The interplay between quantum and thermal fluctuations can induce rich phenomena at finite temperatures in strongly correlated fermion systems. Here we report a numerically exact auxiliary-field quantum Monte Carlo (AFQMC) study for the finite-temperature properties of three-dimensional repulsive Hubbard model at half-filling. We concentrate on the complete temperature-interaction strength phase diagram of the model, which contains the low-temperature antiferromagnetic (AFM) long-range ordered phase and metal-insulator crossover (MIC) in the paramagnetic phase. Enabling access to unprecedented system sizes up to ${20}^3$, we achieve highly accurate results of the Néel transition temperature for representative values of onsite interaction $U$ via finite-size analysis of AFM structure factor. To quantitatively characterize the MIC above the Néel transition, we have developed efficient schemes to compute the thermal entropy versus $U$ at fixed temperature and to calculate the $U$ derivative of double occupancy in AFQMC simulations. Then combining variously thermodynamic and dynamical observables, we establish an efficient scheme to precisely determine the boundaries for the MIC by cross-checking different observables. We also demonstrate the temperature dependence of many commonly used observables. Away from half-filling, we explore the behavior of the sign problem and AFM spin correlation versus hole doping, and demonstrate the persistence of Néel AFM ordered phase to finite doping with limited results.

Landau levels play a key role in theoretical models of the quantum Hall effect. Each Landau level is degenerate, flat, and topologically nontrivial. Motivated by Landau levels, we study tight-binding Hamiltonians whose energy levels are all flat. We demonstrate that in two dimensions, for such Hamiltonians, the flat bands must be topologically trivial. To that end, we show that the projector onto each flat band is necessarily strictly local. Our conclusions do not need the assumption of lattice translational invariance.

The effect of measurements on interacting fermionic systems with particle-number conservation, whose dynamics is governed by a time-independent Hamiltonian, is studied. We develop Keldysh field-theoretical framework that provides a unified approach to observables characterizing entanglement and charge fluctuations. Within this framework, we derive a replicated Keldysh nonlinear sigma model (NLSM), incorporating boundary conditions specifically designed to produce generating functions for charge cumulants and entanglement entropies directly in the NLSM language. By using the renormalization-group approach for the NLSM, we determine the phase diagram and the scaling of physical observables. Crucially, the interaction-induced terms in the NLSM action reduce its symmetry, dramatically affecting the physics of the problem. First, this leads to the “information-charge separation”, where charge cumulants get decoupled from entanglement entropies. Second, the interaction stabilizes the volume-law phase for the entanglement. Third, for spatial dimensionality $d=1$, the interaction stabilizes the phase with logarithmic growth of charge cumulants (in the thermodynamic limit). Thus, in the presence of interaction, there are measurement transitions in any $d$, at variance with free fermions, for which a $d=1$ system is always in the area-law phase. Analytical results are supported by numerical simulations using time-dependent variational principles for matrix product states, which, in particular, confirm the separation of information and charge as a hallmark of the delocalized phase.

Fractional Chern insulators (FCI) with fractionally quantized Hall conductance at fractional fillings and an extended quantum anomalous Hall (EQAH) crystal with an integer quantized Hall conductance over an extended region of doping were recently observed in pentalayer graphene. One particularly puzzling observation is the transition between the EQAH and FCI regimes, driven either by temperature or electrical current. Here we propose a scenario to understand these transitions based on the topologically protected gapless edge modes that are present in both the FCI and EQAH phases and should be most relevant at temperature scales below the energy gap. Our consideration is based on the simple assumption that the edge velocity in FCI is smaller than that in EQAHE and thus contributes to a higher entropy. We further argue that domains with opposite fractionally quantized Hall conductance are ubiquitous in the devices due to disorder, which gives rise to a network of edge modes. The velocity of the edge modes between domains is further reduced due to edge reconstruction. The edge velocity can also be reduced by current when the occupation of the edge mode approaches the gap edge. The edge entropy therefore drives the transition from EQAH to FCI either by temperature or current at a nonzero temperature.

