Abstract The doped quantum spin liquid on the kagome lattice provides a fascinating platform to explore exotic quantum states, such as the reported holon Wigner crystal at low doping. By extending the doping range to δ = 0.027-0.36, we study the kagome-lattice t - J model using the state-of-the-art density matrix renormalization group calculation. On the L y = 3 cylinder ( L y is the number of unit cells along the circumference direction), we establish a quantum phase diagram with increasing doping level. In addition to the charge density wave (CDW) states at lower doping, we find an emergent Fermi-liquid-like phase by melting the holon Wigner crystal at δ ≈ 0.15, which is characterized by suppression of charge density oscillation and power-law decay of various correlation functions. On the wider L y = 4 cylinder, the bond-dimension extrapolated correlation functions also support such a Fermi-liquid-like state, suggesting its stability with increasing system size. In a narrow doping range near δ = 1/3 on the L y 3 cylinder, we find a state with an exponential decay of single-particle correlation but the other correlation functions preserving the features in the Fermi-liquid-like phase, which may be a precursor of a superconducting state. Nevertheless, this peculiar state near δ = 1/3 disappears on the L y 4 cylinder, implying a possible lattice size dependence. Our results reveal a quantum melting from a holon Wigner crystal to a Fermi-liquid-like state with increasing hole density, and suggest a doping regime to explore superconductivity for future study.

Abstract Calculations combining density functional theory (DFT) and dynamical mean-field theory (DMFT) for transition metal (TM) oxides and similar compounds usually focus on improving the description of the TM d states. Here, we emphasize the importance of also accounting for corrections of the ligand p states. We demonstrate that focusing exclusively on improving the description of the TM d states results in difficulties to obtain the correct insulating behavior for a variety of materials, and requires to use values for the local interaction parameters that are inconsistent with values obtained using, e.g ., the constrained random phase approximation (cRPA). We demonstrate that, to a large part, these inconsistencies arise from using local/semi-local DFT as starting point for computing interaction parameters, and we show that applying a simple empirical correction to the low energy states not included in the correlated subspace results in improved values for the interaction parameters that then allow to obtain the correct insulating behavior. Moreover, we show that applying an approximate but realistic Hartree-Fock-like correction specifically to the O p orbitals, when they are explicitly included in the DMFT subspace, significantly improves the quantitative accuracy of the DFT+DMFT description for prototypical Mott insulators, including LaTiO 3 , LaVO 3 , and the perovskite rare-earth nickelates (RNiO 3 ).

Mott insulators are a unique class of materials whose insulating state originates from strong electron-electron correlations: the interactions localize charge carriers, and the resulting on-site Coulomb repulsion opens a charge gap, fundamentally different from conventional insulators, making these systems an exceptional platform for exploring exotic physical phenomena. Significantly, the interplay between strong correlations and charge transfer not only stabilizes the antiferromagnetic ground state but also endows the material with enriched properties, particularly in optics. Herein, we demonstrate a 2D antiferromagnetic charge-transfer Mott insulator, Vanadium Oxychloride (VOCl), which shows giant third-harmonic generation (THG) anisotropy (ρTHG = Ix/Iy, where Ix and Iy represent the THG intensities corresponding to the excitation polarization parallel to crystal’s x- and y-axes), with ρTHG reaching up to 187 at 1280 nm excitation wavelength. Notably, it is the highest THG anisotropic ratio within the van der Waals materials family. The nonlinear anisotropy is further modulated across a broadband infrared (IR) excitation wavelength range from 2028 to 1280 nm, during which ρTHG rises from 2.6 to 187, corresponding to a 72-fold enhancement relative to its value at 2028 nm. Additionally, VOCl demonstrates layer-independent third-order susceptibilities (χ(3) ~ 10-19 m2/V2) and band structures attributed to its extremely weak interlayer electronic coupling. Moreover, the colossal THG anisotropic ratio in 2D VOCl can be ascribed to the synergistic effect of the correlated charge-transfer Mott insulator behavior and intrinsic C3 symmetry breaking, as supported by theoretical calculations. The colossal nonlinear optical anisotropy in 2D VOCl positions it as an excellent candidate for nanophotonic and optoelectronic applications, enabling next-generation nanodevices based on 2D correlated Mott insulators.

