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Emil J. Bergholtz

Publications and source records attributed to Emil J. Bergholtz.

At least 19 recordsLinked to original sources
arXiv2026

Spontaneous Chern-Euler Duality Transitions

Topological phase transitions are typically characterized by abrupt changes in a quantized invariant. Here we report a contrasting paradigm in spontaneous parity-time symmetry-breaking transitions induced by non-Hermiticity. The topological invariant remains conserved, but its nature transitions between the Chern number, characteristic of chiral transport in complex bands, and the Euler number, which characterizes the number of nodal points in pairs of real bands. This conserved morphing of topological properties applies to all pairs of bands whose spectral gaps to other bands remain open during the transition. It features qualitative changes in the non-Abelian geometric phases, which quantize in different forms across the transition. Our findings establish a generic topological duality principle governing transitions across symmetry classes and reveal unique connections among topology, symmetry, and non-Abelian gauge structure in non-unitary processes.

cond-mat.mes-hall↗
arXiv2026

Read-Rezayi fractional Chern insulators in modulated Bernal graphene

Fibonacci anyons provide a universal platform for topological quantum computation, and emerge as low-energy excitations in the $\mathbb{Z}_3$ Read-Rezayi phase in the fractional quantum Hall effect. However, realistic microscopic realizations of this phase in the absence of a magnetic field have remained elusive. We study a model of periodically modulated Bernal bilayer graphene with gate-screened Coulomb interactions. Using the recently developed target-phase optimization method in conjunction with band-projected exact diagonalization, we identify at filling $ν=3/5$ a region of parameter space whose ground state is consistent with a Read-Rezayi fractional Chern insulator. The partially filled band from which it arises is a part of a two-band complex which mimics geometric aspects of the lowest and first Landau levels, with the ground state at $ν=1/2$ consistent with the Moore-Read state. Our results suggest that modulated Bernal graphene can realize delicate non-Abelian fractional quantum Hall states at zero magnetic field, while demonstrating target-phase optimization as a practical route to discovering such phases in realistic, high-dimensional microscopic models.

cond-mat.str-el↗
arXiv2026

Interferometric Readout of Momentum-Space Topology in a Programmable Dissipative Photonic Circuit

Topology under non-Hermitian dynamics is encoded in the phase of the bulk evolution, yet strong dissipation suppresses the amplitudes carrying it. We resolve this using a programmable photonic integrated circuit that implements such dynamics in synthetic momentum space through unitary dilation, with the phase recovered by phase-shifted interferometry. For the non-Hermitian Su-Schrieffer-Heeger model, the method distinguishes trivial and non-trivial Zak phases and yields a coherence winding $q=\pm 1$ induced by an exceptional point. Extending to a synthetic torus via a Rice-Mele pump gives the first Chern number $\mathrm{Ch}_1=0,1$ for trivial and non-trivial cycles, showing a programmable route to momentum-space topology under strongly dissipative non-Hermitian dynamics.

quant-ph↗
arXiv2026

Topological Order Without Band Topology in Moiré Graphene

The discovery of zero-field fractional Chern insulators (FCIs) in moiré materials has attracted intense interest in the interplay between topology and correlations. Here, we demonstrate that fractionalized topological order can emerge under realistic conditions even within a topologically trivial moiré band. By projecting long-range Coulomb interactions into a trivial band of twisted multilayer graphene, we identify a set of incompressible FCI ground states exhibiting fractional quantized Hall conductance. Their Laughlin-like behavior is further confirmed through the particle-cut entanglement spectrum. We trace the origin of this phase to the strongly inhomogeneous distribution of quantum geometry within the moiré Brillouin zone, which reshapes interaction effects independently of the band topology. Extending this heuristic quantum geometric mechanism, we demonstrate that similarly unexpected Laughlin-like FCIs can also be stabilized in higher-Chern-number moiré bands under experimentally accessible conditions. Our results establish realistic scenarios under which many-body topological order can emerge independently of single-particle band topology.

