arXiv subjects
Publications and source records attributed to Ronny Thomale.
We develop a class of microscopic lattice models in which pair density wave order emerges in the asymptotically exact weak coupling limit. The underlying mechanism is due to non-symmorphic momentum symmetry implied by the models' projective space group representation of electrons. Our mechanism suggests moir\'e systems and extended s-wave altermagnets as potential hosts for pair density wave order.
Triangular-lattice quantum spin-liquid insulators are observed to undergo transitions to superconductivity under pressure or doping, and exhibit enhanced terahertz conductivity when driven by mid-infrared light. We present a general theoretical framework for the emergence of superconducting and charge-ordered phases from a U(1) Dirac spin liquid with fermionic spinons, as well as from its gapped $\mathbb{Z}_2$ and chiral descendants. Numerical studies have provided substantial evidence for these spin-liquid states. The spin-liquid phase hosts fractionalized Dirac spinons coupled to an emergent gauge field, whereas the superconducting and charge-ordered phases are conventional, with neither fractionalized excitations nor emergent gauge dynamics. The transition between these phases is driven by the Higgs condensation of spinless charge-$e$ bosonic chargons (``doublons'' and ``holons''). We show that the projective symmetry group of the Dirac spinons uniquely determines the symmetry and dispersion of the chargons, allowing us to construct an effective low-energy theory near the chargon band minima. Gauge-invariant composites of the chargon Higgs fields provide the order parameters characterizing the phases. The resulting phase diagram contains a rich variety of ordered states, including $d+id$ superconductivity, charge-density waves, bond-density waves, and pair-density waves.
We investigate the emergence of electronic order and unconventional superconductivity in M-valley moir\'e materials. Starting from a first-principles Wannier model of AB-stacked twisted SnSe2, we tackle the (gate-screened) long-ranged Coulomb interaction with functional renormalization group simulations resolving the momentum structure and energy scales of the leading Fermi surface instabilities. Upon doping an antiferromagnetic stripe state at half-filling ($\nu=3$ electrons per moir\'e unit cell) of the moir\'e flat bands, magnetic order gives way to unconventional superconductivity mediated by valley-selective spin fluctuations: Large hole doping ($\nu\approx1$) leads to weak-coupling superconductors with various pairing symmetries, while slight electron- and hole-doping ($\nu\approx2,4$) stabilizes a spin-singlet, extended s-wave state that benefits from scattering between virtual particle and hole states that are detuned from the Fermi level. These findings establish M-point moir\'e materials as a quantum simulation platform with phenomenological parallels to the class of iron pnictide superconductors.
We study an interacting kagome-lattice realization of a quadratic band-touching semimetal at 2/3 filling with onsite and nearest-neighbor repulsive interactions. Combining functional renormalization group and slave-boson approaches, we map its phase diagram from intermediate to strong coupling and uncover a hierarchy of unconventional electronic orders. The leading instabilities comprise loop-current order, spontaneous altermagnetism arising from a spin-Pomeranchuk instability, and spin-loop-current order with distinctive and largely unexplored properties. We demonstrate how the interplay of band kinematics, electronic interactions, and quantum geometry governs the selection of these phases. Our findings establish quadratic band-touching semimetals as a promising platform for unconventional symmetry breaking and suggest analogous phenomena in other parabolic semimetals.
We formulate a functional renormalization group (FRG) ansatz for correlated electron models that incorporates electronic interactions as well as electron-phonon coupling (EPC) stemming from dispersive phonon bands. Particularizing to the RG flow of the electron-electron interaction vertex, we treat phonon- and electron-mediated Fermi liquid instabilities on equal footing as we analyze tentative electronic order parameters related to charge, spin, nematicity, and superconducting pairing. We illustrate the approach at the example of Peierls-type transitions we find for the Hubbard model on the square lattice coupled to acoustic phonon bands. Our method allows to incorporate full electronic and phononic ab initio input, and thus lends itself to the analysis of electronic order from intertwined electronic interactions and EPC at a microscopically most substantiated level.
