagen, Mandy and Ravasio, Alessandra and Hernandez, Jean Alexis}, issn = {2469-9969}, journal = {Physical Review B}, number = {13}, publisher = {American Physical Society}, title = {{Ab initio calculation of the reflectivity of molecular fluids under shock compression}}, doi = {10.1103/PhysRevB.107.134109}, volume = {107}, year = {2023}, } @article{11337, abstract = {Nonanalytic points in the return probability of a quantum state as a function of time, known as dynamical quantum phase transitions (DQPTs), have received great attention in recent years, but the understanding of their mechanism is still incomplete. In our recent work [Phys. Rev. Lett. 126, 040602 (2021)], we demonstrated that one-dimensional DQPTs can be produced by two distinct mechanisms, namely semiclassical precession and entanglement generation, leading to the definition of precession (pDQPTs) and entanglement (eDQPTs) dynamical quantum phase transitions. In this manuscript, we extend and investigate the notion of p- and eDQPTs in two-dimensional systems by considering semi-infinite ladders of varying width. For square lattices, we find that pDQPTs and eDQPTs persist and are characterized by similar phenomenology as in 1D: pDQPTs are associated with a magnetization sign change and a wide entanglement gap, while eDQPTs correspond to suppressed local observables and avoided crossings in the entanglement spectrum. However, DQPTs show higher sensitivity to the ladder width and other details, challenging the extrapolation to the thermodynamic limit especially for eDQPTs. Moving to honeycomb lattices, we also demonstrate that lattices with an odd number of nearest neighbors give rise to phenomenologies beyond the one-dimensional classification.}, author = {De Nicola, Stefano and Michailidis, Alexios and Serbyn, Maksym}, issn = {2469-9950}, journal = {Physical Review B}, publisher = {American Physical Society}, title = {{Entanglement and precession in two-dimensional dynamical quantum phase transitions}}, doi = {10.1103/PhysRevB.105.165149}, volume = {105}, year = {2022}, } @article{11469, abstract = {Thermalizing and localized many-body quantum systems present two distinct dynamical phases of matter. Recently the fate of a localized system coupled to a thermalizing system viewed as a quantum bath received significant theoretical and experimental attention. In this work, we study a mobile impurity, representing a small quantum bath, that interacts locally with an Anderson insulator with a finite density of localized particles. Using static Hartree approximation to obtain an effective disorder strength, we formulate an analytic criterion for the perturbative stability of the localization. Next, we use an approximate dynamical Hartree method and the quasi-exact time-evolved block decimation (TEBD) algorithm to study the dynamics of the system. We find that the dynamical Hartree approach which completely ignores entanglement between the impurity and localized particles predicts the delocalization of the system. In contrast, the full numerical simulation of the unitary dynamics with TEBD suggests the stability of localization on numerically accessible timescales. Finally, using an extension of the density matrix renormalization group algorithm to excited states (DMRG-X), we approximate the highly excited eigenstates of the system. We find that the impurity remains localized in the eigenstates and entanglement is enhanced in a finite region around the position of the impurity, confirming the dynamical predictions. Dynamics and the DMRG-X results provide compelling evidence for the stability of localization.}, author = {Brighi, Pietro and Michailidis, Alexios and Kirova, Kristina and Abanin, Dmitry A. and Serbyn, Maksym}, issn = {2469-9969}, journal = {Physical Review B}, number = {22}, publisher = {American Physical Society}, title = {{Localization of a mobile impurity interacting with an Anderson insulator}}, doi = {10.1103/physrevb.105.224208}, volume = {105}, year = {2022}, } @article{11470, abstract = {Many-body localization (MBL) is an example of a dynamical phase of matter that avoids thermalization. While the MBL phase is robust to weak local perturbations, the fate of an MBL system coupled to a thermalizing quantum system that represents a “heat bath” is an open question that is actively investigated theoretically and experimentally. In this work, we consider the stability of an Anderson insulator with a finite density of particles interacting with a single mobile impurity—a small quantum bath. We give perturbative arguments that support the stability of localization in the strong interaction regime. Large-scale tensor network simulations of dynamics are employed to corroborate the presence of the localized phase and give quantitative predictions in the thermodynamic limit. We develop a phenomenological description of the dynamics in the strong interaction regime, and we demonstrate that the impurity effectively turns the Anderson insulator into an MBL phase, giving rise to nontrivial entanglement dynamics well captured by our phenomenology.