cond-mat.mes-hall↗
arXiv2026

Quantum spin Hall crystals at fractional filling of twisted MoTe$_2$

We predict and classify interaction-driven quantum spin Hall crystals (QSHCs), a class of states emerging at fractional filling through an interplay of topology and spontaneous translation-symmetry breaking. QSHCs form nearly degenerate manifolds whose members can realize distinct topological phases protected by time-reversal or valley $U(1)_v$ symmetry, with time-reversal acting nontrivially within the manifold. As a representative of this broad class of states we provide evidence for 9-fold quasi-degenerate $\sqrt{3}\times\sqrt{3}$ charge ordered QSHCs at $ν= -8/3$ of twisted bilayer MoTe$_2$ near a $5^\circ$ twist. Here a $\mathbb{Z}_3$ index organizes states related by lattice translation into three time-reversal invariant states with nontrivial $\mathbb{Z}_2$ topology and three time-reversal related doublets whose individual members spontaneously break time-reversal and carry a $U(1)_v$ protected spin-Chern number. Finally, we determine the conditions that favor QSHCs over closely competing intervalley-coherent crystals.

cond-mat.str-el↗
arXiv2026

Universal aspects of bulk density of states in non-Hermitian lattices

Non-Hermitian lattice Hamiltonians generally exhibit strong boundary sensitivity, with periodic and open boundary conditions producing distinct density of states (DOS) in the complex-energy plane. This has led to the view that extended non-Hermitian systems lack a unique bulk DOS, with different prescriptions representing inequivalent bulk physics. Here, we show that this apparent ambiguity is largely illusory. For any finite-range tight-binding Hamiltonian, we establish a universal bulk structure: all DOS definitions arising as thermodynamic limits of finite systems share identical multipole moments and generate identical bulk dynamics at finite times and for observables measured far from boundaries. This universality is intimately tied to the thermodynamic Green's functions, which we show to be independent of the boundary condition for large enough complex frequencies. Among all equivalent descriptions, we identify the Brown measure - obtained via Hermitization and resolvent analysis - as a canonical and convenient representative of the bulk DOS, defined directly from the infinite-volume Hamiltonian. We further show that point-gap topology imposes additional universal constraints: boundary-dependent Green's functions are forced to coincide throughout topologically trivial point gaps. This, in particular, provides a systematic criterion, valid in arbitrary dimension, for determining where and how eigenvalues of different boundary truncations can accumulate in the complex plane, and precisely delineates the regime in which the DOS ambiguity retains physical significance.

cond-mat.mes-hall↗
arXiv2026

Topological fine structure of an energy band

A band with a nonzero Chern number cannot be fully localized by weak disorder. There must remain at least one extended state, which ``carries the Chern number.'' Here we show that a trivial band can behave in a similar way. Instead of fully localizing, arbitrarily weak disorder leads to the emergence of two sets of extended states, positioned at two different energy intervals, which carry opposite Chern numbers. Thus, a single trivial band can show the same behavior as two separate Chern bands. We show that this property is predicted by a topological invariant called a ``localizer index.'' Even though the band as a whole is trivial as far as the Chern number is concerned, the localizer index allows access to a topological fine structure. This index changes as a function of energy within the bandwidth of the trivial band, causing nontrivial extended states to appear as soon as disorder is introduced. Our work points to a previously overlooked manifestation of topology, which impacts the response of systems to impurities beyond the information included in conventional topological invariants.

cond-mat.mes-hall↗
arXiv2026

Quantum dynamical signatures of non-Hermitian boundary modes

The non-Hermitian bulk-boundary correspondence features an interplay between the non-Hermitian skin effect and anomalous boundary-mode behavior. Whereas the skin effect is known to manifest itself in quantum dynamics in the form of chiral damping, it has remained less clear what impact the boundary modes may have. Here we derive experimentally accessible signatures of the boundary modes. We also establish clear criteria, based on the generalized Brillouin zone, that determine when bulk and boundary effects can be dynamically discerned using the Liouvillian separation gap. This leads to telltale signatures in both stable regimes -- where particle number remains finite -- and in the unstable regimes -- where a macroscopic boundary mode population occurs.

cond-mat.mes-hall↗
arXiv2026

Topological Order and Non-Hermitian Skin Effect in Generalized Ideal Chern Bands

Fractionalization in ideal Chern bands and non-Hermitian topological physics are two active but so far separate research directions. Merging these, we generalize the notion of ideal Chern bands to the non-Hermitian realm and uncover several striking consequences both on the level of band theory and in the strongly interacting regime. Specifically, we show that the lowest band of a Kapit--Mueller lattice model with an imaginary gauge potential satisfies a generalized ideal condition with complex Berry curvature in sync with a complex quantum metric. The ideal band remains purely real and exactly flat on both the torus and cylinder: eigenstates are extended on the torus, while on the cylinder all right and left eigenstates localize at the boundaries, yielding a non-Hermitian skin effect without spectral winding. In the interacting regime, we find that the generalized ideal condition stabilizes an incompressible liquid at fractional fillings, retaining intrinsic non-Hermitian features on both cylinder and torus, while strikingly distinct on different manifolds. On the cylinder, the ground states are always skin-Laughlin states. In contrast, on the torus, we instead observe an unconventional competition between topologically ordered Laughlin-like states and negative collective modes, arising purely from non-Hermiticity.