Bose-Fermi mixtures can be realized in semiconductor heterostructures, with bosons as excitons and fermions as dopant charges. However, the complexity of these hybrid systems challenges understanding of the mechanisms determining properties such as mobility. Here, we investigate interlayer exciton diffusion in WSe2/WS2 heterobilayers at ultra-low exciton density and low temperatures to examine how charges affect exciton mobility. Remarkably, near the electronic Mott insulator phase, we observe a giant thousand-fold enhancement of exciton diffusion relative to charge neutrality. We attribute this to mobile valence holes, which experience a suppressed moiré potential due to charge order and recombine non-monogamously with conduction electrons. Our results show exciton diffusion as a probe of correlated electron states and Bose-Fermi interplay.

Within the framework of an one-dimension model of interacting electrons, the ground state of an electron liquid is studied. Using the exact solution of the model, the ground state phase diagram and zero-energy Majorana edge functions in a finite chain are calculated. The winding number invariant reflects the topological nature of the electron liquid. The phase diagram includes two topological phases with different winding number invariants, the topologically trivial Mott insulator phase, and three critical phase transition points. Numerical calculations confirm and illustrate the analytical results.

Correlated materials are known to display qualitatively distinct emergent behaviors at low energy. Conveniently, upon absorbing rapid quantum fluctuations, these rich low-energy behaviors can always be effectively described by dressed particles with fully quantized charge, spin, and orbital structure. Such a powerful and simple description is, however, difficult to access through bare particles used in most many-body computations, especially when fluctuations are strong such as in 4d and 5d compounds. To decipher the dominant quantized structure, we propose an easy-to-implement ‘interaction annealing’ approach that utilizes suppressed charge fluctuation through enhancing ionic charging energy. We establish its theoretical foundation using an exactly treated two-site Hubbard model as a generic example. We then demonstrate its applications with more affordable density functional calculations to a representative 3d Mott insulator La2CuO4 and a highly fluctuating 5d semi-metal WTe2. In the latter, it reveals an emergent local electronic structure that makes possible an unprecedented explanation of several experimental observations. Finally, we demonstrate the effectiveness of this approach in studying competing local electronic structures in functional materials.

Revealing quantum phase string effect in a doped Mott insulator: A tensor network state study

Abstract The Mott metal-insulator transition arises from electron-electron interactions determined by the ratio of Coulomb to kinetic energy scales ( U / t ). While temperature, pressure, and doping can induce Mott transitions, direct control of U in solid-state systems remains largely unexplored, particularly in the inhomogeneous environments of emerging neuromorphic devices, where conductive filaments create complex gradients of local properties. Here we show that interface-induced screening can continuously tune the electron-electron interaction strength U to drive an isothermal Mott transition. Using thickness-graded LaTiO 3 /SrTiO 3 heterostructures, we used diffraction and photoemission spectroscopy to reveal a continuous, isothermal quantum phase transition from a Fermi liquid quasiparticle with incoherent excitations to a Mott insulator with Hubbard bands. The primary determinant of the transition is the enhanced local screening environment, which directly influences the interaction strength U , driving the system metallic. This demonstrates that interface engineering of the local screening environment provides a promising approach to manipulate Mott physics through correlation control, beyond traditional bandwidth or filling approaches.