Fractionally charged magnetoelectron (anyon) complexes formed by the creation of magnetic flux quanta vortices in single-electron states are detected in a three-electron Wigner quantum dot $\mathrm{InP}/{\mathrm{GaInP}}_2$ (Wigner-Seitz radius $r_{\mathrm{s}}=2.5$) using low-temperature (30 K) magnetophotoluminescence spectroscopy measurements. In zero magnetic field, vortices induce their own field $\widehat{\mathcal{B}}$, so such vortices and corresponding complexes can be identified as elementary magnetic poles and Dirac anyons (DAs), respectively. In this quantum dot, DA structures with an average number of vortices per electron from 3 to $\frac{2}{5}$ and $\widehat{\mathcal{B}}$ from −7 to 0 T were identified in the magnetic field range $0-10\mathrm{T}$. Spectral data and calculations of electron density distributions using the configurational interaction approach show that at $B<7$ T the structures are triangular molecules with a side of $\sim 50$ nm and a DA size of $\sim 30$ nm, whereas at higher field it is a DA puddle of $\sim 80$ nm, and thus the molecular states are suppressed by the strong magnetic field. The recognition of magnetoelectron complexes as DAs and the observation of the molecular-puddle transition in the DA composites induced by a magnetic field in $\mathrm{InP}/{\mathrm{GaInP}}_2$ Wigner quantum dots are important steps in the investigation of these unique magnetoelectronic quantum states that can be exploited in anyon-based quantum computing. We also show the connection of DAs with the quantum Hall effect states, which clarifies unresolved issues in their description.

A ferroic alignment of a time-reversal-even axial vector, which is called the ferroaxial ordered state, is identified by the spontaneous rotational distortion of the lattice structure to break vertical mirror symmetry. We theoretically investigate what happens in the electronic structure once ferroaxial ordering occurs by analyzing a tetragonal $d\text{−}p$ cluster model with transition metal oxide in mind. By adopting the symmetry-adapted multipole representation, we elucidate the emergent cross-product form of the spin-orbit coupling by the interplay between the atomic spin-orbit coupling and the $d\text{−}p$ hybridization according to vertical mirror symmetry breaking, which corresponds to the electronic order parameter of ferroaxial ordering.

Non-Hermitian skin localization, as a hallmark feature unique to non-Hermitian systems, has attracted enormous interests. Recent theoretical work reveals that the coupling between a nonreciprocal chain with skin-localized states and a Hermitian chain with extended states can induce a phase with a pseudo-mobility-edge (PME) under the weak interchain couplings. However, such a phenomenon remains to be confirmed in experiments. Here, we experimentally realize the non-Hermitian PME by designing a hybridized non-Hermitian circuit ladder. Through measuring the admittance spectrum and eigenstates, the transition from the PME phase to the skin-localized phase for the open boundary condition and to the extended phase for the mixed boundary condition (MBC) are, respectively, successfully observed with increasing the ac current feed frequency. Moreover, these localization behaviors are also manifested by measuring the voltage response to a local current feed. In addition, we observe the bulk-boundary correspondence between the spectral winding topology and the PME transition under the MBC. Our paper provides a fertile platform to study unconventional non-Hermitian localization.