cond-mat.mes-hall↗
arXiv2026

Nonreciprocal conductance in uniformly dissipative devices

When studying non-Hermitian electronic systems, an obvious question is how various non-Hermitian effects affect measurable quantities like the conductance. Here, we show that uniformly dissipative circuits can exhibit nonreciprocal conductance, meaning that the two nonlocal conductances are different. We describe how this happens through a difference in transmission times between left-moving and right-moving electrons. We consider a specific case of a dissipative Rashba nanowire with a skewed magnetic field, and show how this difference in transmission times comes about through interference inside the circuit, and how this is modified as the dissipation strength changes.

cond-mat.mes-hall↗
arXiv2026

Filling-Sensitive Spectral Complexity from Hilbert-Space Holonomy in Fragmented Non-Hermitian Systems

We show that Hilbert-space holonomy provides a geometric organizing principle for spectral reality in fragmented non-Hermitian many-body systems, complementary to conventional symmetry protection. In two minimal fragmented models, complex spectra can arise only within the most symmetric sectors: half filling in the fermion model and zero magnetization in the spin chain. Adding or removing a single particle, or flipping a single spin, renders the spectra entirely real despite unchanged periodic boundary conditions, reminiscent of boundary-condition sensitivity in systems with a non-Hermitian skin effect. We explain this by viewing nonreciprocal hopping amplitudes as a discrete gauge field on the Krylov graph: trivial holonomy permits a diagonal similarity transformation to the Hermitian limit, whereas nontrivial holonomy obstructs it and allows complex spectra. In certain regimes, trivial holonomy admits an emergent-boundary interpretation, and longer-range models exhibit finite real and complex regions governed by the same criterion.

cond-mat.str-el↗
arXiv2026

Anti-topological crystal and non-Abelian liquid in twisted semiconductor bilayers

We show that electron crystals compete closely with non-Abelian fractional Chern insulators in the half-filled second moiré band of twisted bilayer MoTe$_2$. Depending on the twist angle and microscopic model, these crystals can have non-zero or zero Chern numbers $C$. The $C=0$ crystal occurs because contributions to the total Chern number from the full first band (+1) and half-full second band (-1) cancel. This is counterintuitive because the first two non-interacting bands in a given valley have the same Chern number $+1$. For these two reasons, we call this crystal an anti-topological crystal. The anti-topological crystal is a novel type of electron crystal that may occur in systems with multiple Chern bands at filling factors $n>1$.

cond-mat.mes-hall↗
arXiv2026

Symmetry-Fractionalized Skin Effects in Non-Hermitian Luttinger Liquids

In one dimension, strongly correlated gapless systems are highly constrained due to conformal invariance, leading to the decoupling of low energy degrees of freedom corresponding to different symmetry sectors. The most familiar example of this is spin-charge separation. Here, we extend this mechanism to the non-Hermitian realm by demonstrating that skin effects corresponding to different symmetry sectors exhibit an emergent decoupling. We establish this for $N$ flavor fermions and demonstrate it numerically for the special case of the Hubbard model, in which spin and charge skin effects separate at low energies. Finally, we construct an interaction-enabled $E_8$ skin effect with no free fermion counterpart.

cond-mat.str-el↗
arXiv2026

Exceptional topology on nonorientable manifolds

We classify gapped phases and characteristic nodal points of non-Hermitian band structures on two-dimensional nonorientable parameter spaces. Such spaces arise in a wide range of physical systems in the presence of nonsymmorphic parameter space symmetries. For gapped phases, we find that nonorientable spaces provide a natural setting for exploring fundamental structural problems in braid group theory, such as torsion and conjugacy. Gapless systems, which host exceptional points (EPs), explicitly violate fermion doubling, even in two-band models. We demonstrate that EPs traversing the nonorientable parameter space exhibit non-Abelian charge inversion. These braided phases and their transitions leave distinct signatures in the form of bulk Fermi arc degeneracies, offering a concrete route toward experimental realization and verification.