}, author = {Brighi, Pietro and Michailidis, Alexios A. and Abanin, Dmitry A. and Serbyn, Maksym}, issn = {2469-9969}, journal = {Physical Review B}, number = {22}, publisher = {American Physical Society}, title = {{Propagation of many-body localization in an Anderson insulator}}, doi = {10.1103/physrevb.105.l220203}, volume = {105}, year = {2022}, } @article{11737, abstract = {Spin-orbit coupling in thin HgTe quantum wells results in a relativistic-like electron band structure, making it a versatile solid state platform to observe and control nontrivial electrodynamic phenomena. Here we report an observation of universal terahertz (THz) transparency determined by fine-structure constant α≈1/137 in 6.5-nm-thick HgTe layer, close to the critical thickness separating phases with topologically different electronic band structure. Using THz spectroscopy in a magnetic field we obtain direct evidence of asymmetric spin splitting of the Dirac cone. This particle-hole asymmetry facilitates optical control of edge spin currents in the quantum wells.}, author = {Dziom, Uladzislau and Shuvaev, A. and Gospodarič, J. and Novik, E. G. and Dobretsova, A. A. and Mikhailov, N. N. and Kvon, Z. D. and Alpichshev, Zhanybek and Pimenov, A.}, issn = {2469-9969}, journal = {Physical Review B}, number = {4}, publisher = {American Physical Society}, title = {{Universal transparency and asymmetric spin splitting near the Dirac point in HgTe quantum wells}}, doi = {10.1103/PhysRevB.106.045302}, volume = {106}, year = {2022}, } @article{12139, abstract = {We demonstrate the formation of robust zero-energy modes close to magnetic impurities in the iron-based superconductor FeSe1-z Tez. We find that the Zeeman field generated by the impurity favors a spin-triplet interorbital pairing as opposed to the spin-singlet intraorbital pairing prevalent in the bulk. The preferred spin-triplet pairing preserves time-reversal symmetry and is topological, as robust, topologically protected zero modes emerge at the boundary between regions with different pairing states. Moreover, the zero modes form Kramers doublets that are insensitive to the direction of the spin polarization or to the separation between impurities. We argue that our theoretical results are consistent with recent experimental measurements on FeSe1-z Tez.}, author = {Ghazaryan, Areg and Kirmani, Ammar and Fernandes, Rafael M. and Ghaemi, Pouyan}, issn = {2469-9969}, journal = {Physical Review B}, number = {20}, publisher = {American Physical Society}, title = {{Anomalous Shiba states in topological iron-based superconductors}}, doi = {10.1103/physrevb.106.l201107}, volume = {106}, year = {2022}, } @article{12150, abstract = {Methods inspired from machine learning have recently attracted great interest in the computational study of quantum many-particle systems. So far, however, it has proven challenging to deal with microscopic models in which the total number of particles is not conserved. To address this issue, we propose a variant of neural network states, which we term neural coherent states. Taking the Fröhlich impurity model as a case study, we show that neural coherent states can learn the ground state of nonadditive systems very well. In particular, we recover exact diagonalization in all regimes tested and observe substantial improvement over the standard coherent state estimates in the most challenging intermediate-coupling regime. Our approach is generic and does not assume specific details of the system, suggesting wide applications.}, author = {Rzadkowski, Wojciech and Lemeshko, Mikhail and Mentink, Johan H.}, issn = {2469-9969}, journal = {Physical Review B}, number = {15}, publisher = {American Physical Society}, title = {{Artificial neural network states for nonadditive systems}}, doi = {10.1103/physrevb.106.155127}, volume = {106}, year = {2022}, } @article{12269, abstract = {We study the thermalization of a small XX chain coupled to long, gapped XXZ leads at either side by observing the relaxation dynamics of the whole system. Using extensive tensor network simulations, we show that such systems, although not integrable, appear to show either extremely slow thermalization or even lack thereof since the two cannot be distinguished within the accuracy of our numerics. We show that the persistent oscillations observed in the spin current in the middle of the XX chain are related to eigenstates of the entire system located within the gap of the boundary chains. We find from exact diagonalization that some of these states remain strictly localized within the XX chain and do not hybridize with the rest of the system. The frequencies of the persistent oscillations determined by numerical simulations of dynamics match the energy differences between these states exactly. This has important implications for open systems, where the strongly interacting leads are often assumed to thermalize the central system. Our results suggest that, if we employ gapped systems for the leads, this assumption does not hold.