arXiv subjects

Michael G. Scheer

Publications and source records attributed to Michael G. Scheer.

11 recordsLinked to original sources

arXiv2026

Bootstrap bounds for Quantum Spin Systems using String Operators

Bootstrap is a numerical many-body method that provides rigorous bounds on ground-state observables by imposing a set of necessary constraints on the expectation values of operators. The quality of the resulting bounds is sensitive to the choice of operators entering the constraints. In particular, bounds on ground-state correlations are often loose in spontaneous symmetry-breaking (SSB) phases, since local operator sets cannot exclude domain-wall excitations. In this work, we introduce non-local, string-like operators into the bootstrap and show that the program can be formulated directly in thermodynamic limit. We then apply our construction to several 1D spin models. First, we obtain a significant tightening of the bounds in the SSB phase of the 1D transverse-field Ising model. Using the 1D axial next-nearest-neighbor Ising model, we further show that this tightening allows for a quantitative estimate of the locations of phase boundaries. Finally, we generalize the string operators to the 1D $\mathbb{Z}_3$ chiral clock model and track the behavior of the bounds across the phase diagram. Our results broaden the class of constraints available to the bootstrap and open a route toward bootstrapping more general symmetry-broken and topological phases, where the relevant constraints may involve non-local or extended operators.

cond-mat.str-el↗

arXiv2025

Defect Bootstrap: Tight Ground State Bounds in Spontaneous Symmetry Breaking Phases

The recent development of bootstrap methods based on semidefinite relaxations of positivity constraints has enabled rigorous two-sided bounds on local observables directly in the thermodynamic limit. However, these bounds inevitably become loose in symmetry broken phases, where local constraints are insufficient to capture long-range order. In this work, we identify the origin of this looseness as order parameter defects which are difficult to remove using local operators. We introduce a $\textit{defect bootstrap}$ framework that resolves this limitation by embedding the system into an auxiliary $\textit{defect model}$ equipped with ancilla degrees of freedom. This construction effectively enables local operators to remove order parameter defects, yielding tighter bounds in phases with spontaneous symmetry breaking. This approach can be applied broadly to pairwise-interacting local lattice models with discrete or continuous internal symmetries that satisfy a property we call $\textit{defect diamagnetism}$, which requires that the ground state energy does not decrease upon adding any finite number of symmetry defects. Applying the method to the transverse field Ising models in 1D and 2D, we obtain significantly improved bounds on energy densities and spin correlation functions throughout the symmetry broken phase in 1D and deep within the phase in 2D. Our results demonstrate that physically motivated constraint sets can dramatically enhance the power of bootstrap methods for quantum many-body systems.

cond-mat.str-el↗

arXiv2025

Intervalley-Coupled Twisted Bilayer Graphene from Substrate Commensuration

We show that intervalley coupling can be induced in twisted bilayer graphene (TBG) by aligning the bottom graphene layer with either of two types of commensurate insulating triangular Bravais lattice substrate. The intervalley coupling folds the $\pm K$ valleys of TBG to the $\Gamma$-point and hybridizes the original TBG flat bands into a four-band model equivalent to the $p_x$-$p_y$ orbital honeycomb lattice model, in which the second conduction and valence bands have quadratic band touchings and can become flat due to geometric frustration. The spin-orbit coupling from the substrate opens gaps between the bands, yielding topological bands with spin Chern numbers $\mathcal{C}$ up to $\pm 4$. For realistic substrate potential strengths, the minimal bandwidths of the hybridized flat bands are still achieved around the TBG magic angle $\theta_M=1.05^\circ$, and their quantum metrics are nearly ideal. We identify two candidate substrate materials Sb$_2$Te$_3$ and GeSb$_2$Te$_4$, which nearly perfectly realize the commensurate lattice constant ratio of $\sqrt{3}$ with graphene. These systems provide a promising platform for exploring strongly correlated topological states driven by geometric frustration.

