Three-dimensional electron gases in strong magnetic fields host partially flat bands that disperse along the field direction yet exhibit Landau-level quantization in the transverse dimensions. Early work established that for spin-polarized electrons confined to the lowest Landau level band, repulsion triggers a charge density wave (CDW) in which electrons 'self-layer' into integer quantum Hall states, while attraction generates a non-Fermi liquid (rather than a superconductor). We revisit this problem with physically motivated deformations – including generalized local interactions, higher Landau level bands, restoration of spin, and explicit breaking of spatial symmetries – paying particular attention to the competition between CDWs and superconductivity. Our main findings are: (1) Generic local interactions can stabilize a nematic CDW in which integer quantum Hall layers spontaneously 'tilt', yielding unconventional Hall response. (2) We numerically establish that the non-Fermi liquid appears stable to perturbations that preserve effective dipole conservation symmetries that emerge within a Landau level band. (3) Upon explicitly breaking translation symmetry, attraction catalyzes a novel layered superconductor that hosts Weyl nodes, superconducts within each layer, and insulates transverse to the layers. These results expand the rich phenomenology of interacting bulk electrons in the high-field regime and potentially inform the design of field-resistant superconductivity in low-carrier-density materials.

Rhombohedral graphene multilayers host various broken-symmetry metallic phases as well as superconductors whose pairing mechanism and order parameter symmetry remain unsettled. Strikingly, experiments have revealed prominent superconducting regions in rhombohedral bilayer and trilayer graphene devices with proximity-induced Ising spin-orbit coupling. We propose that these superconductors descend from a common spin-canted normal state that spontaneously breaks a U(1) spin symmetry and thus supports soft magnon modes. In particular, we show that these soft modes can mediate pairing through interband scattering events that are symmetry forbidden in the absence of spin-orbit coupling, thus providing a promising explanation for spin-orbit-enabled pairing. Numerous other experimental observations—including nontrivial dependence of superconductivity on the spin-orbit coupling strength, in-plane magnetic fields, and Fermi surface structure—also naturally follow from our scenario.

Snapshots, i.e. projective measurements of local degrees of freedom, are the most standard data taken in experiments on quantum simulators. Snapshots are usually used to probe local physics. In this work we propose a simple protocol to experimentally probe physics of defects with these snapshots. Our protocol relies only on snapshots from the bulk system, without introducing the defect explicitly; as such, the physics of different kinds of defects can be probed using the same dataset. In particular, we demonstrate that with snapshots of local spin configurations of, for example, the 1d Rydberg atom realization of the quantum Ising criticality, we can (1) extract the “defect entropy", and (2) access the continuous line of fixed points of effective defect conformal field theory, which was recently discussed in the context of the “weak-measurement altered criticality".

Topological quantum computation relies on braiding non-Abelian anyons, but requires the underlying topological order to survive imperfect state preparation and environmental noise. We show that the instability of topological order to wavefunction deformations and to decoherence, with the latter probed by syndrome distributions, are generically captured by stat-mech models whose symmetries naturally expose the corrupting anyonic excitations. As an example, we combine this framework with Monte-Carlo simulations to resolve the stability of D_4 topological order under deformations and quantum channels that proliferate multiple non-Abelian anyon species that individually are unable to condense. We show that beyond a finite threshold, proliferation of two non-Abelian anyon species parasitically condenses a shared Abelian-anyon fusion outcome, destroying the topological order. Our symmetry-based approach sharply differentiates the resulting trivial phase from that obtained by condensing all Abelian charges; in other words, the trivial phase "remembers" which anyons condensed. This framework provides a first step into identifying the relevant symmetry for optimal decoders, conditioned on syndrome measurements, of non-Abelian topological order.

Entangled many-body states enable high-precision quantum sensing beyond the standard quantum limit. We develop interferometric sensing protocols based on quantum critical wavefunctions and compare their performance with Greenberger-Horne-Zeilinger (GHZ) and spin-squeezed states. Building on the idea of symmetries as a metrological resource, we introduce a symmetry-based algorithm to identify optimal measurement strategies. We illustrate this algorithm both for magnetic systems with internal symmetries and Rydberg-atom arrays with spatial symmetries. We study the robustness of criticality for quantum sensing under non-unitary deformations, symmetry-preserving and symmetry-breaking decoherence, and qubit loss – identifying regimes where critical systems outperform GHZ states and showing that non-unitary deformation can even enhance sensing precision. Combined with recent results on log-depth preparation of critical wavefunctions, interferometric sensing in this setting appears increasingly promising.

