arXiv subjects

Steven H. Simon

Publications and source records attributed to Steven H. Simon.

At least 19 recordsLinked to original sources

arXiv2026

Symmetry and Quantum Geometry in Bloch Bands

Quantum geometric quantities have featured heavily in the discussion of the properties of quantum systems in recent years. Among quantities most commonly discussed is the variance of Berry curvature and the integral of the trace of the quantum metric tensor. Despite their usefulness, it is known that they suffer from one significant complication: for a tight-binding model, the quantum geometric quantities depend not only on the parameters of the tight-binding model itself, but also the real space geometry of the tight-binding model, the so-called "orbital embedding". One explicitly geometry-independent quantity is therefore the minimal value of the quantum geometric quantity out of all possible real space geometries. In this work, we demonstrate that, if the tight-binding model is compatible with certain spatial symmetries, then the real space geometry that minimizes the variance of the Berry curvature or the integral of the trace of the quantum metric tensor must obey all those spatial symmetries. We further show that the statement is applicable to systems with magnetic translation symmetries and other composite symmetries, with implications for the quantum geometry of the Hofstadter model.

cond-mat.str-el↗

arXiv2026

Exactly solvable pair-density wave in topological flat bands from magnetic translation symmetries

Pair-density wave (PDW) superconductors are exotic phases in which Cooper pairs carry finite center-of-mass momentum. Despite a variety of theoretical and experimental reports on PDW states, exact PDW ground states in topological bands have remained elusive. Here we construct exactly solvable models with PDW ground states in topological flat bands using a generalized version of the recently proposed quantum geometric nesting (QGN) framework. Our construction broadly applies to systems with non-commuting magnetic translation symmetries (MTS) and time-reversal symmetry, exemplified by the time-reversal invariant version of the Kapit-Mueller model with two ideal flat Chern bands with opposite Chern number. Our construction thus provides a platform for further studies of band topology and quantum geometry in PDW superconductors.

cond-mat.supr-con↗

arXiv2026

Engineering electrically-switchable quantum anomalous Hall states by spin-orbit coupling

Nonvolatile gate-driven switching of quantum anomalous Hall (QAH) states in graphene moir\'e systems provides a promising route toward topological electronics based on chiral edge states. However, deliberate use of this switching mechanism requires control over both the magnetic properties and metastability of QAH states. While previous demonstrations mostly relied on the intrinsic magnetic energy landscape of moir\'e devices, here we show that this landscape can be engineered through proximity coupling to WSe2. We find that proximitizing twisted monolayer-bilayer graphene by WSe2 reshapes the magnetization reversals responsible for nonvolatile electrical switching of QAH states. We attribute this effect to the proximity-induced spin-orbit coupling (SOC), which can lock spin and valley and modify the magnetization of the competing states involved in switching compared with non-proximitized graphene systems. Our findings establish proximity-induced SOC as a new way to engineer magnetic properties and switchable magnetic states in graphene-based systems. We further demonstrate that strong magnetic metastability in tMBG allows the magnetic states to be gate-tuned between QAH and metallic regimes, and between QAH states with Chern numbers |C| = 2 and 1 without resetting the magnetic state. This functionality points toward new device architectures based on QAH chiral edge states.

cond-mat.mes-hall↗

arXiv2026

Does a Fractional Quantum Hall Edge Have a Protected Intrinsic Dipole Moment?

We investigate the claims by Park and Haldane [Phys. Rev. B 90, 045123 (2014)] of an intrinsic protected value of the electric dipole moment at the physical edge of fractional quantum Hall (FQH) systems. Contrary to prevailing expectations, we find that the edge dipole takes the expected intrinsic value only in certain very special cases. We identify key limitations in earlier numerical studies and employ density matrix renormalization group (DMRG) methods to accurately compute the ground-state dipole. We focus on three representative systems: the $\nu=1/3$-vacuum edge, the $\nu=2/3$-vacuum edge, and the interface between Pfaffian and anti-Pfaffian phases. We find that the expected intrinsic dipole value occurs only at $\nu=1/3$, whereas the other systems do not exhibit the claimed intrinsic value. We give arguments based on composite fermions as to why hierarchy states should generally not have protected intrinsic dipoles. These results have important implications for the energetics and edge structure of FQH states.

