Correlated Quantum Matter Research Articles

Highly Resolved Spectral Functions of Two-Dimensional Systems with Neural Quantum States.

Spectral functions are central to link experimental probes to theoretical models in condensed matter physics. However, performing exact numerical calculations for interacting quantum matter has remained a key challenge especially beyond one spatial dimension. In this work, we develop a versatile approach using neural quantum states to obtain spectral properties based on simulations of the dynamics of excitations initially localized in real or momentum space. We apply this approach to compute the dynamical structure factor in the vicinity of quantum critical points (QCPs) of different two-dimensional quantum Ising models, including one that describes the complex density wave orders of Rydberg atom arrays. When combined with deep network architectures we find that our method reliably describes dynamical structure factors of arrays with up to 24×24 spins, including the diverging timescales at critical points. Our approach is broadly applicable to interacting quantum lattice models in two dimensions and consequently opens up a route to compute spectral properties of correlated quantum matter in yet inaccessible regimes.

Pendulum Atomic Force Microscopy for Imaging Fluctuation Dynamics in Correlated Quantum Materials at Millikelvin Temperatures.

Pendulum Atomic Force Microscopy for Imaging Fluctuation Dynamics in Correlated Quantum Materials at Millikelvin Temperatures.

Infinite-layer nickelates as Ni-eg Hund’s metals

The recent and exciting discovery of superconductivity in the hole-doped infinite-layer nickelate Nd1−δSrδNiO2 draws strong attention to correlated quantum materials. From a theoretical view point, this class of unconventional superconducting materials provides an opportunity to unveil a physics hidden in correlated quantum materials. Here we study the temperature and doping dependence of the local spectrum as well as the charge, spin and orbital susceptibilities from first principles. By using ab initio LQSGW+DMFT methodology, we show that onsite Hund’s coupling in Ni-d orbitals gives rise to multiple signatures of Hund’s metallic phase in Ni-eg orbitals. The proposed picture of the nickelates as an eg (two orbital) Hund’s metal differs from the picture of the Fe-based superconductors as a five orbital Hund’s metal as well as the picture of the cuprates as doped charge transfer insulators. Our finding uncover a new class of the Hund’s metals and has potential implications for the broad range of correlated two orbital systems away from half-filling.

Photoinduced Phase Transition in Infinite-Layer Nickelates.

The quantum phase transition caused by regulating the electronic correlation in strongly correlated quantum materials has been a research hotspot in condensed matter science. Herein, a photon-induced quantum phase transition from the Kondo-Mott insulating state to the low temperature metallic one accompanying with the magnetoresistance changing from negative to positive in the infinite-layer NdNiO2 films is reported, where the antiferromagnetic coupling among the Ni1+ localized spins and the Kondo effect are effectively suppressed by manipulating the correlation of Ni-3d and Nd-5d electrons under the photoirradiation. Moreover, the critical temperature Tc of the superconducting-like transition exhibits a dome-shaped evolution with the maximum up to ≈42K, and the electrons dominate the transport process proved by the Hall effect measurements. These findings not only make the photoinduction a promising way to control the quantum phase transition by manipulating the electronic correlation in Mott-like insulators, but also shed some light on the possibility of the superconducting in electron-doped nickelates.

Ground-state and spectral properties of the doped one-dimensional optical Hubbard-Su-Schrieffer-Heeger model

We present a density matrix renormalization group study of the doped one-dimensional (1D) Hubbard-Su-Schrieffer-Heeger (Hubbard-SSH) model, where the atomic displacements linearly modulate the nearest-neighbor hopping integrals. Focusing on an optical variant of the model in the strongly correlated limit relevant for cuprate spin chains, we examine how the SSH interaction modifies the model's ground- and excited-state properties. The SSH coupling weakly renormalizes the model's single- and two-particle response functions for electron-phonon $(e\text{\ensuremath{-}}\mathrm{ph})$ coupling strengths below a parameter-dependent critical value ${g}_{\mathrm{c}}$. For larger $e\text{\ensuremath{-}}\mathrm{ph}$ coupling, the sign of the effective hopping integrals changes for a subset of orbitals, which drives a lattice dimerization distinct from the standard nesting-driven picture in 1D. The spectral weight of the one- and two-particle dynamical response functions are dramatically rearranged across this transition, with significant changes in the ground-state correlations. We argue that this dimerization results from the breakdown of the linear approximation for the $e\text{\ensuremath{-}}\mathrm{ph}$ coupling and thus signals a fundamental limitation of the linear SSH interaction. Our results have consequences for our understanding of how SSH-like interactions can enter the physics of strongly correlated quantum materials, including the recently synthesized doped cuprate spin chains.