Conformal field theories (CFTs) feature prominently in high-energy physics1,2, statistical mechanics3 and condensed matter4-6. For example, CFTs govern emergent universal properties of systems tuned to quantum phase transitions4,7, including their entanglement, correlations and low-energy excitation spectra. Much of the rich structure predicted by CFTs nevertheless remains unobserved in experiment. Here we directly observe the energy excitation spectra of emergent CFTs at quantum phase transitions-recovering universal energy ratios characteristic of the underlying field theories8,9. Specifically, we develop and implement a modulation technique to resolve the finite-size spectra of a Rydberg chain, variably tuned to quantum phase transitions described by either Ising or tricritical Ising CFTs. We also use local control to distinguish parities of excitations under reflection and, in the tricritical Ising chain, to induce transitions between distinct CFT spectra associated with changing boundary conditions. By using a variant of the modulation technique, we furthermore study the dynamical structure factor of the critical system, which is closely related to the correlation of an underlying Ising conformal field. Our work not only probes the emergence of CFT features in a quantum simulator but also provides a technique for diagnosing a priori unknown universality classes in future experiments.

Conformal field theories (CFTs) feature prominently in high-energy physics, statistical mechanics, and condensed matter. For example, CFTs govern emergent universal properties of systems tuned to quantum phase transitions, including their entanglement, correlations, and low-energy excitation spectra. Much of the rich structure predicted by CFTs nevertheless remains unobserved in experiment. Here we directly observe the energy excitation spectra of emergent CFTs at quantum phase transitions – recovering universal energy ratios characteristic of the underlying field theories. Specifically, we develop and implement a modulation technique to resolve a Rydberg chain's finite-size spectra, variably tuned to quantum phase transitions described by either Ising or tricritical Ising CFTs. We also employ local control to distinguish parities of excitations under reflection and, in the tricritical Ising chain, to induce transitions between distinct CFT spectra associated with changing boundary conditions. By utilizing a variant of the modulation technique, we furthermore study the dynamical structure factor of the critical system, which is closely related to the correlation of an underlying Ising conformal field. Our work not only probes the emergence of CFT features in a quantum simulator, but also provides a technique for diagnosing a priori unknown universality classes in future experiments.

Local non-unitary deformations of topologically ordered wavefunctions can drive transitions into peculiar states that challenge modern perspectives on gapped quantum matter. The strongly deformed toric code offers a curious case, hosting m anyon condensation alongside perimeter-law scaling of Wilson loops charged under an exact 1-form symmetry—properties that typically do not coexist in gapped ground states. Nevertheless, we rigorously construct local gapped parent Hamiltonians for these strongly deformed toric code states. The Hamiltonians we construct are not strictly finite-range, but contain sums of Wilson loop operators whose coefficients decay exponentially in their diameter. If one adopts standard locality bounds used to define gapped phases—which allow for such exponentially decaying terms—our construction shows that these states realize a trivial gapped phase. Within this locality class, we demonstrate that perimeter-law scaling of Wilson loops does not imply a spontaneously broken 1-form symmetry, and from a dual perspective, that long-range ferromagnetic order and perimeter-law disorder parameter correlations can coexist in a 2D gapped ground state. We evade a recent no-go theorem [Sahay et al., arXiv:2503.01977] by relaxing its assumptions in a manner that we quantify as benign in the thermodynamic limit. More broadly, our results highlight that stronger notions of locality are necessary for prohibiting these counterintuitive properties within a gapped phase.