Abstract The interplay between spin and charge degrees of freedom in Mott insulators remains a central topic in strongly correlated electron systems. Using variable-temperature scanning tunneling microscopy/spectroscopy (STM/STS), we investigate the Van der Waals magnet RuBr 3 , a candidate Kitaev quantum spin liquid material. At low temperatures, RuBr 3 exhibits a large correlated Mott gap exceeding 3 eV. As temperature increases, the gap softens significantly, decreasing to ~0.7 eV by 200 K. This evolution coincides with magnetic phase transitions: a sharp reduction occurs near the Néel temperature ( T N ≈ 34 K) upon loss of long-range antiferromagnetic order, followed by a gradual decline through the Kitaev paramagnetic regime. Comparison with α-RuCl 3 reveals that the dominant spin correlations—whether long-range order or short-range Kitaev interactions—govern the Mott gap renormalization. Our results highlight the essential role of spin-charge coupling in Mott physics and provide key insights into the electronic behavior of Kitaev materials across different magnetic phases.

Mixed-valence Mott insulator and composite excitation in twisted bilayer graphene

Tunneling spectroscopy of the spinon-Kondo effect in one-dimensional Mott insulators

Terahertz nonlinear response in cuprate superconductors and the Higgs field in doped Mott insulators

Characterizing electronic thermal states at low temperatures is an important but challenging task in quantum chemistry and condensed matter physics, making it a prime candidate for a useful application in quantum computing. One of the most successful methods for state preparation on quantum computers is the Adaptive, Problem-Tailored (ADAPT) Variational Quantum Eigensolver (VQE), which has recently been generalized to treat excited states within a state-averaged framework as well as Gibbs states. In this work, we introduce Helmholtz-Optimized Thermal (HOT) ADAPT-VQE, an ancilla-free strategy for preparing Gibbs states that directly minimizes the Helmholtz free energy by targeting the dominant eigenstates of the thermal ensemble. We demonstrate the usefulness of HOT-ADAPT-VQE by predicting the free energy of two model systems with strongly correlated ground states: (1) the Fe2+ cation in a magnetic field and (2) a [Cu2O7]10- fragment of the Mott insulator La2CuO4. Our results demonstrate that HOT-ADAPT-VQE significantly improves upon Gibbs-state estimates from multistate variants of ADAPT-VQE, often with substantially shallower quantum circuits, making it a promising candidate for thermal-state calculations.

We investigate the effects of artificial magnetic fields on the ground-state of the two-dimensional Bose-Hubbard model. Using an asymmetric Bose-Hubbard model, we demonstrate that anisotropic hopping amplitude localizes bosons and enlarges the insulating and supersolid regions. We show these increases in the presence of artificial gauge fields up to the symmetric point of the field. Moreover, our calculations exhibit real-space modulations of the superfluid and supersolid phases. The bosonic current exhibits vortices in these phases, whose configurations depend on the commensuration between the magnetic field and the lattice. Although the magnetic field explicitly breaks the translational symmetry of the square lattice, this symmetry is restored in the Mott insulator phase. The local densities shows a checkerboard pattern in the density-wave and supersolid phases, regardless of the magnetic field strength. We investigate thermal fluctuations and demonstrate the robustness of insulating and supersolid phases up to temperatures comparable to the interaction energy, which supports the feasibility of observing such phases in experiments.

Intrinsic phase fluctuations and superfluid density in doped Mott insulators

Abstract In this work, we explore the influence of shaking parameters on the single-particle excitation spectra of bosonic atoms confined in a one-dimensional shaken optical lattice. Using mean-field theory to solve the two-band Bose–Hubbard model, we obtain a phase diagram that qualitatively aligns with experimental observations. We employ the Random Phase Approximation (RPA) based on mean-field states to examine excitation spectra across different phases during the phase transitions. Notably, the gapless superfluid (SF) and π -SF phases exhibit roton-maxon excitations, whereas the gapped Mott insulator (MI) phase can manifest as a direct or indirect band-gap MI. These calculations provide detailed insights into how excitations evolve across different phases and how spectral weights areredistributed during the transitions.