cond-mat.str-el↗

arXiv2026

Phases of itinerant anyons in Laughlin's quantum Hall states on a lattice

We study phases of itinerant anyons when hole-doping Laughlin-like states in fractional Chern insulators (FCIs). In light of the recent observation of time-reversal-broken superconductivity near FCIs in van der Waals materials, a theoretical understanding of doped fractional quantum Hall states on a lattice has been developed by Shi and Senthil [Phys. Rev. X 15, 031069], reviving old ideas about "anyon superconductivity". We test these ideas analytically within an effective parton mean-field theory and numerically with variational Monte Carlo, pointing out that the predicted state depends on whether the Laughlin order at $\nu=1/m$ is described by a U(1), or an SU(m) Chern-Simons field, the latter implying a symmetry between the m parton species. Our results demonstrate that the interplay between band Berry curvature and effective anyon dispersion has crucial implications for which anyonic phase is realized. In the experimentally relevant scenario of hole-doping the $\nu=1/3$ fermionic FCI, our results uncover a mechanism for the formation of an anyon superconducting state of half-integer central charge in the case when the energetically cheapest excitations are the fundamental 1/3 charge anyons, bypassing the need for these anyons to pair into charge-2/3 composites, which has generally been assumed in similar anyon superconductivity constructions.

cond-mat.str-el↗

arXiv2025

Mean-field Modelling of Moir\'e Materials: A User's Guide with Selected Applications to Twisted Bilayer Graphene

We review the theoretical modelling of moir\'e materials, focusing on various aspects of magic-angle twisted bilayer graphene (MA-TBG) viewed through the lens of Hartree-Fock mean-field theory. We first provide an elementary introduction to the continuum modelling of moir\'e bandstructures, and explain how interactions are incorporated to study correlated states. We then discuss how to implement mean-field simulations of ground state structure and collective excitations in this setting. With this background established, we rationalize the power of mean-field approximations in MA-TBG, by discussing the idealized "chiral-flat" strong-coupling limit, in which ground states at electron densities commensurate with the moir\'e superlattice are exactly captured by mean-field ans\"atze. We then illustrate the phenomenological shortcomings of this limit, leading us naturally into a discussion of the intermediate-coupling incommensurate Kekul\'e spiral (IKS) order and its origins in ever-present heterostrain. IKS and its placement within an expanded Hartree-Fock manifold form our first "case study". Our second case study involves time-dependence, and focuses on the collective modes of various broken-symmetry insulators in MA-TBG. As a third and final case study, we return to the strong-coupling picture, which can be stabilized by aligning MA-TBG to an hBN substrate. In this limit, we show how mean field theory can be adapted to the translationally non-invariant setting in order to quantitatively study the energetics of domain walls in orbital Chern insulating states. We close with a discussion of extensions and further applications. Used either as a standalone reference or alongside the accompanying open-source code, this review should enable readers with a basic knowledge of band theory and many-body physics to systematically build and analyze detailed models of generic moir\'e systems.

cond-mat.str-el↗

arXiv2025

Monte Carlo Sampling for Wave Functions Requiring (Anti)Symmetrization

Many strongly correlated states, such as those arising in the fractional quantum Hall effect and spin liquids, are described by wave functions obtained by dividing particles into multiple clusters, constructing a readily evaluable wave function in each cluster, and (anti)symmetrizing across these clusters. We introduce a method to compute quantities such as energies and correlators, using Monte Carlo simulations for these states. Our framework overcomes the factorial scaling of explicit (anti)symmetrization, allowing for studies of systems beyond the reach of exact diagonalization.

cond-mat.str-el↗

arXiv2025

Putting a new spin on the incommensurate Kekul\'e spiral: from spin-valley locking and collective modes to fermiology and implications for superconductivity

We revisit the global phase diagram of magic-angle twisted bilayer and [symmetric] trilayer graphene (MA-TBG/TSTG) in light of recent scanning tunneling microscopy (STM) measurements on these materials. These experiments both confirmed the importance of strain in stabilizing the predicted incommensurate Kekul\'{e} spiral (IKS) order near filling $|\nu|=2$ of the weakly dispersive central bands in both systems, and suggested a key role for electron-phonon couplings and short-range Coulomb interactions in selecting between various competing orders at low strain in MA-TBG. Here, we show that such interactions $\textit{also}$ play a crucial role in selecting the spin structure of the strain-stabilized IKS state. This in turn influences the visibility of the IKS order in STM in a manner that allows us to infer their relative importance. We use this insight in conjunction with various other pieces of experimental data to build a more complete picture of the phase diagram, focusing on the spectrum of low-lying collective modes and the nature of the doped Fermi surfaces. We explore the broad phenomenological implications of these results for superconductivity.