Helical trilayer graphene realizes a versatile moiré system for exploring correlated topological states emerging from high Chern bands. Motivated by recent experimental observations of anomalous Hall effects at fractional fillings of magic-angle helical trilayers, we focus on the higher Chern number |C_{band}|=2 band and explore gapped many-body Hall states beyond the conventional Landau level paradigm. Through extensive exact diagonalization, we predict novel phases unattainable in a single |C_{band}|=1 band. At filling ν=2/3 and ν=1/3, a sqrt[3]×sqrt[3] charge-ordered quantum Hall crystal and a Halperin fractional Chern insulator with Hall conductance |σ_{H}|=2e^{2}/3h are predicted, respectively, indicating strong particle-hole asymmetry of the system. At half-filling ν=1/2, an extensively degenerate pseudospin Hall ferromagnet featuring emergent SU(2) symmetry is found without the band being flat. Inspired by striking robustness of the ferromagnetic degeneracy, we develop a method to unveil and quantify the emergent symmetry via pseudospin operator construction in the presence of band dispersion and Coulomb interaction and demonstrate persistence of the SU(2) quantum numbers even far away from the chiral limit. Incorporating spin-valley degrees of freedom, we identify an optimal filling regime ν_{total}=3+ν for realizing the above states. Notably, interflavor interactions renormalize the bandwidth and stabilize all the gapped phases even in realistic sublattice corrugation parameter regimes.

The effect of decoherence on topological order (TO) has been most deeply understood for the toric code, the paragon of Abelian TOs. We show that certain non-Abelian TOs can be analyzed and understood to a similar degree, despite being significantly richer. We consider both wavefunction deformations and quantum channels acting on D_4 TO, which has recently been realized on a quantum processor. By identifying the corresponding local statistical mechanical spin or rotor model with D_4 symmetry, we find a remarkable stability against proliferating non-Abelian anyons. This is shown by leveraging a reformulation in terms of the tractable O(2) loop model in the pure state case, and n coupled O(2) loop models for Rényi-n quantities in the decoherence case – corresponding to worldlines of the proliferating anyon with quantum dimension 2. In particular, we find that the purity (n=2) remains deep in the D_4 TO for any decoherence strength, while the n →∞ limit becomes critical upon maximally decohering a particular anyon type, similar to our wavefunction deformation result. The information-theoretic threshold (n→ 1) appears to be controlled by a disordered version of these stat-mech models, akin to the toric code case although significantly more robust. We furthermore use Monte Carlo simulations to explore the phase diagrams when multiple anyon types proliferate at the same time, leading to a continued stability of the D_4 TO in addition to critical phases with emergent U(1) symmetry. Instead of loop models, these are now described by net models corresponding to different anyon types coupled together according to fusion rules.This opens up the exploration of statistical mechanical models for decohered non-Abelian TO, which can inform optimal decoders, and which in an ungauged formulation examples of non-Abelian strong-to-weak symmetry breaking.

Coulomb repulsion can, counterintuitively, mediate Cooper pairing via the Kohn-Luttinger mechanism. However, it is commonly believed that observability of the effect requires special circumstances, e.g., vicinity of the Fermi level to Van Hove singularities, significant lattice-induced band distortions, or nontrivial Fermi surface topologies. Here, we establish that quantum geometric properties of the constituent electrons can dramatically promote pairing from repulsion via dependence of screening on the quantum metric. We demonstrate quantum-geometry-enhanced superconductivity in two microscopic models with tunable quantum geometry, highlighting the crucial roles of quantum metric anisotropy and inhomogeneity. Our analysis provides an experimentally accessible figure of merit for the importance of quantum geometry to inducing unconventional superconductivity, indicating its relevance to graphene multilayers.

Measurements can qualitatively alter correlations and entanglement emerging in gapless quantum matter. We show how a single round of measurements on gapless quantum systems can, upon rotating the measurement basis, induce non-trivial transitions separating regimes displaying universal characteristics governed by distinct boundary conformal field theories. We develop the theory of such `measurement-induced boundary transitions' by investigating a gapless parent of the one-dimensional cluster state, obtained by appropriately symmetrizing a commuting projector Hamiltonian for the latter. Projective measurements on the cluster state are known to convert the wavefunction, after post-selection or decoding, into a long-range-ordered Greenberger-Horne-Zeilinger (GHZ) state. Similar measurements applied to the gapless parent (i) generate long-range order coexisting with power-law correlations when post-selecting for uniform outcomes, and (ii) yield power-law correlations distinct from those in the pre-measurement state upon decoding. In the post-selection scenario, rotating the measurement basis preserves long-range order up until a critical tilt angle marking a measurement-induced boundary transition to a power-law-ordered regime. Such a transition -- which does not exist in the descendant cluster state -- establishes new connections between measurement effects on many-body states and non-trivial renormalization-group flows. We extend our analysis to tricritical Ising and three-state Potts critical theories, which also display measurement-induced boundary transitions, and propose general criteria for their existence in other settings.

