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Abstract Overdoped cuprate superconductors are strange metals above their superconducting transition temperature. In such materials, the electrical resistivity has a strong linear dependence on temperature (T) and electrical current is not carried by electron quasiparticles as in conventional metals. Here we demonstrate that the strange metal behaviour co-exists with strongly temperature-dependent critical spin fluctuations showing dynamical scaling across the cuprate phase diagram. Our neutron scattering observations and the strange metal behaviour are consistent with a spin density wave quantum phase transition in a metal with spatial disorder in the tuning parameter. Numerical computations using a theory of spin density waves in a disordered metal yield an extended ‘Griffiths phase’ with scaling properties in agreement with experimental observations. Thus we establish that low-energy spin excitations and spatial disorder are central to the strange metal behaviour. 

The cuprate pseudogap phase displays Fermi arc spectral weight in photoemission and scanning tunneling microscopy, while recent magnetotransport observations yield evidence for the existence of hole pockets of fractional areap/8, wherepis the doping density. We present a Monte Carlo study of a thermal SU(2) lattice gauge theory which can reconcile these observations. Our simulation includes the SU(2) gauge fieldUof aπ-flux spin liquid, and a SU(2) fundamental chargeeHiggs bosonB. There is a Yukawa coupling betweenB, the fermionic spinons of the spin liquid, and the hole pockets of a fractionalized Fermi liquid. At the higher temperatures of the pseudogap, the finite-doping sign problem is evaded by including only thermal fluctuations ofBandU, while the fermions are diagonalized exactly for each boson background. Our study also yields a fractionalized description of intertwined orders at lower temperatures, including the onset ofd-wave superconductivity by the expulsion of vortices with flux $h/\left(2e\right)$, each with charge-order halos. We discuss conditions under which quantum oscillations in the density of states from hole pockets of area $p/8$could be observable in clean under-hole-doped cuprates. 

A<sc>bstract</sc> We compare different limits of the Sachdev-Ye-Kitaev model ofNcomplex fermion withp-fermion interactions. First, we compute the fermion Green’s function and free energy in the limit of largeNfollowed subsequently by the limit of largep. Next, we examine the ‘double-scaling’ limit in which the largeN,plimits are taken at fixedλ=p²/N. Earlier results on the latter limit are resummed for smallλ, and shown to match our results for the first limit. We also describe the holographic match of our results to two-dimensional Jackiw-Teitelboim gravity with an additional U(1) gauge field. 

Abstract We investigate the phase diagram of a relativistic, parametrically driven O(N)-symmetric theory coupled to a Markovian thermal bath. Our analysis reveals a rich variety of phases, including both uniform and spatially modulated symmetry-broken states, some of which feature an order parameter oscillating at half the drive frequency. When coupled to a background electromagnetic potential, these phases exhibit a Meissner effect, in the sense that the photon acquires a mass term. However, if the order parameter oscillates around a sufficiently small value, a fraction of an externally applied magnetic field can penetrate the sample in the form of a standing wave. We dub this property aMeissner polariton, that is, a collective mode resulting from the hybridization of light with order parameter oscillations. Furthermore, near the onset of symmetry breaking, strong fluctuations give rise to a superconducting-like response even in the absence of a Meissner effect or of a Meissner polariton. Our results are relevant to experiments on light-induced orders, particularly superconductivity. 

Exact numerical results for the dc magnetoconductivity tensor of the two-dimensional spatially disordered Yukawa-Sachdev-Ye-Kitaev (2D-YSYK) model on a square lattice, at first order in applied perpendicular magnetic field, are obtained from the self-consistent disorder-averaged solution of the 2D-YSYK saddle-point equations. This system describes fermions endowed with a Fermi surface and coupled to a bosonic scalar field through spatially random Yukawa interactions. The resulting local and energy-dependent fermionic self-energies are employed in the Kubo formalism to calculate the longitudinal and Hall conductivities, the Hall coefficient, the carrier mobility, and the cotangent of the Hall angle, at fixed fermion density. From the interplay between YSYK interactions and square-lattice embedding, and the non-Boltzmann frequency-dependent self-energies, we find nontrivial evolution of the magnetotransport coefficients as a function of temperature and YSYK interaction strength, notably a superlinear evolution of the Hall-angle cotangent and the inverse carrier mobility with temperature, concomitant with linear-in-temperature resistivity, in an extended crossover regime above the low-temperature marginal Fermi liquid ground state. Our model and results provide a controlled theoretical framework to interpret magnetotransport experiments, at linear order in applied magnetic field, in strange-metal phases found in strongly correlated solid-state electron systems. 