}, author = {Ljubotina, Marko and Roy, Dibyendu and Prosen, Tomaž}, issn = {2469-9969}, journal = {Physical Review B}, number = {5}, publisher = {American Physical Society}, title = {{Absence of thermalization of free systems coupled to gapped interacting reservoirs}}, doi = {10.1103/physrevb.106.054314}, volume = {106}, year = {2022}, } @article{10067, abstract = {The search for novel entangled phases of matter has lead to the recent discovery of a new class of “entanglement transitions,” exemplified by random tensor networks and monitored quantum circuits. Most known examples can be understood as some classical ordering transitions in an underlying statistical mechanics model, where entanglement maps onto the free-energy cost of inserting a domain wall. In this paper we study the possibility of entanglement transitions driven by physics beyond such statistical mechanics mappings. Motivated by recent applications of neural-network-inspired variational Ansätze, we investigate under what conditions on the variational parameters these Ansätze can capture an entanglement transition. We study the entanglement scaling of short-range restricted Boltzmann machine (RBM) quantum states with random phases. For uncorrelated random phases, we analytically demonstrate the absence of an entanglement transition and reveal subtle finite-size effects in finite-size numerical simulations. Introducing phases with correlations decaying as 1/r^α in real space, we observe three regions with a different scaling of entanglement entropy depending on the exponent α. We study the nature of the transition between these regions, finding numerical evidence for critical behavior. Our work establishes the presence of long-range correlated phases in RBM-based wave functions as a required ingredient for entanglement transitions.}, author = {Medina Ramos, Raimel A and Vasseur, Romain and Serbyn, Maksym}, issn = {2469-9969}, journal = {Physical Review B}, number = {10}, publisher = {American Physical Society}, title = {{Entanglement transitions from restricted Boltzmann machines}}, doi = {10.1103/physrevb.104.104205}, volume = {104}, year = {2021}, } @article{10649, abstract = {Harnessing the properties of vortices in superconductors is crucial for fundamental science and technological applications; thus, it has been an ongoing goal to locally probe and control vortices. Here, we use a scanning probe technique that enables studies of vortex dynamics in superconducting systems by leveraging the resonant behavior of a raster-scanned, magnetic-tipped cantilever. This experimental setup allows us to image and control vortices, as well as extract key energy scales of the vortex interactions. Applying this technique to lattices of superconductor island arrays on a metal, we obtain a variety of striking spatial patterns that encode information about the energy landscape for vortices in the system. We interpret these patterns in terms of local vortex dynamics and extract the relative strengths of the characteristic energy scales in the system, such as the vortex-magnetic field and vortex-vortex interaction strengths, as well as the vortex chemical potential. We also demonstrate that the relative strengths of the interactions can be tuned and show how these interactions shift with an applied bias. The high degree of tunability and local nature of such vortex imaging and control not only enable new understanding of vortex interactions, but also have potential applications in more complex systems such as those relevant to quantum computing.}, author = {Naibert, Tyler R. and Polshyn, Hryhoriy and Garrido-Menacho, Rita and Durkin, Malcolm and Wolin, Brian and Chua, Victor and Mondragon-Shem, Ian and Hughes, Taylor and Mason, Nadya and Budakian, Raffi}, issn = {2469-9969}, journal = {Physical Review B}, number = {22}, publisher = {American Physical Society}, title = {{Imaging and controlling vortex dynamics in mesoscopic superconductor-normal-metal-superconductor arrays}}, doi = {10.1103/physrevb.103.224526}, volume = {103}, year = {2021}, } @article{8198, abstract = {We investigate how the critical driving amplitude at the Floquet many-body localized (MBL) to ergodic phase transition differs between smooth and nonsmooth drives. To this end, we numerically study a disordered spin-1/2 chain which is periodically driven by a sine or square-wave drive over a wide range of driving frequencies. In both cases the critical driving amplitude increases monotonically with the frequency, and at large frequencies it is identical for the two drives. However, at low and intermediate frequencies the critical amplitude of the square-wave drive depends strongly on the frequency, while that of the sinusoidal drive is almost constant over a wide frequency range. By analyzing the density of drive-induced resonances we conclude that this difference is due to resonances induced by the higher harmonics which are present (absent) in the Fourier spectrum of the square-wave (sine) drive. Furthermore, we suggest a numerically efficient method for estimating the frequency dependence of the critical driving amplitudes for different drives which is based on calculating the density of drive-induced resonances. We conclude that delocalization occurs once the density of drive-induced resonances reaches a critical value determined only by the static system.