Fermionic wave functions from neural-network constrained hidden states.

We introduce a systematically improvable family of variational wave functions for the simulation of strongly correlated fermionic systems. This family consists of Slater determinants in an augmented Hilbert space involving "hidden" additional fermionic degrees of freedom. These determinants are projected onto the physical Hilbert space through a constraint that is optimized, together with the single-particle orbitals, using a neural network parameterization. This construction draws inspiration from the success of hidden-particle representations but overcomes the limitations associated with the mean-field treatment of the constraint often used in this context. Our construction provides an extremely expressive family of wave functions, which is proved to be universal. We apply this construction to the ground-state properties of the Hubbard model on the square lattice, achieving levels of accuracy that are competitive with those of state-of-the-art variational methods.

Linear resistivity and Sachdev-Ye-Kitaev (SYK) spin liquid behavior in a quantum critical metal with spin-1/2 fermions.

"Strange metals" with resistivity depending linearly on temperature T down to low T have been a long-standing puzzle in condensed matter physics. Here, we consider a lattice model of itinerant spin-[Formula: see text] fermions interacting via onsite Hubbard interaction and random infinite-ranged spin-spin interaction. We show that the quantum critical point associated with the melting of the spin-glass phase by charge fluctuations displays non-Fermi liquid behavior, with local spin dynamics identical to that of the Sachdev-Ye-Kitaev family of models. This extends the quantum spin liquid dynamics previously established in the large-M limit of [Formula: see text] symmetric models to models with physical [Formula: see text] spin-[Formula: see text] electrons. Remarkably, the quantum critical regime also features a Planckian linear-T resistivity associated with a T-linear scattering rate and a frequency dependence of the electronic self-energy consistent with the marginal Fermi liquid phenomenology.

Nanoscale Femtosecond Dynamics of Mott Insulator (Ca0.99Sr0.01)2RuO4.

Ca2RuO4 is a transition-metal oxide that exhibits a Mott insulator-metal transition (IMT) concurrent with a symmetry-preserving Jahn-Teller distortion (JT) at 350 K. The coincidence of these two transitions demonstrates a high level of coupling between the electronic and structural degrees of freedom in Ca2RuO4. Using spectroscopic measurements with nanoscale spatial resolution, we interrogate the interplay of the JT and IMT through the temperature-driven transition. Then, we introduce photoexcitation with subpicosecond temporal resolution to explore the coupling of the JT and IMT via electron-hole injection under ambient conditions. Through the temperature-driven IMT, we observe phase coexistence in the form of a stripe phase existing at the domain wall between macroscopic insulating and metallic domains. Through ultrafast carrier injection, we observe the formation of midgap states via enhanced optical absorption. We propose that these midgap states become trapped by lattice polarons originating from the local perturbation of the JT.

Designing and controlling the properties of transition metal oxide quantum materials.

This Perspective addresses the design, creation, characterization and control of synthetic quantum materials with strong electronic correlations. We show how emerging synergies between theoretical/computational approaches and materials design/experimental probes are driving recent advances in the discovery, understanding and control of new electronic behaviour in materials systems with interesting and potentially technologically important properties. The focus here is on transition metal oxides, where electronic correlations lead to a myriad of functional properties including superconductivity, magnetism, Mott transitions, multiferroicity and emergent behaviour at picoscale-designed interfaces. Current opportunities and challenges are also addressed, including possible new discoveries of non-equilibrium phenomena and optical control of correlated quantum phases of transition metal oxides.

Disentangling lattice and electronic contributions to the metal-insulator transition from bulk vs. layer confined RNiO3.

In complex oxide materials, changes in electronic properties are often associated with changes in crystal structure, raising the question of the relative roles of the electronic and lattice effects in driving the metal-insulator transition. This paper presents a combined theoretical and experimental analysis of the dependence of the metal-insulator transition of [Formula: see text] on crystal structure, specifically comparing properties of bulk materials to 1- and 2-layer samples of [Formula: see text] grown between multiple electronically inert [Formula: see text] counterlayers in a superlattice. The comparison amplifies and validates a theoretical approach developed in previous papers and disentangles the electronic and lattice contributions, through an independent variation of each. In bulk [Formula: see text], the correlations are not strong enough to drive a metal-insulator transition by themselves: A lattice distortion is required. Ultrathin films exhibit 2 additional electronic effects and 1 lattice-related effect. The electronic effects are quantum confinement, leading to dimensional reduction of the electronic Hamiltonian and an increase in electronic bandwidth due to counterlayer-induced bond-angle changes. We find that the confinement effect is much more important. The lattice effect is an increase in stiffness due to the cost of propagation of the lattice disproportionation into the confining material.