Quantum spin liquids are often introduced through a low-dimensional intuition: weak coordination and strong zero-point motion frustrate conventional magnetic order. This view has shaped much of the field, but it misses another route to quantum disorder. In many frustrated magnets, the more natural starting point is not a fluctuating version of an ordered state, but a locally constrained manifold of low-energy configurations. Within such a manifold, quantum dynamics can generate an emergent gauge theory, with fractionalized excitations and collective modes absent in ordinary magnets. Here we ask why such phases can be stable in three spatial dimensions. We argue that three-dimensional quantum spin liquids need not be regarded as fragile exceptions to the tendency of 3D magnets to order. They can arise when local constraints suppress premature order selection, coherent tunneling processes connect the constrained manifold, and the topology of gauge defects permits a deconfined regime. For compact gauge theories, three dimensions can even reverse the usual dimensional intuition: regimes that are unstable or fine-tuned in lower dimensions may become stable over finite regions of parameter space. We organize the discussion around constraint-driven Coulomb phases, weak harmonic order-by-disorder selection, and the role of spin-orbit or multipolar interactions in generating the required microscopic dynamics. We close with experimental diagnostics, candidate materials, and open theoretical questions for three-dimensional quantum spin liquids
We study the emergence of superconductivity in the one-band Hubbard model using the spin-rotation-invariant Kotliar-Ruckenstein slave-boson (SB) approach. Motivated by its intrinsically renormalized mean-field ground state, we construct an effective pairing vertex from dynamical fluctuations about the saddle point. Solving the anisotropic, frequency-dependent gap equation on the square lattice, we map the pairing instabilities across doping, interaction, temperature and real-frequency gap structure that qualitatively match experimental cuprate observations. This framework merges strong-correlation SB-type renormalizations with RPA-type pairing transparency, providing a scalable route to modeling multi-orbital superconductivity at strong coupling.
The kagome superconductor family AV3Sb5 (A=Cs, Rb, K) provides a rich platform for exploring diverse electronic symmetry breaking phenomena, including superconductivity and various forms of density wave orders. Although these compounds share the identical lattice structure in the normal state, they exhibit distinct forms of symmetry breaking upon entering the charge density wave (CDW) phase, and the microscopic origin of which remain elusive. Here, we investigate the lattice and charge degrees of freedom in AV3Sb5 using angle-resolved polarized Raman spectroscopy. Our comprehensive polarization-resolved measurements reveal that the lifting of the twofold-degeneracy of the E2g phonon mode in the CDW phase-previously reported only in CsV3Sb5 with a 3 GHz splitting-also appears ubiquitously in the other two compounds. In contrast, the collective CDW excitations exhibit markedly different polarization dependences depending on the alkali-metal species. These distinct behaviors in the lattice and charge channels provide crucial insight into the enigmatic material-dependent symmetry breaking phenomena that appear in the CDW phase. Furthermore, our experiments, together with first-principles calculations and an effective Hamiltonian model, shed light on the nature of the charge order structure in AV3Sb5 kagome superconductors.
The $\mathrm{U}(1)$ Dirac spin liquid provides a useful organizing framework for frustrated magnets: it offers an algebraic parent state from which competing orders, confinement patterns, and low-energy spectral features can be understood. Whether such a state can occur as a stable ground state of a two-dimensional spin Hamiltonian remains an open question, because monopole operators of the compact gauge field can proliferate and confine the spinons. Here we determine the symmetry quantum numbers of the fundamental monopoles of a maple-leaf-lattice Dirac spin liquid whose generic six-node regime realizes QED$_3$ with $N_f=12$ two-component Dirac fermions. The charge-one monopoles span a $924$-dimensional complex representation. In the spin-singlet, zero-momentum, zero-$C_6$-angular-momentum sector we find five complex charge-one directions, of which three are mapped to their Hermitian conjugates under time reversal. Their real and imaginary Hermitian combinations therefore supply six independent monopole perturbations that are trivial under translations, $C_6$, time reversal, and spin rotation. The Dirac spin liquid phase is thus not protected by symmetry exclusion of charge-one monopoles: its stability depends on whether these allowed perturbations are relevant in the renormalization group sense. Existing large-$N_f$ and numerical estimates of the charge-one monopole scaling dimension lie close to the relevance threshold, making the maple-leaf lattice a concrete platform for testing the stability of compact QED$_3$ in a quantum magnet. Our complete monopole classification also identifies the spin, momentum, and rotation sectors in which monopole excitations should appear, providing symmetry-resolved benchmarks for exact-diagonalization and variational tests of the $N_f=12$ Dirac spin liquid.
By means of slave-boson theory for the Hubbard model on the checkerboard lattice, we calculate dynamical altermagnetic spin susceptibilities from the metallic to the Mott-insulating regime. We track magnon dispersion and lifetime renormalization, allowing us to uncover a crossover from a chirality-selective dissipation of magnon modes to coherent yet strongly deformed chiral magnon branches across the metal insulator transition. Our formalism lends itself to a quantitative description of collective spin dynamics in correlated altermagnets.