On flat bands of the magic-angle twisted bilayer graphene, exotic correlation physics unfolds. Phonons, through mediating an effective electron-electron interaction, can play a crucial role in selecting various electronic phases. In this study, we derive the full electron-phonon coupling (EPC) vertex from the microscopic tight-binding lattice, and identify the significance of each phonon mode. We then project the EPC vertices onto the topological heavy fermion (THF) basis [Z.-D. Song and B. A. Bernevig, Phys. Rev. Lett. 129, 047601 (2022)], and show that an anti-Hund's interaction ${\widehat{H}}_{\mathrm{A}}$ is induced on each moiré-scale local $f$ orbital, with strengths 1 to 4 meV. We analyze the phonon-induced multiplet splittings, which can significantly affect the local correlation. As an example, we elaborate on the phonon-favored symmetry-breaking orders at even-integer fillings. Through systematic self-consistent Hartree-Fock calculations, we uncover a tight competition between $\mathrm{\Gamma }$-phonon-favored orbital orders, $K$-phonon-favored intervalley coherent orders, and the kinetic and Coulomb-favored orders. Contrary to EPC, the carbon atom Hubbard repulsion induces an on $f$-site Hund's interaction ${\widehat{H}}_{\mathrm{H}}$ with strengths 1 to 3 meV that partly counteracts the effect of ${\widehat{H}}_{\mathrm{A}}$. The combined influence of ${\widehat{H}}_{\mathrm{A},\mathrm{H}}$ on the multiplet splitting and symmetry-breaking states is discussed. In the end, we explore the possibility of finding an exotic Dirac semimetal formed solely by $c$ electrons at the charge-neutrality point, while $f$ impurities exhibit a symmetric Mott gap by forming nondegenerate singlets under ${\widehat{H}}_{\mathrm{A},\mathrm{H}}$. Experimental features that distinguish such a state are discussed.

Motivated by the recently discovered high-$T_c$ nickelate superconductor ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$, we investigate the $S_{\pm }$-wave superconductivity (SC) in a two-dimensional Hubbard model on a square lattice that consists of two layers of hybridizing $d_{x^2\text{−}{y}^2}$ and $d_{z^2}$ orbitals. Employing cluster dynamical mean-field theory, we establish phase diagrams resolving the crucial dependence of superconducting $T_c$ on electron hybridization $V$ between $d_{x^2\text{−}{y}^2}$ and $d_{z^2}$ orbitals at the same layer and on hopping $t_{\perp }$ between two $d_{z^2}$ orbitals at different layers. Here, $V$ and $t_{\perp }$ are presumably linked to the pairing phase coherence and the pairing glue of the system, respectively. Our result in general favors a two-component theory explanation of SC in a composite system. The influence of the pseudogap effect and Hund's coupling on SC are discussed as well as the implication of our result to the understanding of ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ SC.

Altermagnetism, a new phase of collinear spin-order sharing similarities with antiferromagnets and ferromagnets, has introduced a new guiding principle for spintronic and thermoelectric applications because of its direction-dependent magnetic properties. Fulfilling the promise to exploit altermagnetism for device design depends on identifying materials with tuneable transport properties. The search for intrinsic altermagnets has so far focused on the role of anisotropy in the crystallographic symmetries and in the band structure. Here, we present a different mechanism that approaches this goal by leveraging the interplay between a Hubbard local repulsion and the itinerant magnetism given by the presence of van Hove singularities. We show that altermagnetism is stable for a broad range of interactions and dopings and we focus on tunability of the spin-charge conversion ratio.

We present a bunch of phenomena stemming from the pair spin-orbit interaction (PSOI), which does not rely on structure inversion asymmetry but instead arises from Coulomb fields of interacting electrons in materials with a strong Rashba effect. First, PSOI can induce $p$-wave superconducting order without the need for any mediators of attraction. Depending on the sign and strength of the PSOI coupling, two distinct superconducting phases emerge in 3D systems, analogous to the A and B phases observed in superfluid ${}^3\mathrm{He}$. In contrast, 2D systems exhibit $p^x\pm i{p}^y$ order parameter, leading to the time-reversal-invariant topological superconductivity. Second, a sufficiently strong PSOI can induce ferromagnetic ordering. It is associated with a deformation of the Fermi surface, which eventually leads to a Lifshitz transition from a spherical to a toroidal Fermi surface, with a number of experimentally observable signatures. Finally, in sufficiently clean Rashba materials, ferromagnetism and $p$-wave superconductivity may coexist. This state resembles the ${\mathrm{A}}_1$ phase of ${}^3\mathrm{He}$, yet it may avoid nodal points due to the toroidal shape of the Fermi surface.