The effect of decoherence on topological order (TO) has been most deeply understood for the toric code, the paragon of Abelian TOs. We show that certain non-Abelian TOs can be analyzed and understood to a similar degree, despite being significantly richer. We consider both wave-function deformations and quantum channels acting on D4 TO, which has recently been realized on a quantum processor. By identifying the corresponding local statistical mechanical spin or rotor model with D4 symmetry, we find a remarkable stability against proliferating non-Abelian anyons. This is shown by leveraging a reformulation in terms of the tractable O(2) loop model in the pure state case and n coupled O(2) loop models for Renyi-n quantities in the decoherence case-corresponding to worldlines of the proliferating anyon with quantum dimension 2. In particular, we find that the purity (n 1/4 2) remains deep in the D4 TO for any decoherence strength, while the n-* infinity limit becomes critical upon maximally decohering a particular anyon type, similar to our wave-function deformation result. The information-theoretic threshold (n-* 1) appears to be controlled by a disordered version of these statistical mechanical models, akin to the toric code case although significantly more robust. We furthermore use Monte Carlo simulations to explore the phase diagrams when multiple anyon types proliferate at the same time, leading to a continued stability of the D4 TO in addition to critical phases with emergent U(1) symmetry. Instead of loop models, these are now described by net models corresponding to different anyon types coupled together according to fusion rules. This opens up the exploration of statistical mechanical models for decohered non-Abelian TO, which can inform optimal decoders and which in an ungauged formulation provides examples of non-Abelian strong-to-weak symmetry breaking.

Graphene and transition metal dichalcogenide flat-band systems show similar phase diagrams, replete with magnetic1-5 and superconducting6-11 phases. An abiding question has been whether magnetic ordering competes with superconductivity or facilitates pairing. For example, recent studies of Bernal bilayer graphene in the presence of enhanced spin-orbit coupling show a substantial increase in the observed domain and critical temperature Tc of superconducting states12-14; however, the mechanism for this enhancement remains unknown. Here we show that introducing spin-orbit coupling in rhombohedral trilayer graphene (RTG) by substrate proximity effect generates new superconducting pockets for both electron and hole doping, with maximal Tc ≈ 300 mK, which is three times larger than in RTG encapsulated by hexagonal boron nitride. Using local magnetometry, we show that superconductivity straddles a transition between a spin-canted state with a finite in-plane magnetic moment and a state with complete spin-valley locking. This transition is reproduced in our Hartree-Fock calculations, in which this transition is driven by the competition between spin-orbit coupling and the carrier-density-tuned Hund's interaction. Our experiment suggests that the enhancement of superconductivity by spin-orbit coupling is driven by a quantitative change in the canting angle rather than a change in the ground state symmetry. These results align with a recently proposed mechanism for the enhancement of superconductivity15, in which fluctuations in the spin-canting order contribute to the pairing interaction.

Weak measurements have been predicted to dramatically alter universal properties of quantum critical wavefunctions, though experimental validation remains an open problem. Here we devise a practical scheme for realizing measurement-altered criticality in a chain of Rydberg atoms tuned to Ising and tricritical Ising phase transitions. In particular, we show that projectively measuring a periodic subset of atoms alters quantum critical correlations in distinct ways that one can control via the choice of measured sites and the measurement outcomes. While our protocol relies on post-selection, the measurement outcomes yielding the most dramatic consequences occur with surprisingly large probabilities: O(10

Coulomb repulsion can, counterintuitively, mediate Cooper pairing via the Kohn-Luttinger mechanism. However, it is commonly believed that observability of the effect requires special circumstances -- e.g., vicinity of the Fermi level to van Hove singularities, significant lattice-induced band distortions, or non-trivial Fermi surface topologies. Here we establish that quantum geometric properties of the constituent electrons can dramatically promote pairing from repulsion via dependence of screening on the quantum metric. We demonstrate quantum-geometry-enhanced superconductivity in two microscopic models with tunable quantum geometry, highlighting the crucial roles of quantum metric anisotropy and inhomogeneity. Our analysis provides an experimentally accessible figure of merit for the importance of quantum geometry to inducing unconventional superconductivity, indicating its relevance to graphene multilayers.

