Conference field notes · Volume I
CCMP Reports
Ten editorial lecture notes tracing current ideas in high-temperature superconductivity, topology, quantum geometry, magnetic symmetry, fractonic matter and boundary conformal field theory.
A research notebook designed as a small proceedings volume.
This collection records selected talks from CCMP 2026. Each report pairs a concise scientific abstract with a direct link to the complete PDF note. PDF files are loaded only when requested, keeping the page fast and reliable even on mobile connections.
σ-bonding High-Tc Superconductivity and Neural Tensor Network State
This talk connects two frontiers: material design via metallizing \( \sigma \)-bonding electrons (exemplified by MgB\(_2\)), and variational many-body solvers using Neural Tensor Network States (\( \nu \)TNS). Xiang emphasizes that hole doping in cuprates creates Zhang-Rice singlets rather than simple rigid-band carriers. He presents recent \( \nu \)TNS benchmarks on the frustrated \( J_1 \)-\( J_2 \) square-lattice Heisenberg model at \( J_2/J_1 \sim 0.5 \), where the numerical data favor a gapless quantum spin liquid over competing VBS or Néel orders.
Phase Stiffness, Soft Modes, and Competing Orders in High-Tc Superconductors
Uemura argues that \( T_{\rm c} \) in underdoped cuprates is controlled primarily by superfluid density (phase stiffness) rather than by the pairing gap. Using \( \mu \)SR measurements of \( \lambda^{-2} \propto n_s/m^* \), he presents the empirical Uemura relation \( T_{\rm c} \propto n_s/m^* \). The talk covers the Emery-Kivelson phase-fluctuation picture, Nernst-effect evidence for vortex-like excitations above \( T_{\rm c} \), and the role of stripe/CDW competing orders in suppressing global phase coherence.
Electric Current-Induced Superconductivity and Perfect Superconducting Diode
Yanase systematically introduces the superconducting diode effect (SDE) arising from finite-momentum Cooper pairs, including Rashba helical states and FFLO-type pairing. He highlights the Daido-Yanase bilayer dissipation model that achieves perfect SDE (vanishing critical current in one direction), and the trigonal Fulde-Ferrell scenario where a finite current selects a single FF domain to produce a zero-resistance state. Light-driven and correlation-induced nonreciprocal mechanisms are also discussed.
Stable Topology in Exactly Flat Bands (CTFB)
Song addresses the no-go theorem that forbids strictly flat, finite-range, gapped bands with stable topology. By relaxing the gapped condition and allowing critical band touching, he constructs Critical Topological Flat Bands (CTFB) where the projector remains continuous (though non-analytic) at the touching point. Using bipartite kernel constructions and symmetry indicators (\( \Delta B \)), he shows how stable Chern/\( Z_2 \) topology can coexist with exact flatness, providing a rigorous starting point for fractional Chern insulators.
Spin Space Group, Altermagnetism, and Symmetry Classification of Magnetic Orders
Liu introduces spin space groups to redefine ferromagnets and antiferromagnets based on spin-space operations rather than net magnetization. He focuses on altermagnetism — a collinear compensated phase with zero net moment but momentum-dependent spin splitting, arising from nonrelativistic crystal symmetry. The talk also covers spin translational groups for classifying complex AFM geometries (spiral, multi-\( q \)), and how oriented spin space groups diagnose allowed responses such as AHE, magnetoelectricity, and topology.
Driven Fermions, Baths, Floquet Steady States, and Dissipation-Shaped Quantum Geometry
Shi shows that Floquet band structure alone does not determine occupation; the nature of the bath (fermionic vs. bosonic) selects distinct non-equilibrium steady states. Fermionic baths yield Floquet Fermi liquids with nested Fermi surfaces, while bosonic baths produce ultracritical Floquet non-Fermi liquids with sharp but non-Fermi singularities. In the second half, he warns that the \( \Gamma^0 \) term in second-order nonlinear transport — often assumed to be purely quantum-geometric — is in fact shaped by dissipation, making bath identification essential for extracting quantum metrics.
Fractonic Fractional Quantum Hall Effect – from Kane wires to lineons
This talk generalizes Kane's coupled-wire construction by gluing adjacent Laughlin strips with different filling fractions \( 1/m_j \), using Haldane's null-vector criterion. The non-uniform gluing generates position-dependent anyon condensation rules, which split the ordinary 2D FQH anyons into mobility-restricted excitations: lineons (1D motion), spread lineons (local interface crossing), and fully mobile C-anyons. This provides a natural route to fractonic topological order without requiring crystalline translation symmetry.
Chirality Trinity – Chirality, Time Chirality, and Chirality Prime
Cheong classifies handedness using \( P \) (parity), \( T \) (time-reversal), and \( PT \) symmetries. Ordinary chirality (\( \mathbf{H}\cdot\mathbf{k} \)) is \( P \)-odd/\( T \)-even; time chirality (\( \mathbf{k}\cdot\mathbf{E} \)) is \( P \)-even/\( T \)-odd; chirality prime (\( \mathbf{E}\cdot\mathbf{H} \)) is \( P \)-odd/\( T \)-odd. Superchirality occurs when all three are broken. He applies this framework to ferro-rotational (electric toroidal) orders, circular dichroism, chiral vs. time-chiral phonons, and shows how these selection rules dictate Hall, Edelstein, and magnetoelectric responses without detailed microscopic calculations.
Kagome CDW, Loop Current, and Superconductivity in CsV3Sb5
Chen presents experimental evidence that the CDW in CsV\(_3\)Sb\(_5\) is not a simple Peierls nesting instability. The transition is accompanied by a giant anomalous Hall effect, NMR-detected orbital ordering, electronic nematicity, and a double-dome superconducting phase under pressure. He interprets the CDW as a multi-component order parameter involving charge, bond, orbital, and possibly loop-current modulations, drawing on the Capponi-Wu-Zhang bilayer model where \( \operatorname{Im}\langle c_i^\dagger c_j \rangle \) serves as the order parameter for spontaneous circulating currents.
Boundary Conformal Field Theory – Cardy condition and anomaly
This is a pedagogical note on BCFT, starting from the gluing condition \( T(z) = \bar{T}(\bar{z}) \) on the boundary, leading to Ishibashi states and Cardy states. The annulus partition function is computed in both open and closed channels, and their equality yields the Cardy condition, which is then solved via the Verlinde formula. The final section explains Oshikawa's criterion: existence of a \( G \)-invariant Cardy boundary state diagnoses the absence of 't Hooft anomaly, illustrated with \( \mathrm{SU}(N)_k \) WZW models where center symmetry dictates \( k \in N\mathbb{Z} \) for anomaly-free gapping.
