CyberSec Research

Understanding the emergence of unconventional superconductivity, where the order parameter deviates from simple isotropic s-wave pairing, is a central puzzle in condensed matter physics. Transition-metal dichalcogenides (TMDCs), though generally regarded as conventional superconductors, display signatures of this unusual behavior and thus provide a particularly intriguing platform to explore how exotic states arise. Here we investigate the misfit compound (SnS)$_{1.15}$(TaS$_2$), a heterostructure composed of alternating SnS and 1H-TaS$_2$ layers. Using transport, photoemission, and scanning tunneling spectroscopy, we demonstrate that the SnS layers effectively decouple the TaS$_2$ into electronically isolated 1H sheets. In this limit, the tunneling density of states reveals a clear two-gap superconducting spectrum with T$_c \sim$ 3.1 K. A theoretical model based on lack of inversion symmetry and finite-range attraction reproduces the observed multi-gap structure as a mixed singlet-triplet state. These results establish misfit compounds as a powerful platform for studying unconventional superconductivity in isolated 1H layers and for realizing multiple uncoupled superconductors within a single crystal.

Exotic collective phenomena emerge when bosons strongly interact within a lattice. However, creating a robust and tunable solid-state platform to explore such phenomena has been elusive. Dual moir\'e systems$-$compromising two Coulomb-coupled moir\'e lattices$-$offer a promising system for investigating strongly correlated dipolar excitons (composite bosons) with electrical control. Thus far, their implementation has been hindered by the relative misalignment and incommensurability of the two moir\'e patterns. Here we report a dual moir\'e system with perfect translational and rotational alignment, achieved by utilizing twisted hexagonal boron nitride (hBN) bilayer to both generate an electrostatic moir\'e potential and separate MoSe$_{2}$ and WSe$_{2}$ monolayers. We observe strongly correlated electron phases driven by intralayer interactions and identify interlayer Rydberg trions, which become trapped in the presence of the Mott insulating state. Importantly, our platform is electrostatically programmable, allowing the realization of different lattice symmetries with either repulsive or attractive interlayer interactions. In particular, we implement the latter scenario by optically injecting charges, which form a dipolar excitonic phase. Our results establish a versatile platform for the exploration and manipulation of exotic and topological bosonic quantum many-body phases.

We introduce a hybrid approach for computing dynamical observables in strongly correlated systems using higher-order moments. This method integrates memory kernel coupling theory (MKCT) with the density matrix renormalization group (DMRG), extending our recent work on MKCT to strongly correlated systems. The method establishes that correlation functions can be derived from the moments. Within our framework, operators and wavefunctions are represented as matrix product operators (MPOs) and matrix product states (MPSs), respectively. Crucially, the repeated application of the Liouville operator is achieved through an iterative procedure analogous to the DMRG algorithm itself. We demonstrate the effectiveness and efficiency of MKCT-DMRG by computing the spectral function of the Hubbard model. Furthermore, we successfully apply the method to compute the electronic friction in the Hubbard-Holstein model. In all cases, the results show excellent agreement with time-dependent DMRG (TD-DMRG) benchmarks. The advantage of MKCT-DMRG over TD-DMRG is the computational efficiency, which avoids expensive real-time propagation in TD-DMRG. These findings establish MKCT-DMRG as a promising and accurate framework for simulating challenging dynamical properties in strongly correlated quantum systems.

Collective modes capture the dynamical aspects of fractional quantum Hall (FQH) fluids. Depending on the active degrees of freedom, different types of collective modes can arise in a FQH state. In this work, we consider spinful FQH states in the lowest Landau level (LLL) along the Jain sequence of fillings $\nu{=}n/(2n{\pm}1)$ and compute the Coulomb dispersion of their spin-flip and spin-conserving collective modes in the spherical geometry. We use the LLL-projected density-wave and composite fermion (CF) exciton states as trial wave functions for these modes. To evaluate the dispersion of density-wave states, we derive the commutation algebra of spinful LLL-projected density operators on the sphere, which enables us to extract the gap of the density-wave excitations from the numerically computed density-density correlation function, i.e., the static structure factor, of the FQH ground state. We find that the CF excitons provide an accurate description of the collective modes at all wavelengths, while the density-wave states fail to do so. Specifically, the spin-flip density wave reliably captures the spin-flip collective mode only for the Laughlin and Halperin states, and that too only in the long-wavelength limit. Interestingly, for spin-singlet primary Jain states, the spin-conserving density mode is inaccurate even in the long-wavelength regime. We show that this discrepancy stems from the presence of an additional high-energy spin-conserving parton mode, similar to that found in fully polarized secondary Jain states at $\nu{=}n/(4n{\pm}1)$. We propose an ansatz for this parton mode and compute its Coulomb dispersion in the singlet state at $\nu{=}2/5$. The predicted parton mode can be observed in circularly polarized inelastic light scattering experiments.