cond-mat.mes-hall↗

arXiv2025

Spectroscopy of the Fractal Hofstadter Energy Spectrum

Hofstadter's butterfly, the predicted energy spectrum for non-interacting electrons confined to a two-dimensional lattice in a magnetic field, is one of the most remarkable fractal structures in nature. At rational ratios of magnetic flux quanta per lattice unit cell, this spectrum shows self-similar distributions of energy levels that reflect its recursive construction. For most materials, Hofstadter's butterfly is predicted under experimental conditions that are unachievable using laboratory-scale magnetic fields. More recently, electrical transport studies have provided evidence for Hofstadter's butterfly in materials engineered to have artificially large lattice constants, such as those with moir\'e superlattices. Yet to-date, direct spectroscopy of the fractal energy spectrum predicted by Hofstadter nearly 50 years ago has remained out of reach. Here we use high-resolution scanning tunneling microscopy / spectroscopy (STM / STS) to probe the flat electronic bands in twisted bilayer graphene near the predicted second magic angle, an ideal setting for spectroscopic studies of Hofstadter's spectrum. Our study shows the fractionalization of flat moir\'e bands into discrete Hofstadter subbands and discerns experimental signatures of self-similarity of this spectrum. Moreover, our measurements uncover a spectrum that evolves dynamically with electron density, displaying phenomena beyond that of Hofstadter's original model due to the combined effects of strong correlations, Coulomb interactions, and the quantum degeneracy of electrons in twisted bilayer graphene.

cond-mat.mes-hall↗

arXiv2024

Correlated topological flat bands in rhombohedral graphite

Flat bands and nontrivial topological physics are two important topics of condensed matter physics. With a unique stacking configuration analogous to the Su-Schrieffer-Heeger (SSH) model, rhombohedral graphite (RG) is a potential candidate for realizing both flat bands and nontrivial topological physics. Here we report experimental evidence of topological flat bands (TFBs) on the surface of bulk RG, which are topologically protected by bulk helical Dirac nodal lines via the bulk-boundary correspondence. Moreover, upon {\it in situ} electron doping, the surface TFBs show a splitting with exotic doping evolution, with an order-of-magnitude increase in the bandwidth of the lower split band, and pinning of the upper band near the Fermi level. These experimental observations together with Hartree-Fock calculations suggest that correlation effects are important in this system. Our results demonstrate RG as a new platform for investigating the rich interplay between nontrivial band topology, correlation effects, and interaction-driven symmetry-broken states.

cond-mat.str-el↗

arXiv2024

Bootstrapping Quantum Hamiltonians with Symmetry

We describe a semidefinite relaxation method which finds lower bounds to the ground state energy of a quantum Hamiltonian subject to Hermitian linear constraints along with approximations of ground state expectation values. We show that symmetry can be used to significantly reduce the computational requirements, and we include unitary, antiunitary, discrete, and continuous symmetries in our analysis. We demonstrate our method using the 1D Hubbard model and find quantitative agreement with both exact diagonalization and the Bethe ansatz.

cond-mat.str-el↗

arXiv2024

Twistronics of Kekulé Graphene: Honeycomb and Kagome Flat Bands

Kekulé-O order in graphene, which has recently been realized experimentally, induces Dirac electron masses on the order of $m \sim 100 \text{meV}$. We show that twisted bilayer graphene in which one or both layers have Kekulé-O order exhibits nontrivial flat electronic bands on honeycomb and kagome lattices. When only one layer has Kekulé-O order, there is a parameter regime for which the lowest four bands at charge neutrality form an isolated two-orbital honeycomb lattice model with two flat bands. The bandwidths are minimal at a magic twist angle $θ\approx 0.7^\circ$ and Dirac mass $m \approx 100 \text{meV}$. When both layers have Kekulé-O order, there is a large parameter regime around $θ\approx 1^\circ$ and $m\gtrsim 100 \text{meV}$ in which the lowest three valence and conduction bands at charge neutrality each realize isolated kagome lattice models with one flat band, while the next three valence and conduction bands are flat bands on triangular lattices. These flat band systems may provide a new platform for strongly correlated phases of matter.