Length scales of interfacial coupling between metal and insulator phases in oxides.

Controlling phase transitions in transition metal oxides remains a central feature of both technological and fundamental scientific relevance. A well-known example is the metal-insulator transition, which has been shown to be highly controllable. However, the length scale over which these phases can be established is not yet well understood. To gain insight into this issue, we atomically engineered an artificially phase-separated system through fabricating epitaxial superlattices that consist of SmNiO3 and NdNiO3, two materials that undergo a metal-to-insulator transition at different temperatures. We demonstrate that the length scale of the interfacial coupling between metal and insulator phases is determined by balancing the energy cost of the boundary between a metal and an insulator and the bulk phase energies. Notably, we show that the length scale of this effect exceeds that of the physical coupling of structural motifs, which introduces a new framework for interface-engineering properties at temperatures against the bulk energetics.

Quantum Phase Transition at Nonzero Doping in a Random t-J Model.

We present exact diagonalization results on finite clusters of a t-J model of spin-1/2 electrons with random all-to-all hopping and exchange interactions. We argue that such random models capture qualitatively the strong local correlations needed to describe the cuprates and related compounds, while avoiding lattice space group symmetry breaking orders. The previously known spin glass ordered phase in the insulator at doping p=0 extends to a metallic spin glass phase up to a transition p=p_{c}≈1/3. The dynamic spin susceptibility shows signatures of the spectrum of the Sachdev-Ye-Kitaev models near p_{c}. We also find signs of the phase transition in the entropy, entanglement entropy, and compressibility, all of which exhibit a maximum near p_{c}. The electron energy distribution function in the metallic phase is consistent with a disordered extension of the Luttinger-volume Fermi surface for p>p_{c}, while this breaks down for p

Topological order in the pseudogap metal.

We compute the electronic Green's function of the topologically ordered Higgs phase of a SU(2) gauge theory of fluctuating antiferromagnetism on the square lattice. The results are compared with cluster extensions of dynamical mean field theory, and quantum Monte Carlo calculations, on the pseudogap phase of the strongly interacting hole-doped Hubbard model. Good agreement is found in the momentum, frequency, hopping, and doping dependencies of the spectral function and electronic self-energy. We show that lines of (approximate) zeros of the zero-frequency electronic Green's function are signs of the underlying topological order of the gauge theory and describe how these lines of zeros appear in our theory of the Hubbard model. We also derive a modified, nonperturbative version of the Luttinger theorem that holds in the Higgs phase.

Deep Learning the Hohenberg-Kohn Maps of Density Functional Theory.

A striking consequence of the Hohenberg-Kohn theorem of density functional theory is the existence of a bijection between the local density and the ground-state many-body wave function. Here we study the problem of constructing approximations to the Hohenberg-Kohn map using a statistical learning approach. Using supervised deep learning with synthetic data, we show that this map can be accurately constructed for a chain of one-dimensional interacting spinless fermions in different phases of this model including the charge ordered Mott insulator and metallic phases and the critical point separating them. However, we also find that the learning is less effective across quantum phase transitions, suggesting an intrinsic difficulty in efficiently learning nonsmooth functional relations. We further study the problem of directly reconstructing complex observables from simple local density measurements, proposing a scheme amenable to statistical learning from experimental data.

Nonlinear Spectroscopy of Collective Modes in an Excitonic Insulator.

The nonlinear optical response of an excitonic insulator coupled to lattice degrees of freedom is shown to depend in strong and characteristic ways on whether the insulating behavior originates primarily from electron-electron or electron-lattice interactions. Linear response optical signatures of the massive phase mode and the amplitude (Higgs) mode are identified. Upon nonlinear excitation resonant to the phase mode, a new in-gap mode at twice the phase mode frequency is induced, leading to a huge second harmonic response. Excitation of in-gap phonon modes leads to different and much smaller effects. A Landau-Ginzburg theory analysis explains these different behaviors and reveals that a parametric resonance of the strongly excited phase mode is the origin of the photoinduced mode in the electron-dominant case. The difference in the nonlinear optical response serves as a measure of the dominant mechanism of the ordered phase.

Nature of Symmetry Breaking at the Excitonic Insulator Transition: Ta_{2}NiSe_{5}.

Ta_{2}NiSe_{5} is one of the most promising materials for hosting an excitonic insulator ground state. While a number of experimental observations have been interpreted in this way, the precise nature of the symmetry breaking occurring in Ta_{2}NiSe_{5}, the electronic order parameter, and a realistic microscopic description of the transition mechanism are, however, missing. By a symmetry analysis based on first-principles calculations, we uncover the discrete lattice symmetries which are broken at the transition. We identify a purely electronic order parameter of excitonic nature that breaks these discrete crystal symmetries and contributes to the experimentally observed lattice distortion from an orthorombic to a monoclinic phase. Our results provide a theoretical framework to understand and analyze the excitonic transition in Ta_{2}NiSe_{5} and settle the fundamental questions about symmetry breaking governing the spontaneous formation of excitonic insulating phases in solid-state materials.