Pairing of holes by confining strings in antiferromagnets

In strongly correlated quantum materials, the behavior of charge carriers is dominated by strong electron-electron interactions. These can lead to insulating states with spin order, and upon doping to competing ordered states including unconventional superconductivity. The underlying pairing mechanism remains poorly understood however, even in strongly simplified theoretical models. Recent advances in quantum simulation allow to study pairing in paradigmatic settings, e.g. in the t-Jt−J and t-J_zt−Jz Hamiltonians. Even there, the most basic properties of paired states of only two dopants, such as their dispersion relation and excitation spectra, remain poorly studied in many cases. Here we provide new analytical insights into a possible string-based pairing mechanism of mobile holes in an antiferromagnet. We analyze an effective model of partons connected by a confining string and calculate the spectral properties of bound states. Our model is equally relevant for understanding Hubbard-Mott excitons consisting of a bound doublon-hole pair or confined states of dynamical matter in lattice gauge theories, which motivates our study of different parton statistics. Although an accurate semi-analytic estimation of binding energies is challenging, our theory provides a detailed understanding of the internal structure of pairs. For example, in a range of settings we predict heavy states of immobile pairs with flat-band dispersions - including for the lowest-energy dd-wave pair of fermions. Our findings shed new light on the long-standing question about the origin of pairing and competing orders in high-temperature superconductors.

Extracting electronic many-body correlations from local measurements with artificial neural networks

The characterization of many-body correlations provides a powerful tool for analyzing correlated quantum materials. However, experimental extraction of quantum entanglement in correlated electronic systems remains an open problem in practice. In particular, the correlation entropy quantifies the strength of quantum correlations in interacting electronic systems, yet it requires measuring all the single-particle correlators of a macroscopic sample. To circumvent this bottleneck, we introduce a strategy to obtain the correlation entropy of electronic systems solely from a set of local measurements. We show that, by combining local particle-particle and density-density correlations with a neural-network algorithm, the correlation entropy can be predicted accurately. Specifically, we show that for a generalized interacting fermionic model, our algorithm yields an accurate prediction of the correlation entropy from a set of noisy local correlators. Our work shows that the correlation entropy in interacting electron systems can be reconstructed from local measurements, providing a starting point to experimentally extract many-body correlations with local probes.

Proximity-induced charge density wave in a metallic system

Non-local quasiparticles in correlated quantum materials can exhibit the proximity effect. For instance, in metal superconductor hybrid systems, the leaking of cooper pairs to the metallic region induces superconducting correlations in a standard metal. This paper explores the proximity effects of charge density wave (CDW) on metal using the attractive Hubbard model, which harbors CDW state at half-filling. Our fully self-consistent calculations demonstrate that periodic charge modulations develop in a metal due to the tunneling of finite momentum particle-hole pairs from the CDW region. Upon doping the normal region, the commensurate CDW changes to an incommensurate one by incorporating regular phase shifts. Furthermore, the induced CDW produces a soft gap in the density of states and thus can be detected in tunneling experiments. We discuss our results in light of recent reports of such proximity-induced charge order in different two-dimensional heterostructures.

Quantum-well states at the surface of a heavy-fermion superconductor

Two-dimensional electronic states at surfaces are often observed in simple wide-band metals such as Cu or Ag (refs. 1–4). Confinement by closed geometries at the nanometre scale, such as surface terraces, leads to quantized energy levels formed from the surface band, in stark contrast to the continuous energy dependence of bulk electron bands2,5–10. Their energy-level separation is typically hundreds of meV (refs. 3,6,11). In a distinct class of materials, strong electronic correlations lead to so-called heavy fermions with a strongly reduced bandwidth and exotic bulk ground states12,13. Quantum-well states in two-dimensional heavy fermions (2DHFs) remain, however, notoriously difficult to observe because of their tiny energy separation. Here we use millikelvin scanning tunnelling microscopy (STM) to study atomically flat terraces on U-terminated surfaces of the heavy-fermion superconductor URu2Si2, which exhibits a mysterious hidden-order (HO) state below 17.5 K (ref. 14). We observe 2DHFs made of 5f electrons with an effective mass 17 times the free electron mass. The 2DHFs form quantized states separated by a fraction of a meV and their level width is set by the interaction with correlated bulk states. Edge states on steps between terraces appear along one of the two in-plane directions, suggesting electronic symmetry breaking at the surface. Our results propose a new route to realize quantum-well states in strongly correlated quantum materials and to explore how these connect to the electronic environment.