cond-mat.mes-hall↗

arXiv2023

Kagome and honeycomb flat bands in moiré graphene

We propose a class of graphene-based moiré systems hosting flat bands on kagome and honeycomb moiré superlattices. These systems are formed by stacking a graphene layer on a 2D substrate with lattice constant approximately $\sqrt{3}$ times that of graphene. When the moiré potentials are induced by a 2D irreducible corepresentation in the substrate, the model shows a rich phase diagram of low energy bands including eigenvalue fragile phases as well as kagome and honeycomb flat bands. Spin-orbit coupling in the substrate can lift symmetry protected degeneracies and create spin Chern bands, and we observe spin Chern numbers up to three. We additionally propose a moiré system formed by stacking two graphene-like layers with similar lattice constants and Fermi energies but with Dirac Fermi velocities of opposite sign. This system exhibits multiple kagome and honeycomb flat bands simultaneously. Both models we propose resemble the hypermagic model of [Scheer $\textit{et al.}$, Phys. Rev. B $\textbf{106}$, 115418 (2022)] and may provide ideal platforms for the realization of strongly correlated topological phases.

cond-mat.mes-hall↗

arXiv2023

DEC-QED: A flux-based 3D electrodynamic modeling approach to superconducting circuits and materials

Modeling the behavior of superconducting electronic circuits containing Josephson junctions is crucial for the design of superconducting information processors and devices. In this paper, we introduce DEC-QED, a computational approach for modeling the electrodynamics of superconducting electronic circuits containing Josephson junctions in arbitrary three-dimensional electromagnetic environments. DEC-QED captures the non-linear response and induced currents in BCS superconductors and accurately captures phenomena such as the Meissner effect, flux quantization and Josephson effects. Using a spatial coarse-graining formulation based on Discrete Exterior Calculus (DEC), DEC-QED can accurately simulate transient and long-time dynamics in superconductors. The expression of the entire electrodynamic problem in terms of the gauge-invariant flux field and charges makes the resulting classical field theory suitable for second quantization.

quant-ph↗

arXiv2022

Magic angles in twisted bilayer graphene near commensuration: Towards a hypermagic regime

The Bistritzer-MacDonald continuum model (BM model) describes the low-energy moiré bands for twisted bilayer graphene (TBG) at small twist angles. We derive a generalized continuum model for TBG near any commensurate twist angle, which is characterized by complex interlayer hoppings at commensurate $AA$ stackings (rather than the real hoppings in the BM model), a real interlayer hopping at commensurate $AB/BA$ stackings, and a global energy shift. The complex phases of the $AA$ stacking hoppings and the twist angle together define a single angle parameter $ϕ_0$. We compute the model parameters for the first six distinct commensurate TBG configurations, among which the $38.2^\circ$ configuration may be within experimentally observable energy scales. We identify the first magic angle for any $ϕ_0$ at a condition similar to that of the BM model. At this angle, the lowest two moiré bands at charge neutrality become flat except near the $\boldsymbolΓ_M$ point and retain fragile topology but lose particle-hole symmetry. We further identify a hypermagic parameter regime centered at $ϕ_0 = \pmπ/2$ where many moiré bands around charge neutrality (often $8$ or more) become flat simultaneously. Many of these flat bands resemble those in the kagome lattice and $p_x$, $p_y$ 2-orbital honeycomb lattice tight-binding models.

cond-mat.mes-hall↗

arXiv2019

Computational modeling of decay and hybridization in superconducting circuits

We present a framework for modeling superconducting circuits that integrates classical microwave analysis with circuit quantization. Our framework enables the calculation of the lossy eigenmodes of superconducting circuits, and we demonstrate the method by analyzing several circuits relevant to multiplexed, Purcell filtered transmon readout architectures. We show that the transmon relaxation times obtained by our method agree with the established approximation $T_1 \approx C/\text{Re}[Y(iω_q)]$ away from environmental resonances and do not vanish on resonance. We also show that the hybridization of the modes in the readout circuit is highly sensitive to the bandwidth of the Purcell filter.

quant-ph↗