We introduce the Cyclic Variational Quantum Eigensolver (CVQE), a hardware-efficient framework for accurate ground-state quantum simulation on noisy intermediate-scale quantum (NISQ) devices. CVQE departs from conventional VQE by incorporating a measurement-driven feedback cycle: Slater determinants with significant sampling probability are iteratively added to the reference superposition, while a fixed entangler (e.g., single-layer UCCSD) is reused throughout. This adaptive reference growth systematically enlarges the variational space in most promising directions, avoiding manual ansatz or operator-pool design, costly searches, and preserving compile-once circuits. The strategy parallels multi-reference methods in quantum chemistry, while remaining fully automated on quantum hardware. Remarkably, CVQE exhibits a distinctive staircase-like descent pattern, where successive energy drops sharply signal efficient escape from barren plateaus. Benchmarks show that CVQE consistently maintains chemical precision across correlation regimes, outperforms fixed UCCSD by several orders of magnitude, and achieves favorable accuracy-cost trade-offs compared to the Selected Configuration Interaction. These results position CVQE as a scalable, interpretable, and resource-efficient paradigm for near-term quantum simulation.

We investigate the nature of the topological phase transition of the antiferromagnetic Kitaev model on the honeycomb lattice in the presence of a magnetic field along the [111] direction. The field opens a topological gap in the Majorana fermion spectrum and leads to a sequence of topological phase transitions before the field polarised state is reached. At mean field level the gap first closes at the three $M$ points in the Brillouin zone, where the Majorana fermions form Dirac cones, resulting in a change of Chern number by three. An odd number of Dirac fermions in the infrared is unusual and requires Berry curvature compensation in the UV, which occurs via topological, ring-like hybridisation gaps with higher-energy bands. We perform a renormalisation-group analysis of the topological phase transition at the three $M$ points within the Yukawa theory, allowing for intra- and inter-valley fluctuations of the spin-liquid bond operators. We find that the latter lead to a breaking of Lorentz invariance and hence a different universality compared to the standard Ising Gross-Neveu-Yukawa class.

We report ultrahigh magnetic field Faraday rotation results on the chiral helimagnet Cu2OSeO3, the first Mott insulator showing skyrmion lattice phases and a linear magnetoelectric effect. Between 180 and 300 T, we find signatures of a Bose-Einstein condensation (BEC) of magnons, which can be described as a canted XY ferrimagnet. Due to the magnetoelectric coupling, the transverse magnetic order of the indivual Cu2+ spins is accompanied by a characteristic dome-like electric polarization which is crucial for the observation of the condensate via the Faraday rotation effect.

In conventional superconductors, the energy scale associated with the superfluid stiffness is much larger compared to the pairing energy and hence, the superconducting transition temperature (Tc) is entirely dictated by the superconducting (SC) energy gap. The phase rigidity of the SC condensate in unconventional superconductors, on the other hand, can be low enough to enable destruction of superconductivity via phase incoherence and persistence of an energy gap even at the absence of macroscopic superconductivity above Tc. This is considered a possible mechanism of the pseudogap (PG) state of cuprate high temperature superconductors (HTSCs). We have investigated the electronic energy ({\omega}) and momentum-separation vector (q) dependence of the joint density of states (JDOS), derived from the autocorrelated Angle Resolved Photoemission Spectroscopy (ARPES) data, from moderately underdoped Bi2Sr2CaCu2O8+{\delta}HTSC samples at temperatures below and above Tc. We found that q-space structure of the constant {\omega} JDOS intensity maps and the dispersions of the JDOS peaks are essentially the same both below and above Tc. Furthermore, the dispersions of the JDOS peaks above Tc are particle-hole symmetric. These observations evince similarity between the nature of the energy gap below and above Tc, which supports preformed pairing scenario for the PG state at least in the moderately underdoped regime.

