An electronic nematic order that originates from superconducting fluctuation but persists above the superconducting transition temperature is often referred to as a vestigial nematic phase. Such a vestigial order belongs to the broader class of composite orders discussed in earlier literature, characterized by ordering in gauge-invariant combinations of superconducting order parameters while the individual superconducting order parameters remain disordered. These states include metallic superfluids, paired phases, and composite (charge-4⁢𝑒) superconductors. Whether and under what conditions such a vestigial phase can emerge in realistic models of nematic superconductors remains an open question. Recent analytical work [P. T. How and S. K. Yip, Phys. Rev. B 107, 104514 (2023)] concluded that vestigial nematic phases—and related mechanisms—do not appear in the widely studied models proposed for, e.g., Bi_2⁢Se₃-based candidates. To shed light on this question, we perform large-scale Monte Carlo simulations of a three-dimensional Ginzburg-Landau model of a nematic superconductor. Consistent with the findings of How and Yip, our numerical results confirm that commonly considered models do not exhibit vestigial nematic phases or nematic-fluctuation-induced charge-4⁢𝑒 superconductivity. Extending the analysis to include coupling to a gauge field, we show that vestigial nematic order can, under restrictive conditions, be stabilized through an alternative mechanism: intercomponent coupling mediated by the gauge field or the effects of strong correlations.

Understanding mechanisms of quantum ordering in strongly correlated systems remains a central challenge in condensed matter physics, with implications for designing novel quantum materials. Here, we investigate kinetic antiferromagnetism on a triangular lattice under an applied magnetic field, where spin polarons emerge as charge-magnon bound states with mutual attraction. Using large-scale diagrammatic Monte Carlo simulations, we show that this interaction drives high-temperature phase separation into charge- and magnon-rich regions, bordered by polarized Mott insulating voids. Spectral function analysis reveals a substantial energy correction from magnon interactions, indicating that these carrier-rich regions form a strongly bound charge-magnon liquid. These findings shed new light on recent experiments on MoTe_{2}/WSe_{2} moiré bilayers, underscoring kinetic magnetism as a unique pathway for strong intercarrier attraction and high-temperature quantum ordering, with potential applications in quantum materials.

In classes of Weyl semimetals where the symmetry protects nodes with higher than unit charge, the nematic Weyl liquid appears as interactions destroy this underlying symmetry. In the symmetry-broken phase, the multiple-charge nodes are split into objects of unit charge, the position of which in momentum space is determined by the nematic order parameter. We examine the phenomenology of this phase, focusing on topological edge states and Landau levels. We find that the symmetry-broken phase itself, as well as the orientation of the nematic order are identifiable from the resulting edge states. We also find that the nematic order couples to an in-plane magnetic field, indicating that it can be controlled in situ via an external field. Finally, we provide an estimate for the critical coupling where spontaneous symmetry breaking occurs for contact interaction.

Recent mean-field calculations suggest that the superconducting state of twisted bilayer graphene exhibits either a nematic order or a spontaneous breakdown of the time-reversal symmetry. The two-dimensional character of the material and the large critical temperature relative to the Fermi energy dictate that the material should have significant fluctuations. We study the effects of these fluctuations using Monte Carlo simulations. We show that in a model proposed earlier for twisted bilayer graphene there is a fluctuation-induced phase with quadrupling fermionic order for all considered parameters. This four-electron condensate, instead of superconductivity, shows a spontaneous breaking of time-reversal symmetry. Our results suggest that twisted bilayer graphene is an especially promising platform to study different types of condensates, beyond the pair-condensate paradigm.