Nonequilibrium noise as a probe of pair-tunneling transport in the BCS-BEC crossover.

The detection of elementary carriers in transport phenomena is one of the most important keys to understand nontrivial properties of strongly correlated quantum matter. Here, we propose a method to identify the tunneling current carrier in strongly interacting fermions from nonequilibrium noise in the Bardeen-Cooper-Schrieffer to Bose-Einstein condensate crossover. The noise-to-current ratio, the Fano factor, can be a crucial probe for the current carrier. Bringing strongly correlated fermions into contact with a dilute reservoir produces a tunneling current in between. The associated Fano factor increases from one to two as the interaction becomes stronger, reflecting the fact that the dominant conduction channel changes from the quasiparticle tunneling to the pair tunneling.

Probing site-resolved correlations in a spin system of ultracold molecules

Synthetic quantum systems with interacting constituents play an important role in quantum information processing and in explaining fundamental phenomena in many-body physics. Following impressive advances in cooling and trapping techniques, ensembles of ultracold polar molecules have emerged as a promising platform that combines several advantageous properties1-11. These include a large set of internal states with long coherence times12-17 and long-range, anisotropic interactions. These features could enable the exploration of intriguing phases of correlated quantum matter, such as topological superfluids18, quantum spin liquids19, fractional Chern insulators20 and quantum magnets21,22. Probing correlations in these phases is crucial to understanding their properties, necessitating the development of new experimental techniques. Here we use quantum gas microscopy23 to measure the site-resolved dynamics of quantum correlations of polar 23Na87Rb molecules confined in a two-dimensional optical lattice. By using two rotational states of the molecules, we realize a spin-1/2 system with dipolar interactions between particles, producing a quantum spin-exchange model21,22,24,25. We study the evolution of correlations during the thermalization process of an out-of-equilibrium spin system for both spatially isotropic and anisotropic interactions. Furthermore, we examine the correlation dynamics of a spin-anisotropic Heisenberg model engineered from the native spin-exchange model by using periodic microwave pulses26-28. These experiments push the frontier of probing and controlling interacting systems of ultracold molecules, with prospects for exploring new regimes of quantum matter and characterizing entangled states that are useful for quantum computation29,30 and metrology31.

Efficient quantum information probes of nonequilibrium quantum criticality

Quantum information-based approaches, in particular the fidelity, have been flexible probes for phase boundaries of quantum matter. A major hurdle to a more widespread application of fidelity and other quantum information measures to strongly correlated quantum materials is the inaccessibility of the fidelity susceptibility to most state-of-the-art numerical methods. This is particularly apparent away from equilibrium where, at present, no general critical theory is available and many standard techniques fail. Motivated by the usefulness of quantum information-based measures we show that a widely accessible quantity, the single-particle affinity, is able to serve as a versatile instrument to identify phase transitions beyond Landau’s paradigm. We demonstrate that it not only is able to signal previously identified nonequilibrium phase transitions but also has the potential to detect hitherto unknown phases in models of quantum matter far from equilibrium.