Neural quantum states (NQS) have emerged as a promising approach to solve second-quantised Hamiltonians, because of their scalability and flexibility. In this work, we design and benchmark an NQS impurity solver for the quantum embedding methods, focusing on the ghost Gutzwiller Approximation (gGA) framework. We introduce a graph transformer-based NQS framework able to represent arbitrarily connected impurity orbitals and develop an error control mechanism to stabilise iterative updates throughout the quantum embedding loops. We validate the accuracy of our approach with benchmark gGA calculations of the Anderson Lattice Model, yielding results in excellent agreement with the exact diagonalisation impurity solver. Finally, our analysis of the computational budget reveals the method's principal bottleneck to be the high-accuracy sampling of physical observables required by the embedding loop, rather than the NQS variational optimisation, directly highlighting the critical need for more efficient inference techniques.

We investigate interacting Su-Schrieffer-Heeger (SSH) chains with two- and three-site unit cells using density matrix renormalization group (DMRG) simulations. By selecting appropriate filling fractions and sweeping across interaction strength \( J_z \) and dimerization \( \delta \), we map out their phase diagrams and identify transition lines via entanglement entropy and magnetization measurements. In the two-site model, we observe the emergence of an interaction-induced antiferromagnetic intermediate phase between the topologically trivial and non-trivial regimes, as well as a critical region at negative \( J_z \) with suppressed magnetization and finite-size scaling of entanglement entropy. In contrast, the three-site model lacks an intermediate phase and exhibits asymmetric edge localization and antiferromagnetic ordering in both positive and negative \( J_z \) regimes. We further examine the response of edge states to Ising perturbations. In the two-site model, zero-energy edge modes are topologically protected and remain robust up to a finite interaction strength. However, in the three-site model, where the edge states reside at finite energy, this protection breaks down. Despite this, the edge-localized nature of these states survives in the form of polarized modes whose spatial profiles reflect the non-interacting limit.

Establishing a universal diagnostic of topological order remains an open theoretical challenge. In particular, diagnosing long-range entanglement through the entropic area law suffers from spurious contributions, failing to unambiguously identify topological order. Here we devise a protocol based on the ZX calculus, a graphical tensor network, to determine the topological order of a state circumventing entropy calculations. The protocol takes as input real-space bipartitions of a state and returns a ZX contour diagram, $\mathcal{D}_{\partial A}$, displaying long-range graph connectivity only for long-range entangled states. We validate the protocol by showing that the contour diagrams of the toric and color codes are equivalent except for the number of non-local nodes, which differentiates their topological order. The number of these nodes is robust to the choice of the boundary and ground-state superposition, and they are absent for trivial states, even those with spurious entropy contributions. Our results single out ZX calculus as a tool to detect topological long-range entanglement by leveraging the advantages of diagrammatic reasoning against entropic diagnostics.

The Kolmogorov-Arnold (KA) representation theorem constructs universal, but highly non-smooth inner functions (the first layer map) in a single (non-linear) hidden layer neural network. Such universal functions have a distinctive local geometry, a "texture," which can be characterized by the inner function's Jacobian $J({\mathbf{x}})$, as $\mathbf{x}$ varies over the data. It is natural to ask if this distinctive KA geometry emerges through conventional neural network optimization. We find that indeed KA geometry often is produced when training vanilla single hidden layer neural networks. We quantify KA geometry through the statistical properties of the exterior powers of $J(\mathbf{x})$: number of zero rows and various observables for the minor statistics of $J(\mathbf{x})$, which measure the scale and axis alignment of $J(\mathbf{x})$. This leads to a rough understanding for where KA geometry occurs in the space of function complexity and model hyperparameters. The motivation is first to understand how neural networks organically learn to prepare input data for later downstream processing and, second, to learn enough about the emergence of KA geometry to accelerate learning through a timely intervention in network hyperparameters. This research is the "flip side" of KA-Networks (KANs). We do not engineer KA into the neural network, but rather watch KA emerge in shallow MLPs.