cond-mat.str-el↗

arXiv2025

Partition function of the Kitaev quantum double model

We compute the degeneracy of energy levels in the Kitaev quantum double model for any discrete group $G$ on any planar graph forming the skeleton of a closed orientable surface of arbitrary genus. The derivation is based on the fusion rules of the properly identified vertex and plaquette excitations, which are selected among the anyons, i.e., the simple objects of the Drinfeld center $\mathcal{Z}(\mathrm{Vec}_G)$. These degeneracies are given in terms of the corresponding $S$-matrix elements and allow one to obtain the exact finite-temperature partition function of the model, valid for any finite-size system.

cond-mat.str-el↗

arXiv2025

Quantum Hall Antidot as a Fractional Coulombmeter

The detection of fractionally charged quasiparticles, which arise in the fractional quantum Hall regime, is of fundamental importance for probing their exotic quantum properties. While electronic interferometers have been central to probe their statistical properties, their interpretation is often complicated by bulk-edge interactions. Antidots, potential hills in the quantum Hall regime, are particularly valuable in this context, as they overcome the geometric limitations of conventional designs and act as controlled impurities within a quantum point contact. Furthermore, antidots allow for quasiparticle charge detection through straightforward conductance measurements, replacing the need for more demanding techniques. In this work, we employ a gate-defined bilayer graphene antidot operating in the Coulomb-dominated regime to study quasiparticle tunneling in both integer and fractional quantum Hall states. We show that the gate-voltage period and the oscillation slope directly reveal the charge of the tunneling quasiparticles, providing a practical method to measure fractional charge in graphene. We report direct measurements of fractional charge, finding $q = e/3$ at $\nu = 4/3$, 5/3 and 7/3, $q = 2e/3$ at $\nu = 2/3$ and $q = 3e/5$ at $\nu = 3/5$, while at $\nu = 8/3$ we observe signatures of both $e/3$ and $2e/3$ tunneling charge. The simplicity and tunability of this design open a pathway to extend antidot-based charge measurements to other van der Waals materials, establishing antidots as a powerful and broadly applicable platform to study the quantum Hall effect.

cond-mat.mes-hall↗

arXiv2025

Majorana edge reconstruction and the $\nu=5/2$ non-Abelian thermal Hall puzzle

Pioneering thermal transport measurements on two-dimensional electron gases in high magnetic fields have demonstrated that the quantized Hall state at filling factor $\nu=5/2$ has a thermal Hall conductance $\kappa$ quantized in half-integer multiples of $\kappa_0 = {\pi^2 k_B^2 T}/{3h}$. Half-integer $\kappa/\kappa_0$ is a signature of neutral Majorana edge modes, in turn linked to the presence of non-Abelian anyon excitations in the bulk. However, the experimentally observed value of $\kappa$ corresponds to the 'PH-Pfaffian' state, in tension with numerical studies which instead favor either the Pfaffian or the AntiPfaffian. A variety of mechanisms have been invoked to explain this discrepancy, but have been either ruled out by further experiments or else involve fine-tuning. Building on density-matrix-renormalization group studies of physically realistic edges and analytic calculations of edge structure, we propose an alternative resolution of this puzzle involving an 'edge reconstruction' solely involving the neutral Majorana sector of the theory. Such a Majorana edge reconstruction can "screen'' a Pfaffian or AntiPfaffian bulk, so that transport signatures become indistinguishable from those of the PH-Pfaffian. We argue that this physically natural scenario is consistent with experiment.

cond-mat.mes-hall↗

arXiv2025

Paired Parton Trial States for the Superfluid-Fractional Chern Insulator Transition

We consider a model of hard-core bosons on a lattice, half-filling a Chern band such that the system has a continuous transition between a fractional Chern insulator (FCI) and a superfluid state (SF) depending on the bandwidth to bandspacing ratio. We construct a parton-inspired trial wavefunction ansatz for the ground states that has remarkably high overlap with exact diagonalization in both phases and throughout the phase transition. Our ansatz is stable to adding some bosonic interactions beyond the on-site hard core constraint. We confirm that the transition is well described by a projective translation symmetry-protected multiple parton band gap closure, as has been previously predicted. However, unlike prior work, we find that our wavefunctions require anomalous (BCS-like) parton correlations to describe the phase transition and SF phase accurately.