We investigate the resilience of spinon quasiparticles in the $J_1$-$J_2$ zig-zag spin chain ($J_2>0$) from the viewpoint of momentum-space entanglement. For small $J_2$, we show that deconfined spinons survive well past the liquid-dimer transition before eventually collapsing towards the Majumdar-Ghosh point. In the highly frustrated zig-zag regime ($J_2 \gg |J_1|$), we model the system as two coupled Heisenberg chains and by Fourier transforming each subchain individually, a framework we dub the double-spinon description. While continuum field theories predict that this decoupled phase is strictly unstable to any finite inter-chain coupling, our analysis reveals that the double-spinon description remains robust over an extensive parameter regime. Notably, we find a stark asymmetry in spinon stability reflecting the underlying renormalization group flow: ferromagnetic coupling ($J_{1} < 0$) is marginally irrelevant and sustains fractionalization deep into the spiral phase, whereas antiferromagnetic coupling ($J_{1} > 0$) is marginally relevant and drives confinement much earlier. The ultimate breakdown of this fractionalized description is driven by a continuum of inter-chain excitations which manifests itself as a sharp ground-state momentum shift distinct from macroscopic thermodynamic phase boundaries. Our results establish momentum cut entanglement analysis as a tool to trace the quasiparticle resilience of spinons, as we show that treating the zig-zag Heisenberg chain as two coupled SU(2)$_1$ Wess-Zumino-Witten models provides a theoretical framework for strongly frustrated quantum magnets applicable beyond the decoupled limit.
We investigate Higgs criticality in candidate U(1) Dirac spin liquids across a family of depleted triangular lattices: the triangular, kagome, and maple-leaf geometries. For each, we identify the symmetry-allowed spinon-pairing channel connecting the U(1) state to a proximate $\mathbb{Z}_2$ spin liquid, deriving the corresponding quantum electrodynamics (QED$_3$)-Higgs theory. While the triangular and kagome lattices share a low-energy description with $N_f=4$ Dirac fermions, the maple-leaf lattice yields an analogous theory with $N_f=12$ and a distinct nodal structure where the Dirac cones can move along high-symmetry lines in momentum space instead of gapping out. Using a large-$N_{f,b}$ expansion, we compute critical exponents and the scaling dimensions of the symmetry-allowed Yukawa couplings. Although Higgs-field fluctuations and a large fermion flavor number strongly suppress the Yukawa coupling---pushing the maple-leaf lattice closer to stability than its counterparts---we find that the coupling remains relevant at leading order in all three cases, substantially reducing its scaling dimension on the maple-leaf lattice and asymptotically breaking Lorentz and conformal invariance. Ultimately, our results provide a unified framework demonstrating how the interplay between fermion flavor count and nodal geometry dictates the fate of the QED$_3$-Higgs transition.
Quantum spin liquids are commonly thought to be highly sensitive to lattice geometry, symmetry, and microscopic exchange patterns, leading to a proliferation of seemingly distinct phases across frustrated magnets. Here, we provide a framework that unifies phases that appear distinct from the viewpoint of this intuition. We postulate that the spin-$\tfrac{1}{2}$ Heisenberg antiferromagnets on the square, Shastry-Sutherland, and checkerboard lattices can realize a single unified quantum phase: a gapless $\mathbb{Z}_2$ Dirac quantum spin liquid, despite their markedly different lattice symmetries. Using a systematic projective symmetry group analysis, we identify a checkerboard spin-liquid state that completes a closed set of adiabatically connected phases linking the well-established square-lattice and Shastry-Sutherland spin liquids. Crucially, we show that this lattice-level unification is mirrored exactly in the continuum description. In all three cases, the spin liquids descend from a common SU(2) $\pi$-flux parent state and are governed by the same gauge theory, QED$_3$ with two Dirac fermion flavors coupled to two adjoint Higgs fields. As a result, we postulate that the surrounding N\'eel and valence-bond-solid phases and their confinement transitions admit a unified interpretation within the framework of deconfined quantum criticality. More broadly, our results suggest that quantum spin liquids are most fundamentally classified not by lattice geometry or microscopic couplings, but by the emergent gauge theory and its Higgs structure. Distinct frustrated lattices can thus host the same quantum phase and exhibit the same confinement mechanisms, despite substantial differences in their microscopic symmetries.
We investigate the emergence of altermagnetic (AM) phases on the square-kagome lattice. Our analysis reveals that matrix element effects due to an orthogonal sublattice weight decomposition of Fermi level eigenstates known as sublattice interference enable decoupled magnetic ordering tendencies on distinct sublattices. Depending on which sublattice undergoes a magnetic instability, we identify a $d_{xy}$-type AM phase and a $d_{x^{2}-y^{2}}$-type AM phase originating from different sublattice polarization patterns. Using the Kotliar-Ruckenstein slave boson formalism we explore the stability of these AM phases as a function of interaction strength. Our findings demonstrate that sublattice-selective magnetic instabilities provide a versatile route to engineer the nature of AM order.