Landau levels (LLs) are the massively-degenerate discrete energy spectrum of a charged particle in a transverse magnetic field and lie at the heart of many intriguing phenomena such as the integer and fractional quantum Hall effects as well as quantized vortices. In this Letter, we consider coupling of LLs of a transversely driven charge neutral particle in a synthetic gauge potential to a quantized field of an optical cavity -- a setting reminiscent of superradiant self-ordering setups in quantum gases. We uncover that this complex system can be surprisingly described in terms of two highly nonlinearly-coupled quantum harmonic oscillators, thus enabling a full quantum mechanical treatment. Light-matter coupling mixes the LLs and the superradiant photonic mode, leading to the formation of hybrid states referred to as ``Landau polaritons''. They inherit partially the degeneracy of the LLs and possess intriguing features such as non-zero light-matter entanglement and quadrature squeezing. Depending on the system parameters and the choice of initial state, the system exhibits diverse nonequilibrium quantum dynamics and multiple steady states, with distinct physical properties. This work lays the foundation for further investigating the novel, driven-dissipative Landau-polariton physics in quantum-gas--cavity-QED settings.

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.

We carry out large-scale, sign-problem-free determinant quantum Monte Carlo simulations of the square lattice $\mathrm{SU}(N)$-symmetric two-channel Kondo lattice model at half-filling. We map out the zero-temperature phase diagram for $N = 2, 4, 6$, and $8$, as a function of the Kondo coupling strength. In the weak-coupling regime, we observe antiferromagnetic order of the localized moments. Remarkably, for $N \geq 6$, sufficiently strong Kondo coupling induces spontaneous channel symmetry breaking, forming a stripe dimerization pattern with a wave vector $\boldsymbol{k}=(\pi,0)$ alternating between channels. These findings are supported by a complementary large-$N$ saddle point analysis, which identifies the striped hybridization pattern as the energetically preferred configuration. The spatial symmetry-breaking results in an anisotropic Fermi surface reconstruction.

Higher-form symmetry in a tensor product Hilbert space is always emergent: the symmetry generators become genuinely topological only when the Gauss law is energetically enforced at low energies. In this paper, we present a general method for defining the 't Hooft anomaly of higher-form symmetries in lattice models built on a tensor product Hilbert space. In (2+1)D, for given Gauss law operators realized by finite-depth circuits that generate a finite 1-form $G$ symmetry, we construct an index representing a cohomology class in $H^4(B^2G, U(1))$, which characterizes the corresponding 't Hooft anomaly. This construction generalizes the Else-Nayak characterization of 0-form symmetry anomalies. More broadly, under the assumption of a specified formulation of the $p$-form $G$ symmetry action and Hilbert space structure in arbitrary $d$ spatial dimensions, we show how to characterize the 't Hooft anomaly of the symmetry action by an index valued in $H^{d+2}(B^{p+1}G, U(1))$.

We study the dynamics and phase structure of Abelian gauge theories in $d=1+1$ dimensions. These include $U(1)$ gauge theory coupled to a scalar and a fermion, as well as the two-flavour Schwinger model with different charges. Both theories exhibit a surprisingly rich phase diagram as masses are varied, with both $c=1$ and $c=1/2$ critical lines or points. We build up to the study of 2d chiral gauge theories, which hold particular interest because they provide a mechanism for symmetric mass generation, a phenomenon in which fermions become gapped without breaking chiral symmetries.

The interplay between topology and strong interactions gives rise to a variety of exotic quantum phases, including fractional quantum Hall (FQH) states and their lattice analogs - fractional Chern insulators (FCIs). Such topologically ordered states host fractionalized excitations, which for spinful systems are often accompanied by ferromagnetism and skyrmions. Here, we study a Hofstadter-Hubbard model of spinful fermions on a square lattice, extended by nearest-neighbor interactions. Using large-scale density matrix renormalization group (DMRG) simulations, we demonstrate the emergence of a spin-polarized $\frac{1}{3}$-Laughlin-like FCI phase, characterized by a quantized many-body Chern number, a finite charge gap, and hidden off-diagonal long-range order. We further investigate the quantum Hall ferromagnet at $\nu=1$ and its skyrmionic excitations upon doping. In particular, we find that nearest-neighbor repulsion is sufficient to stabilize both particle- and hole-skyrmions in the ground state around $\nu=1$, whereas we do not find such textures around $\nu=\frac{1}{3}$. The diagnostic toolbox presented in this work, based on local densities, correlation functions, and spin-resolved observables, is directly applicable in quantum gas microscopy experiments. Our results open new pathways for experimental exploration of FCIs with spin textures in both ultracold atom and electronic systems.