Entanglement, measurement, and classical communication together enable teleportation of quantum states between distant parties, in principle with perfect fidelity. To what extent do correlations and entanglement of a many-body wavefunction transfer under imperfect teleportation protocols? We address this question for the case of an imperfectly teleported quantum critical wavefunction, focusing on the ground state of a critical Ising chain. We demonstrate that imperfections, e.g., in the entangling gate adopted for a given protocol, effectively manifest as weak measurements acting on the otherwise pristinely teleported critical state. Armed with this perspective, we leverage and further develop the theory of measurement-altered quantum criticality to quantify the resilience of critical-state teleportation. We identify classes of teleportation protocols for which imperfection $(i)$ preserves both the universal long-range entanglement and correlations of the original quantum critical state, $(ii)$ weakly modifies these quantities away from their universal values, and $(iii)$ obliterates long-range entanglement altogether while preserving power-law correlations, albeit with a new set of exponents. We also show that mixed states describing the average over a series of sequential imperfect teleportation events retain pristine power-law correlations due to a `built-in' decoding algorithm, though their entanglement structure measured by the negativity depends on errors similarly to individual protocol runs. These results may allow one to design teleportation protocols that optimize against errors -- highlighting a potential practical application of measurement-altered criticality.

Two-dimensional time-reversal-invariant topological superconductors host helical Majorana fermions at their boundary. We study the fate of these edge states under the combined influence of strong interactions and disorder, using the effective 1D lattice model for the edge introduced by Jones and Metlitski [Phys. Rev. B 104, 245130 (2021)]. We specifically develop a strong-disorder renormalization group analysis of the lattice model and identify a regime in which time-reversal is broken spontaneously, creating random magnetic domains; Majorana fermions localize to domain walls and form an infinite-randomness fixed point, identical to that appearing in the random transverse-field Ising model. While this infinite-randomness fixed point describes a fine-tuned critical point in a purely 1D system, in our edge context there is no obvious time-reversal-preserving perturbation that destabilizes the fixed point. Our analysis thus suggests that the infinite-randomness fixed point emerges as a stable phase on the edge of 2D topological superconductors when strong disorder and interactions are present.

Topological quantum computation relies on control of non-Abelian anyons for inherently fault-tolerant storage and processing of quantum information. By now, blueprints for topological qubits are well developed for electrically active topological superconductor and fractional quantum Hall platforms. We leverage recent insights into the creation and detection of non-Abelian anyons in electrically insulating spin systems to propose topological qubit architectures based on quantum spin liquids. We present two types of prototype designs that enable the requisite control in a potentially scalable framework: one invokes spin liquids integrated into magnetic tunnel junction arrays, the other uses semiconductor-spin liquid hybrids. We further identify various protocols for interrogating spin-liquid-based topological qubits, both to validate the underlying principles of topological quantum computation and to establish gates required for universal quantum computation. These results provide long-term direction for experimental investigation of Kitaev materials and potentially other solid-state spin liquid hosts.

We explore Bernal bilayer graphene in the presence of long-range Coulomb interactions, short-range Hund's coupling, and proximity-induced Ising spin-orbit coupling using self-consistent Hartree-Fock simulations. We show that the interplay between these three ingredients produces an intricate phase diagram comprising a multitude of symmetry-broken metallic states tunable via doping and applied displacement field. In particular, we find intervalley coherent and spin-canted ground states that may hold the key to understanding spin-orbit-enabled superconductivity observed in this platform. We also investigate various phase transitions where a continuous U(1) symmetry is broken to ascertain the possible role of critical fluctuations on pairing.