Strongly Correlated Materials from a Numerical Renormalization Group Perspective: How the Fermi-Liquid State of Sr_{2}RuO_{4} Emerges.

The crossover from fluctuating atomic constituents to a collective state as one lowers temperature or energy is at the heart of the dynamical mean-field theory description of the solid state. We demonstrate that the numerical renormalization group is a viable tool to monitor this crossover in a real-materials setting. The renormalization group flow from high to arbitrarily small energy scales clearly reveals the emergence of the Fermi-liquid state of Sr_{2}RuO_{4}. We find a two-stage screening process, where orbital fluctuations are screened at much higher energies than spin fluctuations, and Fermi-liquid behavior, concomitant with spin coherence, below a temperature of 25 K. By computing real-frequency correlation functions, we directly observe this spin-orbital scale separation and show that the van Hove singularity drives strong orbital differentiation. We extract quasiparticle interaction parameters from the low-energy spectrum and find an effective attraction in the spin-triplet sector.

Superradiant Quantum Materials.

There is currently great interest in the strong coupling between the quantized photon field of a cavity and electronic or other degrees of freedom in materials. A major goal is the creation of novel collective states entangling photons with those degrees of freedom. Here we show that the cooperative effect between strong electron correlations in quantum materials and the long-range interactions induced by the photon field leads to the stabilization of coherent phases of light and matter. By studying a two-band model of interacting electrons coupled to a cavity field, we show that a phase characterized by the simultaneous condensation of excitons and photon superradiance can be realized, hence stabilizing and intertwining two collective phenomena which are rather elusive in the absence of this cooperative effect.

Spin-Orbit Coupling and Electronic Correlations in Sr_{2}RuO_{4}.

We investigate the interplay of spin-orbit coupling (SOC) and electronic correlations in Sr_{2}RuO_{4} using dynamical mean-field theory. We find that SOC does not affect the correlation-induced renormalizations, which validates Hund's metal picture of ruthenates even in the presence of the sizable SOC relevant to these materials. Nonetheless, SOC is found to change significantly the electronic structure at k points where a degeneracy applies in its absence. We explain why these two observations are consistent with one another and calculate the effects of SOC on the correlated electronic structure. The magnitude of these effects is found to depend on the energy of the quasiparticle state under consideration, leading us to introduce the notion of an energy-dependent quasiparticle spin-orbit coupling λ^{*}(ω). This notion is generally applicable to all materials in which both the spin-orbit coupling and electronic correlations are sizable.

Thermopower and Entropy: Lessons from Sr_{2}RuO_{4}.

We calculate the in-plane Seebeck coefficient of Sr_{2}RuO_{4} within a framework combining electronic structure and dynamical mean-field theory. We show that its temperature dependence can be interpreted using entropic considerations based on the Kelvin formula and that it provides a meaningful probe of the crossover out of the Fermi liquid regime into an incoherent metal. This crossover proceeds in two stages: The entropy of spin degrees of freedom is released around room temperature, while orbital degrees of freedom remain quenched up to much higher temperatures. This is confirmed by a direct calculation of the corresponding susceptibilities and is a hallmark of "Hund's metals." We also calculate the c-axis thermopower and predict that it exceeds substantially the in-plane one at high temperature, a peculiar behavior which originates from an interlayer "hole-filtering" mechanism.

Rare-earth vs. heavy metal pigments and their colors from first principles.

Many inorganic pigments contain heavy metals hazardous to health and environment. Much attention has been devoted to the quest for nontoxic alternatives based on rare-earth elements. However, the computation of colors from first principles is a challenge to electronic structure methods, especially for materials with localized f-orbitals. Here, starting from atomic positions only, we compute the colors of the red pigment cerium fluorosulfide as well as mercury sulfide (classic vermilion). Our methodology uses many-body theories to compute the optical absorption combined with an intermediate length-scale modelization to assess how coloration depends on film thickness, pigment concentration, and granularity. We introduce a quantitative criterion for the performance of a pigment. While for mercury sulfide, this criterion is satisfied because of large transition matrix elements between wide bands, cerium fluorosulfide presents an alternative paradigm: the bright red color is shown to stem from the combined effect of the quasi-2D and the localized nature of states. Our work shows the power of modern computational methods, with implications for the theoretical design of materials with specific optical properties.

