Strange Metals Traced to Bad Metallicity and Quantum Statistics of Charge Carriers

Strange metals are among the most perplexing states of matter in modern condensed matter physics. Found most famously in the normal state of high-temperature superconducting cuprates, they defy the rules that govern ordinary metals. In a conventional Fermi liquid, electrons behave as long-lived quasiparticles whose scattering rate grows with the square of temperature, and whose conductivity is limited by well-understood collision processes. In a strange metal, by contrast, the electrical resistivity rises linearly with temperature, quasiparticles lose their identity, and the scattering rate appears to approach a universal limit set only by Planck’s constant and the temperature itself. For nearly four decades, the microscopic origin of this behaviour has remained one of the great unsolved puzzles of the field.

A new numerical study published in Nature Physics by Simone Fratini, Ivan Duchemin, Arnaud Ralko and Sergio Ciuchi now offers a strikingly simple answer. Working within the two-dimensional t–J model, the canonical minimal model of doped Mott insulators used to describe cuprate superconductors, the team shows that strange metallicity is not an exotic phase requiring special ingredients. Instead, it emerges pervasively across the temperature-doping phase diagram whenever antiferromagnetic order is suppressed. The strange metal, in their results, is the natural descendant of the bad metal that underlies it, and its hallmark properties follow from the quantum statistics of the charge carriers rather than from any special temperature dependence of the processes that scatter them.

The bad metal concept, introduced in the early 2000s, describes a regime in which the electrical resistivity exceeds the Mott–Ioffe–Regel limit, the value at which an electron’s mean free path becomes comparable to its own wavelength. In such a regime, the very notion of a well-defined quasiparticle travelling between collisions breaks down, and transport must be understood through more general principles of quantum diffusion. Bad metallicity had been observed in numerical studies of doped Mott insulators for years, but its relationship to the strange metal phenomenology of the cuprates, with its linear resistivity and Planckian dissipation, remained ambiguous. The new work argues that the two are, in a precise sense, the same phenomenon viewed at different levels of description.

The technical achievement that makes this conclusion possible lies in recent improvements to the finite-temperature Lanczos method, a numerically exact technique for computing the thermodynamic properties of strongly correlated lattice models at finite temperature. The Lanczos approach works by iteratively building a small set of basis vectors that span the low-energy part of the Hilbert space, allowing accurate evaluation of correlation functions without ever handling the exponentially large full space. Recent methodological advances, building on decades of development since the original finite-temperature Lanczos work of the 1990s, now enable exact calculations at low temperatures and with high spectral resolution, precisely the regime where strange metal behaviour lives and where earlier approximations faltered.

Using this machinery, the researchers computed both the direct-current and the frequency-dependent conductivity of the two-dimensional t–J model across a broad range of temperatures and dopings. The t–J model describes holes moving through an antiferromagnetic background of spin-one-half particles, with a superexchange coupling J between neighbouring spins and a hopping amplitude t that is strongly constrained by the no-double-occupancy condition. This constraint, a remnant of the large on-site repulsion of the underlying Hubbard model, is what makes the model so difficult and so rich. It is also, according to the new results, what makes it strange: the interplay of quantum statistics and the constrained motion of carriers produces transport that looks Planckian without requiring any exotic scattering mechanism.

A central question in the strange metal literature concerns the origin of Planckian relaxation, the observation that the scattering time in these materials is of order ħ divided by the Boltzmann constant times temperature, the fastest timescale that quantum mechanics permits for a thermal system. Some theorists have proposed that Planckian behaviour signals proximity to a quantum critical point, where fluctuations occur at all scales and times. Others have pointed to spatially random interactions, to spin fluctuations, or to specific scattering channels as the culprit. The new study addresses this question directly by extending the analysis into the frequency and time domains, where the dynamics of the charge response can be watched as it unfolds rather than merely inferred from the final resistivity.

What emerges from this time-resolved picture is that Planckian behaviour is rooted in the quantum statistical nature of the charge response itself. The carriers in the doped antiferromagnet are incoherent from the outset, and their transport is governed by the statistical mechanics of a dense quantum fluid rather than by the collision history of individual particles. The temperature dependence of the scattering processes, which in conventional thinking would determine the resistivity, turns out to play a secondary role. In effect, the strange metal does not become strange because something unusual starts scattering its electrons at high temperatures; it is strange because the carriers were never the well-behaved quasiparticles of Fermi liquid theory in the first place.

This reframing has significant implications for how physicists interpret experiments on the cuprates and related materials. The linear-in-temperature resistivity observed over wide doping ranges in compounds such as La2−xSrxCuO4 and Bi-based cuprates has often been treated as a fingerprint of a specific mechanism, to be isolated and identified. If the new numerical results are a faithful guide, the linear resistivity instead reflects a generic property of doped Mott insulators once long-range magnetic order gives way to a quantum paramagnet. The experimental phase diagrams of the cuprates, in which the strange metal region tracks the suppression of antiferromagnetism and the pseudogap boundary, are consistent with this picture, and recent measurements of spin-charge correlations at the onset of the pseudogap add further context for testing it.

The study also connects to a broader theoretical programme aimed at understanding transport in systems where quasiparticles fail. Previous work on the Hubbard model, on extremely correlated Fermi liquid theory, and on random-interaction models of strange metals has each highlighted different aspects of non-quasiparticle transport. By demonstrating that a single, well-defined minimal model reproduces the full phenomenology, from bad metallicity at high temperatures to Planckian strange metal behaviour at lower temperatures, the new results provide a unifying numerical benchmark against which analytical theories can be tested. The authors have made both their data and their code publicly available on GitHub, lowering the barrier for other groups to verify and extend the calculations.

For the field of quantum materials, the message is both humbling and clarifying. The strange metal, the state that parents high-temperature superconductivity and has resisted explanation since the discovery of the cuprates in 1986, may not require new particles, hidden criticality, or exotic interactions. It may simply be what a strongly correlated quantum fluid looks like when the usual quasiparticle picture is abandoned and the quantum statistics of the carriers are taken seriously. If further work confirms that the t–J model captures the essential physics, the path toward a complete theory of the cuprates becomes clearer: understand the constrained quantum statistics of doped antiferromagnets, and the strange metal, along with perhaps the superconductivity that emerges from it, will follow. The puzzle is far from solved, but the new results suggest that the answer may have been hiding in one of the oldest and simplest models in the theorist’s toolkit.

Subject of Research: The microscopic origin of strange metal behaviour and Planckian transport in doped Mott insulators

Article Title: Strange metal behaviour from underlying bad metallicity

Article References: Fratini, S., Duchemin, I., Ralko, A., & Ciuchi, S. (2026). Strange metal behaviour from underlying bad metallicity. Nature Physics. https://doi.org/10.1038/s41567-026-03441-x

Image Credits: AI Generated

DOI: 10.1038/s41567-026-03441-x

Keywords: strange metal, bad metal, Planckian dissipation, t–J model, cuprates, high-temperature superconductivity, Mott insulator, finite-temperature Lanczos method, quantum statistics, antiferromagnetism, electrical resistivity, strongly correlated electrons