The multiscale entanglement renormalization ansatz (MERA) is a hierarchical class of tensor network states motivated by the real-space renormalization group. It is used to simulate strongly correlated quantum many-body systems. For prominent MERA structures in one and two spatial dimensions and different optimization strategies, we determine the optimal scaling of contraction costs as well as corresponding contraction sequences and algorithmic phase diagrams. This is motivated by recent efforts to employ MERA in hybrid quantum-classical algorithms, where the MERA tensors are Trotterized, i.e., chosen as circuits of quantum gates, and observables as well as energy gradients are evaluated by sampling causal-cone states. We investigate whether tensor Trotterization and/or variational Monte Carlo (VMC) sampling can lead to quantum-inspired classical MERA algorithms that perform better than the traditional optimization of full MERA based on the exact evaluation of energy gradients. Algorithmic phase diagrams indicate the best MERA method depending on the scaling of the energy accuracy and the optimal number of Trotter steps with the bond dimension. The results suggest substantial gains due to VMC for two-dimensional systems.

This Letter establishes a Floquet engineering framework in which coherent high frequency light with a time dependent amplitude can be used to parametrically excite and amplify THz plasmons, mirror plasmonic wave packets in time, and generate momentum-gapped plasmonic band structures, entangled plasmon pairs, and THz radiation in two dimensional Dirac systems. Our results show how low frequency plasmons can be coherently excited and manipulated without the need for THz light.

Understanding the extent and role of inhomogeneity is a pivotal challenge in the physics of cuprate superconductors. While it is known that structural and electronic inhomogeneity is prevalent in the cuprates, it has proven difficult to disentangle compound-specific features from universally relevant effects. Here we combine advanced neutron and x-ray diffuse scattering with numerical modeling to obtain insight into bulk structural correlations in ${\mathrm{HgBa}}_2{\mathrm{CuO}}_{4+\delta }$. This cuprate exhibits a high optimal transition temperature of nearly 100 K, pristine charge-transport behavior, and a simple average crystal structure without long-range structural instabilities, and is therefore uniquely suited for investigations of intrinsic inhomogeneity. We uncover diffuse reciprocal-space patterns that correspond to prominent nanoscale correlations of atomic displacements perpendicular to the ${\mathrm{CuO}}_2$ planes. The real-space nature of the correlations is revealed through three-dimensional pair distribution function analysis and complementary numerical refinement. We find that relative displacements of ionic and ${\mathrm{CuO}}_2$ layers play a crucial role, and that the structural inhomogeneity is not directly caused by the presence of conventional point defects. The observed correlations are therefore intrinsic to ${\mathrm{HgBa}}_2{\mathrm{CuO}}_{4+\delta }$, and thus likely important for the physics of cuprates more broadly. It is possible that the structural correlations are closely related to the unusual superconducting fluctuations and Mott-localization in these complex oxides. As advances in scattering techniques yield increasingly comprehensive data, the experimental and analysis tools developed here for large volumes of diffuse scattering data can be expected to aid future investigations of a wide range of materials.

Quantum dots are semiconductor nanostructures where particle motion is confined in all three spatial dimensions. Since their first experimental realization, nanocrystals confining the quanta of polarization waves, termed excitons, have found numerous applications in fields ranging from single photon sources for quantum information processing to commercial displays. A major limitation to further extending the range of potential applications has been the large inhomogeneity in, and lack-of tunability of, exciton energy that is generic to quantum dot materials. Here, we address this challenge by demonstrating electrically defined quantum dots for excitons in monolayer semiconductors where the discrete exciton energies can be tuned using applied gate voltages. Resonance fluorescence measurements show strong spectral jumps and blinking of these resonances, verifying their zero-dimensional nature. Our work paves the way for realizing quantum confined bosonic modes where nonlinear response would arise exclusively from exciton-exciton interactions.

In spatially uniform, but time-dependent dielectric media with equal electric and magnetic response, classical electromagnetic waves propagate exactly like in empty, flat space with transformed time, called conformal time, and so do quantum fluctuations. In empty, flat space the renormalized vacuum energy is exactly zero, but not in time-dependent media, as we show in this paper. This is because renormalization is local and causal, and so cannot compensate fully for the transformation to conformal time. The expanding universe appears as such a medium to the electromagnetic field. We show that the vacuum energy during cosmic expansion effectively reduces the weights of radiation and matter by characteristic factors. This quantum buoyancy naturally resolves the Hubble tension, the discrepancy between the measured and the inferred Hubble constant, and it might resolve other cosmological tensions as well.