Abstract We review a theoretical framework for the cuprate superconductors, rooted in a fractionalized Fermi liquid (FL*) description of the intermediate-temperature pseudogap phase at low doping. The FL* theory predicted hole pockets each of fractional area $p/8$at hole dopingp, in contrast to the area $p/4$in spin density wave theory. Magnetotransport measurements, including observation of the Yamaji angle, show clear evidence of hole pocket quasiparticles which can tunnel coherently between square lattice layers, and are consistent with the FL* description. The FL* phase of a single-band model is described using a layer construction with a pair of ancilla qubits on each site: the Ancilla layer model (ALM). Its mean field theory yields hole pockets of area $p/8$, and matches the gapped photoemission spectrum in the anti-nodal region of the Brillouin zone. Fluctuations are described by the SU(2) gauge theory of a background spin liquid with critical Dirac spinons. A Monte Carlo study of the thermal SU(2) gauge theory transforms the hole pockets into Fermi arcs in photoemission. One route to confinement of FL* upon lowering temperature yields ad-wave superconductor via a Kosterlitz–Thouless transition of $h/\left(2e\right)$vortices, with nodal Bogoliubov quasiparticles featuring anisotropic velocities and vortices surrounded by charge order halos. An alternative route yields a charge-ordered metallic state that has quantum oscillations consistent with observations. These confinement transitions are driven by the condensation of a SU(2) fundamental Higgs field, which also provides a fractionalized description of intertwined orders. Increasing doping from the FL* phase in the ALM drives a transition to a conventional FL at large doping, passing through an intermediate strange metal regime. We formulate a theory of the FL*-FL metal-metal transition without a symmetry-breaking order parameter, using a critical quantum ‘charge’ liquid of mobile electrons in the presence of disorder, developed via an extension of the Sachdev–Ye–Kitaev model to two spatial dimensions. At low temperatures, and across optimal and over doping, we address the regimes of extended non-FL behavior by Griffiths effects near quantum phase transitions in disordered metals. Partly based on lectures by S S atBoulder School 2025, Dynamics of Strongly Correlated Electrons, 14–18 July.Lecture videos.Joint ICTP-WE Heraeus School and Workshop on Advances in Quantum Matter: Pushing the Boundaries, ICTP, Trieste, 4, 6 August 2025.Lecture videos.School on Quantum Dynamics of Matter, Light and Information, ICTP, Trieste, 18, 19 August 2025.Lecture videos.Croucher Advanced Study Institute for Fractional Chern Insulators, University of Hong Kong, 4, 5 September 2025.Lecture slides.Advanced School and Conference on Quantum Matter, ICTP Trieste, 1–12 December 2025.Lecture Notes.Lecture videos. 

Strongly correlated materials feature multiple electronic orbitals, which are crucial to accurately understanding their many-body properties. In such multiband models, quantum interference can lead to flat energy bands with large degeneracy that gives rise to itinerant magnetic phases. We report on signatures of a ferrimagnetic state realized in a Lieb lattice with ultracold fermions, characterized by antialigned magnetic moments with antiferromagnetic correlations, and concomitant with a finite spin polarization. The signatures remain robust when increasing repulsive interactions from the weakly interacting to the Heisenberg regime and emerge when continuously tuning the lattice unit cell from a square to a Lieb geometry. Our flexible approach paves the way toward exploring exotic phases, such as quantum spin liquids in kagome lattices and heavy fermion behavior in Kondo models.