We propose metal-organic frameworks (MOFs) as tunable platforms for nonlinear Hall responses. A universal analytical downfolding scheme maps $C_3$-symmetric frameworks onto star- and honeycomb-lattice models, reproducing first-principles Dirac features. Spin-orbit coupling and broken inversion symmetry gap the Dirac cones, generating Berry-curvature hot spots. Symmetry analysis identifies tailored synthetic pathways, including linker design, as intrinsic routes to engineer nonlinear Hall transport beyond strain and substrate control.
Large-spin two-dimensional magnets are generally expected to develop conventional long-range order once the dominant exchange scale becomes appreciable. The layered spin-$3/2$ maple-leaf compound Na$_2$Mn$_3$O$_7$ defies this expectation: despite sizable antiferromagnetic interactions and no evident disorder, it exhibits no magnetic ordering and displays two well-separated thermodynamic crossover scales. We show that this behavior originates from a crystallography-driven molecularization of the magnetic degrees of freedom. The low-symmetry structure partitions the Mn sublattice into inequivalent exchange pathways, generating a pronounced hierarchy that nearly isolates antiferromagnetic hexagons. Magnetic correlations therefore develop in two stages: first within individual hexagons at a scale set by the dominant exchange, and only at much lower temperatures do frustrated inter-hexagon couplings attempt to establish coherence across the lattice. While isolated hexagons reproduce the two-step thermodynamic structure, the experimentally relevant temperature scales emerge only once the hexagons are embedded in the frustrated two-dimensional network. The resulting quantum ground state is magnetically disordered, characterized by strong intra-hexagon correlations and rapidly decaying inter-hexagon correlations. These results identify crystallographic inequivalence as a materials-level mechanism for stabilizing molecularized and quantum-disordered states even in large-spin two-dimensional magnets.
Twisted photonic lattices that form moir\'e superlattices have attracted significant attention owing to their unique properties, such as strong field confinement and high-quality factors, in which the localized optical modes can serve as efficient light sources. However, in conventional moir\'e lattices, the emission direction of confined modes is typically fixed, and achieving a broad range of emission angles through simple modulation remains a significant challenge. Here, we design and fabricate single-layer moir\'e photonic lattices into cylindrical geometries using a nanomembrane origami technique. This approach enables wide-angle localized-mode emission while maintaining stable single-mode operation and excellent spectral uniformity. The moir\'e supercells support localized flat-band modes under various effective twist angles, resulting in the observation of periodic localized-mode emission over a wide range of azimuthal angles. Our research provides an approach for developing moir\'e light sources on curved surfaces, offering significant potential in applications that demand spatial light control, including three dimensional imaging, light detection and ranging, and topological states manipulation.
We present a fermionic gauge theory for deconfined quantum criticality on the Shastry-Sutherland lattice and reveal its shared low-energy field-theoretic structure with the square lattice. Starting from an SU(2) $\pi$-flux parent state, we construct a continuum theory of Dirac spinons coupled to an SU(2) gauge field and adjoint Higgs fields whose condensates drive transitions to a staggered-flux U(1) spin liquid and a gapless $\mathbb{Z}_{2}$ Dirac spin liquid. While the Shastry-Sutherland lattice permits additional symmetry-allowed fermion bilinears compared to the square lattice, the quantum field theories are identical up to additional irrelevant terms. Consequently, the Higgs potential structure and the leading low-energy theory coincide with the square-lattice case at the quantum critical point. The SO(5) critical point is expected to realize conformal deconfined criticality: we analyze it in a large flavor expansion, calculate its critical exponents, and identify the Yukawa coupling between the fermions and Higgs fields as the relevant perturbation that destabilizes it, consistent with pseudocritical behavior observed in recent Monte Carlo studies. We show that the emergent SO(5) order parameter acquires a large anomalous dimension at the critical point, leading to strongly enhanced N\'eel and VBS susceptibilities-a hallmark of fermionic deconfined quantum criticality consistent with numerical studies. Our results place recent numerical evidence for a gapless $\mathbb{Z}_{2}$ Dirac spin liquid on the Shastry-Sutherland lattice within a controlled field-theoretic framework and demonstrate that fermionic deconfined criticality on the square lattice-including critical exponents and stability-extends to frustrated lattices with reduced symmetry.