cond-mat.str-el↗

arXiv2024

Phase Separation in the Putative Fractional Quantum Hall A phases

We use several techniques to probe the wave functions proposed to describe the ${\cal A}$ phases by Das, Das, and Mandal [Phys. Rev. Lett. 131, 056202 (2023); Phys. Rev. Lett. 132, 106501 (2024); Phys. Rev. B 110, L121303 (2024).]. As opposed to representing fractional quantum Hall liquids, we find these wave functions to describe states that clearly display strong phase separation. In the process of exploring these wave functions, we have also constructed several new methods for diagnosing phase separation and generating such wave functions numerically. Finally, we uncover a new property of entanglement spectra that can be used as a check for the accuracy of numerics.

cond-mat.str-el↗

arXiv2024

A Closed Band-Projected Density Algebra Must be Girvin-MacDonald-Platzman

The band-projected density operators in a Landau level obey the Girvin-MacDonald-Platzman (GMP) algebra, and a large amount of effort in the study of fractional Chern insulators has been directed towards approximating this algebra in a Chern band. In this paper, we prove that the GMP algebra, up to form factors, is the $\textit{only}$ closed algebra that projected density operators can satisfy in two and three dimensions, highlighting the central place it occupies in the study of Chern bands in general. A number of interesting corollaries follow.

cond-mat.str-el↗

arXiv2024

Minimal Quantum Circuits for Simulating Fibonacci Anyons

The Fibonacci topological order is the prime candidate for the realization of universal topological quantum computation. We devise minimal quantum circuits to demonstrate the non-Abelian nature of the doubled Fibonacci topological order, as realized in the Levin-Wen string net model. Our circuits effectively initialize the ground state, create excitations, twist and braid them, all in the smallest lattices possible. We further design methods to determine the fusion amplitudes and braiding phases of multiple excitations by carrying out a single qubit measurement. We show that the fusion channels of the doubled Fibonacci model can be detected using only three qubits, twisting phases can be measured using five, and braiding can be demonstrated using nine qubits. These designs provide the simplest possible settings for demonstrating the properties of Fibonacci anyons and can be used as realistic blueprints for implementation on many modern quantum architectures.

quant-ph↗

arXiv2024

Finite-temperature properties of string-net models

We consider a refined version of the string-net model which assigns a different energy cost to each plaquette excitation. Using recent exact calculations of the energy-level degeneracies we compute the partition function of this model and investigate several thermodynamical quantities. In the thermodynamic limit, we show that the partition function is dominated by the contribution of special particles, dubbed pure fluxons, which trivially braid with all other (product of) fluxons. We also analyze the behavior of Wegner-Wilson loops associated to excitations and show that they obey an area law, indicating confinement, for any finite temperature except for pure fluxons that always remain deconfined. Finally, using a recently proposed conjecture, we compute the topological mutual information at finite temperature, which features a nontrivial scaling between system size and temperature, similar to the one-dimensional classical Ising model.

cond-mat.other↗

arXiv2024

Textured Exciton Insulators

We introduce and study new interacting topological states that arise in time-reversal symmetric bands with an underlying obstruction to forming localized states. If the $U(1)$ valley symmetry linked to independent charge conservation in each time-reversal sector is spontaneously broken, the corresponding `excitonic' order parameter is forced to form a topologically non-trivial texture across the Brillouin zone. We show that the resulting phase, which we dub a textured exciton insulator, cannot be given a local-moment description due to a form of delicate topology. Using toy models of bands with Chern or Euler obstructions to localization we construct explicit examples of the Chern or Euler texture insulators (CTIs or ETIs) they support, and demonstrate that these are generically competitive ground states at intermediate coupling. We construct field theories that capture the response properties of these new states. Finally, we identify the incommensurate Kekul\'e spiral phase observed in magic-angle bi- and trilayer graphene as a concrete realization of an ETI.

cond-mat.str-el↗

arXiv2024

Chern-Textured Exciton Insulators with Valley Spiral Order in Moir\'e Materials

We explore the phase diagrams of moir\'e materials in search of a new class of intervalley-coherent correlated insulating state: the Chern texture insulator (CTI). This phase of matter, proposed in a companion paper, breaks valley $U(1)$ symmetry in a nontrivial fashion wherein the valley order parameter is forced to texture in momentum space as a consequence of band topology. Using detailed Hartree-Fock studies, we establish that the CTI emerges as an energetically competitive intermediate-coupling ground state in several moir\'e systems which lack a twofold rotation symmetry that forbids the single-particle topology essential to the formation of the CTI valley texture.

cond-mat.str-el↗