Fractional quantum Hall states at a half-filled Landau level are believed to carry an integer number $\mathcal{C}$ of chiral Majorana edge modes, reflected in their thermal Hall conductivity. We show that this number determines the primary series of Abelian fractional quantum Hall states that emerge above and below the half-filling point. On a particular side of half filling, each series may originate from two consecutive values of $\mathcal{C}$, but the combination of the series above and below half filling uniquely identifies $\mathcal{C}$. We analyze these states both by a hierarchy approach and by a composite fermion approach. In the latter, we map electrons near a half-filled Landau level to composite fermions at a weak magnetic field and show that a bosonic integer quantum Hall state is formed by pairs of composite fermions and plays a crucial role in the state's Hall conductivity.

Electrons can organize themselves into charge-ordered states to minimize the effects of long-ranged Coulomb interactions. In the presence of a lattice, commensurability constraints lead to the emergence of incompressible Wigner-Mott insulators at various rational electron fillings, $\nu =p/q$. The mechanism for quantum fluctuation-mediated melting of the Mott insulators with increasing electron kinetic energy remains an outstanding problem. Here, using matrix product state techniques, we analyze the bandwidth-tuned transition out of the Wigner-Mott insulator at $\nu =1/5$ in an extended Hubbard model on infinite cylinders of varying circumference. For the two-leg ladder, the transition from the Mott insulator to the Luttinger liquid proceeds via a distinct intermediate phase with gapless Cooper pairs and gapped electronic excitations. The resulting Luther-Emery liquid is the analog of a strongly fluctuating superconductor. We place these results in the context of a low-energy bosonization based theory for the transition. On the five-leg cylinder, we provide numerical evidence for a direct continuous transition between the Wigner-Mott insulator and a metallic phase across which the spin and charge gaps vanish simultaneously. We comment on the connections to ongoing experiments in dual-gated bilayer moiré transition metal dichalcogenide materials.

A striking series of experiments have observed superconductivity in Bernal-stacked bilayer graphene (BBG) when the energy bands are flattened by applying an electrical displacement field. Intriguingly, superconductivity manifests only at nonzero magnetic fields, or when spin-orbit coupling is induced in BBG by coupling to a substrate. We present detailed functional renormalization group and random-phase approximation calculations that provide a unified explanation for the superconducting mechanism in both cases. Both calculations yield a purely electronic $p$-wave instability of the Kohn-Luttinger type. The latter can be enhanced either by magnetic fields or Ising spin-orbit coupling, naturally explaining the behavior seen in experiments.

We study the interplay of the structural phase transition, flat electronic band dispersion, and metal-to-insulator transition (MIT) in the parent compounds of the Ru-pnictide superconductors by using first-principles calculations. Our electron and phonon calculations reveal that Ru(P,As) undergo MIT accompanied by orthorhombic to monoclinic distortion at low temperature, but RuSb stays orthorhombic and metallic in agreement with the experimental findings. It is demonstrated that electronic correlation, as treated in $\mathrm{DFT}+U$, $\mathrm{DFT}+\mathrm{Gutzwiller}$, and dynamical mean-field theory (DMFT), cannot induce MIT in the undistorted crystal structure. We find that, although small monoclinic distortion can remove the van Hove singularity at the Fermi level, it does not immediately gap out the Fermi surface and a large value of monoclinic distortion is necessary for a clear MIT, suggesting the possibility of an intermediate pseudogapped monoclinic metallic phase. Furthermore, we predict a light-induced two-step insulator-to-metal and structural transitions in the monoclinic phases of RuP and RuAs, which can be tested in future ultrafast pump-probe experiments as an alternative ideal playground to ${\mathrm{VO}}_2$.