We study the nature of electronic states induced by the non-magnetic impurities in a hole-doped Mott insulator. We further examine the consequences of doping on the transport and spectral properties. By employing exact diagonalizaton + Monte-Carlo simulation based on the many-body computational techniques, which allows for the thermal and spatial fluctuations besides a fine resolution in the momentum-space spectral function, the current investigation unravels the degree of localization of the electronic states induced by the impurity atoms as a function of temperature. The major consequences of doping impurity, which introduces holes in the systems, include the appearance of impurity states just above the Fermi level and only in the vicinity of momenta where the gap opens along the normal state Fermi surface in the insulating state. The electronic state at the impurity site is split because of the antiferromagnetic background. The pseudogap-like behavior of the density of states is weakened as reflected by the enhanced charge fluctuations even away from the impurity site at an elevated temperature. Our study also reflects on the degree of improvement in conductivity as well as particle-hole asymmetry introduced in the momentum-resolved spectral function, which maximizes towards the high-symmetry points like ([Formula: see text].

Semiconducting transition metal dichalcogenide (TMDC) moiré superlattices provide an unprecedented platform for manipulating excitons. The in-situ control of moiré excitons could enable novel excitonic devices but remains challenging. Meanwhile, as dipolar composite bosons, interlayer excitons in the type-II aligned TMDC moiré superlattices exhibit strong interactions with fermionic charge carriers. Here, we demonstrate active manipulation of exciton diffusivity by tuning their interplay with correlated carriers in moiré potentials. When electrons form Mott insulators, the interlayer exciton energy is blueshifted due to strong electron-exciton repulsion, leading to the enhancement of diffusivity by as much as two orders of magnitude. In contrast, exciton diffusivity is suppressed at fractional fillings, where carriers form generalized Wigner crystals. In between fractional fillings, electrons populate all moiré traps, resulting in enhanced diffusivity with increasing carrier density, owing to the effectively reduced moiré potential confinement experienced by excitons. Our study inspires further engineering and controlling exotic excitonic states in TMDC moiré superlattices for fascinating quantum phenomena and novel excitonic devices.

Many emergent phenomena appear in doped Mott insulators near the insulator-to-metal transition. In high-temperature cuprate superconductors, superconductivity arises when antiferromagnetic (AFM) order is gradually suppressed by carrier doping, and a d-wave superconducting gap forms when an enigmatic nodal gap evolves into a point node. Here, we examine electron-doped Sr_{2}IrO_{4}, the 5d-electron counterpart of cuprates, using angle-resolved photoemission spectroscopy. At low doping levels, we observe the formation of electronic states near the Fermi level, accompanied by a gap at the AFM zone boundary, mimicking the AFM gap in electron-doped cuprates. With increasing doping, a distinct gap emerges along the (0,0)-(π,π) nodal direction, paralleling that observed in hole-doped cuprates. This anomalous nodal gap persists after the collapse of the AFM gap and gradually decreases with further doping. It eventually vanishes into a point node of the reported d-wave gap. These observations replicate the characteristic features in both electron- and hole-doped cuprates, indicating a unified route toward nodal metallicity in doped spin-1/2 AFM Mott insulators.

The Mott insulator α − RuC l 3 , featuring the intertwined interplay of spin-orbit coupling and Kitaev spin correlations, provides an unparalleled platform for probing quantum many-body physics. Using scanning tunneling microscopy/spectroscopy, we compare temperature-dependent dI / dV spectra between grown monolayers and exfoliated bulk samples. Both systems exhibit pronounced Mott gap softening near 110 K, manifested by spectral weight transfer from Hubbard bands toward the Fermi level, resulting in low-energy correlated charge delocalization. Although this gap softening coincides with Kitaev paramagnetic and structural phase transitions in bulk crystals, monolayer studies provide compelling insights. By eliminating structural phase transition in monolayer sample, we suggest that spin correlations, rather than Coulomb interactions alone, may govern charge dynamics within the Mott-Hubbard framework, challenging conventional Mott-Hubbard paradigms. These results resolve a long-standing controversy regarding the Mott gap magnitude in α − RuC l 3 and experimentally confirm the critical role of spin correlations in Mott physics.