Fermi gases and liquids display an excitation spectrum that is simply connected, ensuring closed Fermi surfaces. In strongly correlated systems such as the cuprate superconductors, the existence of open sheets of Fermi surface known as Fermi arcs indicate a distinctly different topology of the spectrum with no equivalent in Fermi-liquid theory. Here, we demonstrate a generic mechanism by which correlation effects in fermionic systems can change the topology of the spectrum. Using diagrammatic Monte Carlo simulations, we demonstrate the existence of disconnected and multiply connected excitation spectra in the attractive Hubbard model in the BCS-BEC crossover regime. These topologically nontrivial spectra are a prerequisite for Fermi arcs.

We study the stability and phenomenology of line-node semimetals in the presence of Coulomb interactions. Our results indicate a phase transition to a chiral insulating state that occurs at a finite interaction threshold, which we determine. We also compute the Landau levels for out-of-plane and in-plane magnetic fields in the symmetric and symmetry-broken phases. We find that the magnetic field couples to the chiral order parameter, implying that this degree of freedom can be manipulated in situ in experiments. Finally, we check the existence of edge states in the symmetry-broken phase. On the system's boundary, we note that the metallic “drum-head” states that exist in the symmetric phase are gapped out. However, the symmetry-broken phase permits topological defects in the macroscopic order parameter in the form of domain walls, which host metallic “interface states.” These consist of linelike gap-closings that occur on the two-dimensional interfaces.

We study the electronic structure of hole-doped transition metal dichalcogenides for small twist angles, where the on-site repulsion is extremely strong. Using unbiased diagrammatic Monte Carlo simulations, we find evidence for magnetic correlations which are driven by delocalization, and can be controlled in situ via the dielectric environment. For weak spin-orbit coupling we find that the moderately doped system becomes antiferromagnetic, while the regime of strong spin-orbit coupling features ferromagnetic correlations. We show that this behavior is accurately predicted by an analytical theory based on moment expansion of the Hamiltonian, and an analysis of corresponding particle trajectories.

Recent progress in optically trapped ultracold atomic gases is now making it possible to access microscopic observables in doped Mott insulators, which are the parent states of high-temperature superconductors. This makes it possible to address longstanding questions about the temperature scales at which attraction between charge carriers are present, and their mechanism. Controllable theoretical results for this problem are not available at low temperature due to the sign problem. In this work, we make important progress with this problem by employing worm-algorithm Monte Carlo, which allows us to obtain completely unbiased results for two charge carriers in a Mott insulator. Our method gives access to lower temperatures than what is currently possible in experiments, and provides evidence for attraction between dopants at a temperature scale that is now feasible in ultracold atomic systems. We also report on spin correlations in the presence of charge carriers, which are directly comparable to experiments.

We describe a controllable and unbiased strong-coupling diagrammatic Monte Carlo technique that is applicable to a wide range of fermionic systems and spin models. Unlike previous strong coupling methods that generally rely on the Grassmannian Hubbard-Stratonovich transformation, our construction is based on Wick's theorem and a recursive procedure to group contractions into effective connected vertices that are nonperturbative in all local physics and can be calculated exactly. The resulting expansion is described by simple diagrammatic rules that make it suitable for systematic treatment via stochastic sampling. Benchmarks against numerical linked cluster expansion display excellent agreement.

Polarons are elementary quasi-particles characterizing several interacting many-body quantum systems. The authors present an unbiased Quantum Monte Carlo simulation of a magnetic polaron in a t-J model at low-temperature, and find excellent agreement with a recent experimental realization in the framework of cold-atoms systems. Polarons are among the most elementary quasiparticles of interacting quantum matter, consisting of a charge carrier dressed by an excited background. In Mott insulators, they take the form of a dopant surrounded by a distorted spin-background. Despite the fundamental importance of polarons for the electronic structure of strongly correlated systems, access to their internal structure was only recently realized in experiments, while controllable theoretical results are still lacking due to the sign problem. Here we report unbiased high-precision data obtained from worm-algorithm Monte Carlo that reveal the real-space structure of a polaron in the t-J model deep inside the region where the sign problem becomes significant. These results are directly comparable to recent quantum gas microscopy experiments, but give access to significantly lower temperatures.