Spectroscopic evidence for Fermi liquid-like energy and temperature dependence of the relaxation rate in the pseudogap phase of the cuprates.

Cuprate high-Tc superconductors exhibit enigmatic behavior in the nonsuperconducting state. For carrier concentrations near "optimal doping" (with respect to the highest Tcs) the transport and spectroscopic properties are unlike those of a Landau-Fermi liquid. On the Mott-insulating side of the optimal carrier concentration, which corresponds to underdoping, a pseudogap removes quasi-particle spectral weight from parts of the Fermi surface and causes a breakup of the Fermi surface into disconnected nodal and antinodal sectors. Here, we show that the near-nodal excitations of underdoped cuprates obey Fermi liquid behavior. The lifetime τ(ω, T) of a quasi-particle depends on its energy ω as well as on the temperature T. For a Fermi liquid, 1/τ(ω, T) is expected to collapse on a universal function proportional to (ℏω)(2) + (pπk(B)T)(2). Magneto-transport experiments, which probe the properties in the limit ω = 0, have provided indications for the presence of a T(2) dependence of the dc (ω = 0) resistivity of different cuprate materials. However, Fermi liquid behavior is very much about the energy dependence of the lifetime, and this can only be addressed by spectroscopic techniques. Our optical experiments confirm the aforementioned universal ω- and T dependence of 1/τ(ω, T), with p ∼ 1.5. Our data thus provide a piece of evidence in favor of a Fermi liquid-like scenario of the pseudogap phase of the cuprates.

Heavy-fermion quantum criticality and destruction of the Kondo effect in a nickel oxypnictide.

A quantum critical point arises at a continuous transformation between distinct phases of matter at zero temperature. Studies in antiferromagnetic heavy-fermion materials have revealed that quantum criticality has several classes, with an unconventional type that involves a critical destruction of the Kondo entanglement. To understand such varieties, it is important to extend the materials basis beyond the usual setting of intermetallic compounds. Here we show that a nickel oxypnictide, CeNiAsO, exhibits a heavy-fermion antiferromagnetic quantum critical point as a function of either pressure or P/As substitution. At the quantum critical point, non-Fermi-liquid behaviour appears, which is accompanied by a divergent effective carrier mass. Across the quantum critical point, the low-temperature Hall coefficient undergoes a rapid sign change, suggesting a sudden jump of the Fermi surface and a destruction of the Kondo effect. Our results imply that the enormous materials basis for the oxypnictides, which has been so crucial in the search for high-temperature superconductivity, will also play a vital role in the effort to establish the universality classes of quantum criticality in strongly correlated electron systems.

Nonexistence of the Luttinger-Ward functional and misleading convergence of skeleton diagrammatic series for hubbard-like models.

The Luttinger-Ward functional Φ[G], which expresses the thermodynamic grand potential in terms of the interacting single-particle Green's function G, is found to be ill defined for fermionic models with the Hubbard on-site interaction. In particular, we show that the self-energy Σ[G]∝δΦ[G]/δG is not a single-valued functional of G: in addition to the physical solution for Σ[G], there exists at least one qualitatively distinct unphysical branch. This result is demonstrated for several models: the Hubbard atom, the Anderson impurity model, and the full two-dimensional Hubbard model. Despite this pathology, the skeleton Feynman diagrammatic series for Σ in terms of G is found to converge at least for moderately low temperatures. However, at strong interactions, its convergence is to the unphysical branch. This reveals a new scenario of breaking down of diagrammatic expansions. In contrast, the bare series in terms of the noninteracting Green's function G0 converges to the correct physical branch of Σ in all cases currently accessible by diagrammatic Monte Carlo calculations. In addition to their conceptual importance, these observations have important implications for techniques based on the explicit summation of the diagrammatic series.

Band Structure and Terahertz Optical Conductivity of Transition Metal Oxides: Theory and Application to CaRuO(3).

Density functional plus dynamical mean field calculations are used to show that in transition metal oxides, rotational and tilting (GdFeO(3)-type) distortions of the ideal cubic perovskite structure produce a multiplicity of low-energy optical transitions which affect the conductivity down to frequencies of the order of 1 or 2 mV (terahertz regime), mimicking non-Fermi-liquid effects even in systems with a strictly Fermi-liquid self-energy. For CaRuO(3), a material whose measured electromagnetic response in the terahertz frequency regime has been interpreted as evidence for non-Fermi-liquid physics, the combination of these band structure effects and a renormalized Fermi-liquid self-energy accounts for the low frequency optical response which had previously been regarded as a signature of exotic physics. Signatures of deviations from Fermi-liquid behavior at higher frequencies (∼100 meV) are discussed.