Mott physics: One of main themes in quantum materials

<sec>The competition and cooperation between the itinerancy behavior and localization behavior of electrons in correlated quantum materials, known as Mott physics, is the physical mechanism behind the diverse states of many quantum materials. This article reviews the manifestation of Mott physics in various quantum materials and establishes it as one of the main themes of quantum materials. Finding and understanding its ever-changing ways of manifestation is one of the central tasks of experimental research on condensed matter physics.</sec><sec>Specifically, the filling-control route of Mott transition is illustrated by exampling the surface K-dosed Sr<sub>2</sub>IrO<sub>4</sub>, which exhibits d-wave gap, pseudogap behavior in underdoped regime, and phase separation with inhomogeneous electronic state distribution. All of these show strong resemblances to the doped cuprate superconductors, another prototypical filling-control type of Mott transition case. On the other hand, the bandwidth-control route of Mott transition could be found in NiS<sub>2–<i>x</i></sub>Se<sub><i>x</i></sub>, where its bandwidth continuously decreases with decreasing Se concentration, until it becomes an insulator. In addition, the essence of various ways of doping in iron-based superconductors is to change their bandwidths. The superconductivity shows up at intermediate bandwidth with moderate correlations, and it diminishes when the bandwidth is large and the electron correlations are weak. For heavily electron-doped iron-selenides, there is even a Mott insulator phase with strong correlations.</sec><sec>For carbon based materials, the phase transition between the antiferromagnetic insulator and superconducting state of A15 Cs<sub>3</sub>C<sub>60</sub> as the volume of fullerene anions decreases could be understood in terms of a bandwidth-control Mott transition; the insulator-superconductor transition discovered in electrically gated “magic angle” twisted-angle bilayer graphene could be understood as a filling-control Mott transition.</sec><sec>For f electron systems, the interplay between itinerancy and localization dominates the heavy fermion behavior and their ground states. The behaviors of the f electrons are demonstrated by using the angle-resolved photoemission data of CeCoIn<sub>5</sub>, whose f electron band becomes more coherent with decreasing temperature, and the c-f hybridization is thus enhanced and the band mass of conduction band continuously increases. The c-f hybridization behaviors of CeCoIn<sub>5,</sub> CeIrIn<sub>5</sub>, and CeRhIn<sub>5</sub> are compared with each other, and the differences in hybridization strength put their ground states into different regimes of the Doniach phase diagram. Similarly, the Skutterudites 4f<sup>2</sup> Kondo lattice system PrOs<sub>4</sub>Sb<sub>12</sub> and its sibling 4f<sup>1</sup> system CeOs<sub>4</sub>Sb<sub>12</sub> also have different ground states due to a slight difference in their c-f hybridization strengths.</sec>

Neural-network quantum states for a two-leg Bose-Hubbard ladder under magnetic flux

Quantum gas systems are ideal analog quantum simulation platforms for tackling some of the most challenging problems in strongly correlated quantum matter. However, they also expose the urgent need for new theoretical frameworks. Simple models in one dimension, well studied with conventional methods, have received considerable recent attention as test cases for new approaches. Ladder models provide the logical next step, where established numerical methods are still reliable, but complications of higher dimensional effects like gauge fields can be introduced. In this paper, we investigate the application of the recently developed neural-network quantum states in the two-leg Bose-Hubbard ladder under strong synthetic magnetic fields. Based on the restricted Boltzmann machine and feedforward neural network, we show that variational neural networks can reliably predict the superfluid-Mott insulator phase diagram in the strong coupling limit comparable with the accuracy of the density-matrix renormalization group. In the weak coupling limit, neural networks also diagnose other many-body phenomena such as the vortex, chiral, and biased-ladder phases. Our work demonstrates that the two-leg Bose-Hubbard model with magnetic flux is an ideal test ground for future developments of neural-network quantum states.

Discovery of charge density wave in a kagome lattice antiferromagnet.

A hallmark of strongly correlated quantum materials is the rich phase diagram resulting from competing and intertwined phases with nearly degenerate ground-state energies1,2. A well-known example is the copper oxides, in which a charge density wave (CDW) is ordered well above and strongly coupled to the magnetic order to form spin-charge-separated stripes that compete with superconductivity1,2. Recently, such rich phase diagrams have also been shown in correlated topological materials. In 2D kagome lattice metals consisting of corner-sharing triangles, the geometry of the lattice can produce flat bands with localized electrons3,4, non-trivial topology5-7, chiral magnetic order8,9, superconductivity and CDW order10-15. Although CDW has been found in weakly electron-correlated non-magnetic AV3Sb5 (A = K, Rb, Cs)10-15, it has not yet been observed in correlated magnetic-ordered kagome lattice metals4,16-21. Here we report the discovery of CDW in the antiferromagnetic (AFM) ordered phase of kagome lattice FeGe (refs. 16-19). The CDW in FeGe occurs at wavevectors identical to that of AV3Sb5 (refs. 10-15), enhances the AFM ordered moment and induces an emergent anomalous Hall effect22,23. Our findings suggest that CDW in FeGe arises from the combination of electron-correlations-driven AFM order and van Hove singularities (vHSs)-driven instability possibly associated with a chiral flux phase24-28, in stark contrast to strongly correlated copper oxides1,2 and nickelates29-31, in which the CDW precedes or accompanies the magnetic order.