cond-mat.mes-hall↗
arXiv2026

Observation of Braid-Protected Unpaired Exceptional Points

Spectral degeneracies (dubbed nodal points in momentum space) play fundamental roles in understanding exotic properties of light and matter. In lattice systems, unpaired band-structure degeneracies are subject to well-established no-go (doubling) theorems that universally apply to both closed Hermitian systems and open non-Hermitian systems. However, the non-Abelian braid topology of non-Hermitian multi-band systems provides a loophole to these constraints. Here we successfully leverage this loophole in a non-Hermitian three-band system, implementing an unpaired third-order exceptional point (EP3), which manifests as a non-Abelian monopole. We explicitly demonstrate the intricate braiding topology and non-Abelian, path-dependent, fusion rules underlying the unpaired EP3. The experiment uses a new design of single-photon interferometry, enabling eigenstate and spectral resolutions for multi-band systems with widely tunable parameters. Thus, the union of state-of-the-art experiments, fundamental theory, and everyday concepts such as braids pave the way toward the highly exotic non-Abelian topology unique to non-Hermitian settings.

cond-mat.mes-hall↗
arXiv2026

Hopf Exceptional Points

Exceptional points at which eigenvalues and eigenvectors of non-Hermitian matrices coalesce are ubiquitous in the description of a wide range of platforms from photonic or mechanical metamaterials to open quantum systems. Here, we introduce a class of Hopf exceptional points (HEPs) that are protected by the Hopf invariants (including the higher-dimensional generalizations) and which exhibit phenomenology sharply distinct from conventional exceptional points. Saliently, owing to their $\mathbb{Z}_2$ topological invariant related to the Witten anomaly, three-fold HEPs and symmetry-protected five-fold HEPs act as their own ``antiparticles". Furthermore, based on higher homotopy groups of spheres, we predict the existence of multifold HEPs and symmetry-protected HEPs with non-Hermitian topology captured by a range of finite groups (such as $\mathbb{Z}_3$, $\mathbb{Z}_{12}$, or $\mathbb{Z}_{24}$) beyond the periodic table of Bernard-LeClair symmetry classes.

cond-mat.mes-hall↗
arXiv2025

Non-Hermitian Exceptional Topology on a Klein Bottle Photonic Circuit

Non-Hermitian physics has unlocked a wealth of unconventional wave phenomena beyond the reach of Hermitian systems, with exceptional points (EPs) driving enhanced sensitivity, nonreciprocal transport, and topological behavior unique to non-Hermitian degeneracies. Here, we present a scalable and reconfigurable silicon photonic integrated circuit capable of emulating arbitrary non-Hermitian time evolution with high precision. Using this programmable platform, we implement a two-band non-Hermitian Hamiltonian defined on a Klein-bottle topology a nonorientable parameter space that enables exceptional phases forbidden on orientable manifolds. Through an on-chip amplitude-and-phase reconstruction protocol, we retrieve the full complex Hamiltonian at multiple points in parameter space and experimentally map the associated Fermi arc where the imaginary eigenvalue gap closes. The orientation of the measured Fermi arc reveals a nontrivial exceptional topology: it implies the presence of same-charge EPs (or an EP monopole) that cannot annihilate locally on the Klein bottle. Our results demonstrate the first photonic realization of exceptional topology on a nonorientable manifold and establish a versatile platform for exploring exotic non-Hermitian and topological models relevant to classical and quantum photonics.

physics.optics↗
arXiv2025

Exciton fractional Chern insulators in moiré heterostructures

Moiré materials have emerged as a powerful platform for exploring exotic quantum phases. While recent experiments have unveiled fractional Chern insulators exhibiting the fractional quantum anomalous Hall effect based on electrons or holes, the exploration of analogous many-body states with bosonic constituents remains largely uncharted. In this work, we predict the emergence of bosonic fractional Chern insulators arising from long-lived excitons in a moiré superlattice formed by twisted bilayer WSe$_2$ stacked on monolayer MoSe$_2$. Performing exact diagonalization on the exciton flat Chern band present in this structure, we provide compelling evidence for the existence of Abelian and non-Abelian phases at band filling $\frac{1}{2}$ and $1$, respectively, through multiple robust signatures including ground-state degeneracy, spectral flow, many-body Chern number, and particle-cut entanglement spectrum. The obtained energy gap of $\sim 10$ meV for the Abelian states suggests a remarkably high stability of this phase, which persists for a relatively wide range of twist angles and vertical electric fields. Our findings establish the presence of robust bosonic fractional Chern insulators in highly tunable and experimentally accessible moiré heterostructures and unveil a promising pathway for realizing non-Abelian anyons.

cond-mat.mes-hall↗