}, author = {Diringer, Asaf A. and Gulden, Tobias}, issn = {2469-9969}, journal = {Physical Review B}, number = {21}, publisher = {American Physical Society}, title = {{Impact of drive harmonics on the stability of Floquet many-body localization}}, doi = {10.1103/PhysRevB.103.214204}, volume = {103}, year = {2021}, } @article{9570, abstract = {We present conductance-matrix measurements in long, three-terminal hybrid superconductor-semiconductor nanowires, and compare with theoretical predictions of a magnetic-field-driven, topological quantum phase transition. By examining the nonlocal conductance, we identify the closure of the excitation gap in the bulk of the semiconductor before the emergence of zero-bias peaks, ruling out spurious gap-closure signatures from localized states. We observe that after the gap closes, nonlocal signals and zero-bias peaks fluctuate strongly at both ends, inconsistent with a simple picture of clean topological superconductivity.}, author = {Puglia, Denise and Martinez, E. A. and Ménard, G. C. and Pöschl, A. and Gronin, S. and Gardner, G. C. and Kallaher, R. and Manfra, M. J. and Marcus, C. M. and Higginbotham, Andrew P and Casparis, L.}, issn = {2469-9969}, journal = {Physical Review B}, number = {23}, publisher = {American Physical Society}, title = {{Closing of the induced gap in a hybrid superconductor-semiconductor nanowire}}, doi = {10.1103/PhysRevB.103.235201}, volume = {103}, year = {2021}, } @article{9770, abstract = {We study an effective one-dimensional quantum model that includes friction and spin-orbit coupling (SOC), and show that the model exhibits spin polarization when both terms are finite. Most important, strong spin polarization can be observed even for moderate SOC, provided that the friction is strong. Our findings might help to explain the pronounced effect of chirality on spin distribution and transport in chiral molecules. In particular, our model implies static magnetic properties of a chiral molecule, which lead to Shiba-like states when a molecule is placed on a superconductor, in accordance with recent experimental data.}, author = {Volosniev, Artem and Alpern, Hen and Paltiel, Yossi and Millo, Oded and Lemeshko, Mikhail and Ghazaryan, Areg}, issn = {2469-9969}, journal = {Physical Review B}, number = {2}, publisher = {American Physical Society}, title = {{Interplay between friction and spin-orbit coupling as a source of spin polarization}}, doi = {10.1103/physrevb.104.024430}, volume = {104}, year = {2021}, } @article{9961, abstract = {The notion of Thouless energy plays a central role in the theory of Anderson localization. We investigate and compare the scaling of Thouless energy across the many-body localization (MBL) transition in a Floquet model. We use a combination of methods that are reliable on the ergodic side of the transition (e.g., spectral form factor) and methods that work on the MBL side (e.g., typical matrix elements of local operators) to obtain a complete picture of the Thouless energy behavior across the transition. On the ergodic side, Thouless energy decreases slowly with the system size, while at the transition it becomes comparable to the level spacing. Different probes yield consistent estimates of Thouless energy in their overlapping regime of applicability, giving the location of the transition point nearly free of finite-size drift. This work establishes a connection between different definitions of Thouless energy in a many-body setting and yields insights into the MBL transition in Floquet systems.}, author = {Sonner, Michael and Serbyn, Maksym and Papić, Zlatko and Abanin, Dmitry A.}, issn = {2469-9969}, journal = {Physical Review B}, number = {8}, publisher = {American Physical Society}, title = {{Thouless energy across the many-body localization transition in Floquet systems}}, doi = {10.1103/PhysRevB.104.L081112}, volume = {104}, year = {2021}, } @article{18193, abstract = {Topological states of matter, such as fractional quantum Hall states, are an active field of research due to their exotic excitations. In particular, ultracold atoms in optical lattices provide a highly controllable and adaptable platform to study such new types of quantum matter. However, finding a clear route to realize non-Abelian quantum Hall states in these systems remains challenging. Here we use the density-matrix renormalization-group (DMRG) method to study the Hofstadter-Bose-Hubbard model at filling factor 𝜈=1 and find strong indications that at 𝛼=1/6 magnetic flux quanta per plaquette the ground state is a lattice analog of the continuum non-Abelian Pfaffian. We study the on-site correlations of the ground state, which indicate its paired nature at 𝜈=1, and find an incompressible state characterized by a charge gap in the bulk. We argue that the emergence of a charge density wave on thin cylinders and the behavior of the two- and three-particle correlation functions at short distances provide evidence for the state being closely related to the continuum Pfaffian. The signatures discussed in this letter are accessible in current cold atom experiments and we show that the Pfaffian-like state is readily realizable in few-body systems using adiabatic preparation schemes.}, author = {Palm, F. A. and Buser, M. and Leonard, Julian and Aidelsburger, M. and Schollwöck, U. and Grusdt, F.}, issn = {2469-9969}, journal = {Physical Review B}, number = {16}, publisher = {American Physical Society}, title = {{Bosonic Pfaffian state in the Hofstadter-Bose-Hubbard model}}, doi = {10.1103/physrevb.103.l161101}, volume = {103}, year = {2021}, }