Cryogenic Electron Microscopy on Strongly Correlated Quantum Materials

Cryogenic Electron Microscopy on Strongly Correlated Quantum Materials

Thermoelectric transport properties of gapless pinned charge density waves

Quantum strongly correlated matter exhibits properties which are not easily explainable in the conventional framework of Fermi liquids. Universal effective field theory tools are applicable in these cases regardless of the microscopic details of the quantum system, since they are based on symmetries. It is necessary, however, to construct these effective tools in full generality, avoiding restrictions coming from particular microscopic descriptions which may inadequately constrain the coefficients that enter in the effective theory. In this work we demonstrate with explicit examples how the hydrodynamic coefficients, which have been recently reinstated in the effective theory of pinned charge density waves (CDWs), can affect the phenomenology of the thermoelectric transport in strongly correlated quantum matter. Our examples, based on two classes of holographic models with pinned CDW, have microscopics which are conceptually different from Fermi liquids. Therefore, the above transport coefficients are nonzero, contrary to the conventional approach. We show how these coefficients allow one to take into account the change of sign of the Seebeck coefficient and the low resistivity of the CDW phase of the cuprate high temperature superconductors, without referring to the effects of Fermi surface reconstruction.

Local density of states and particle entanglement in topological quantum fluids

The understanding of particle entanglement is an important goal in the studies of correlated quantum matter. The widely-used method of scanning tunneling spectroscopy -- which measures the local density of states (LDOS) of a many-body system by injecting or removing an electron from it -- is expected to be sensitive to particle entanglement. In this paper, we systematically investigate the relation between the particle entanglement spectrum (PES) and the LDOS of fractional quantum Hall (FQH) states, the paradigmatic strongly-correlated phases of electrons with topological order. Using exact diagonalization, we show that the counting of levels in both the LDOS and PES in the Jain sequence of FQH states can be predicted from the composite fermion theory. We point out the differences between LDOS and PES characterization of the bulk quasihole excitations, and we discuss the conditions under which the LDOS counting can be mapped to that of PES. Our results affirm that tunneling spectroscopy is a sensitive tool for identifying the nature of FQH states.

On the closedness and geometry of tensor network state sets

Tensor network states (TNS) are a powerful approach for the study of strongly correlated quantum matter. The curse of dimensionality is addressed by parametrizing the many-body state in terms of a network of partially contracted tensors. These tensors form a substantially reduced set of effective degrees of freedom. In practical algorithms, functionals like energy expectation values or overlaps are optimized over certain sets of TNS. Concerning algorithmic stability, it is important whether the considered sets are closed because, otherwise, the algorithms may approach a boundary point that is outside the TNS set and tensor elements diverge. We discuss the closedness and geometries of TNS sets, and we propose regularizations for optimization problems on non-closed TNS sets. We show that sets of matrix product states (MPS) with open boundary conditions, tree tensor network states, and the multiscale entanglement renormalization ansatz are always closed, whereas sets of translation-invariant MPS with periodic boundary conditions (PBC), heterogeneous MPS with PBC, and projected entangled pair states are generally not closed. The latter is done using explicit examples like the W state, states that we call two-domain states, and fine-grained versions thereof.

Pseudogap phase and fractionalization: Predictions for Josephson junction setup

The pseudogap regime of the underdoped cuprates arguably remains one of the most enigmatic phenomena of correlated quantum matter. Recent theoretical ideas suggest that a pair density wave (PDW) or a "fractionalized PDW" could be a key ingredient for the understanding of the pseudogap physics. These ideas are to be contrasted to the scenario where charge density wave order and superconductivity coexist at low temperatures. In this paper, we present a few tests to compare the two scenarios in a Josephson junction setup. For a PDW scenario, we observe a beat-like structure of AC Josephson current. The additional frequencies for the AC Josephson current appear at the half-odd integer multiple of the standard Josephson frequency. We can extract the modulation wavevector of the PDW state by studying the average Josephson current. Furthermore, the usual sharp Shapiro steps break down. In contrast, these signatures are absent for the simple coexistence of orders. Any detection of such signatures in a similar experimental setup will strongly support the PDW scenario for the pseudogap phase.