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DOE OSTI2025

Magnetically tuned metal-insulator transition in LaAlO 3 /SrTiO 3 nanowire arrays

A wide family of two-dimensional (2D) systems, including stripe-phase superconductors, sliding Luttinger liquids, and anisotropic 2D materials, can be modeled by an array of coupled one-dimensional (1D) electron channels or nanowire arrays. Here we report experiments in arrays of conducting nanowires with gate and field tunable interwire coupling, that are programmed at the LaAlO 3 /SrTiO 3 interface. We find a magnetically tuned metal-to-insulator transition in which the transverse resistance of the nanowire array increases by up to four orders of magnitude, which can be further tuned with a gate voltage. To explain this behavior, we develop a minimal model of a coupled two-wire system where a Wenzel-Kramers-Brillouin-based approach is used to estimate the transverse tunneling conductance. We demonstrate the existence of distinct conductance features and highlight the crucial role played by the field dependence of the interwire potential barrier on transport properties. Since our model makes minimal assumptions, we expect our predictions to hold for a wide class of coupled 1D systems. The nanowire arrays can serve as model systems to understand the origin of exotic behavior in correlated materials via analog quantum simulation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Ferromagnetism and doublon localization in a Wannier-Hubbard chain

We derive a “Wannier-Hubbard” model consisting of an array of overlapping atomic orbitals interacting via a local Coulomb interaction. Transforming to an orthogonal Wannier basis set, the resulting Hamiltonian displays long-range hopping and interactions, with new terms such as correlated hopping and ferromagnetic direct exchange, among others. We numerically study the one-dimensional version of the model at half-filling using the density matrix renormalization group method, unveiling a rich phase diagram as a function of the interaction U and the overlap s with metallic and ferromagnetic phases separated by a ferrimagnetic region. Our results indicate a path toward understanding emergent phases under pressure and beyond standard model Hamiltonians.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Superdiffusive transport of energy in one-dimensional metals

Metals in one spatial dimension are described at the lowest energy scales by the Luttinger liquid theory. It is well understood that this free theory, and even interacting integrable models, can support ballistic transport of conserved quantities including energy. In contrast, realistic one-dimensional metals, even without disorder, contain integrability-breaking interactions that are expected to lead to thermalization and conventional diffusive linear response. We argue that the expansion of energy when such a nonintegrable Luttinger liquid is locally heated above its ground state shows superdiffusive behavior (i.e., spreading of energy that is intermediate between diffusion and ballistic propagation), by combining an analytical anomalous diffusion model with numerical matrix-product–state calculations on a specific perturbed spinless fermion chain. Different metals will have different scaling exponents and shapes in their energy spreading, but the superdiffusive behavior is stable and should be visible in time-resolved experiments.

Bulchandani, Vir B.↗

DOE OSTI2020

Off-shell effective energy theory: A unified treatment of the Hubbard model from $\textit{d} = 1$ to $\textit{d = ∞}$

Here we propose an exact formalism, off-shell effective energy theory (OET), which provides a thermodynamic description of a generic quantum Hamiltonian. The OET is based on a partitioning of the Hamiltonian and a corresponding density matrix ansatz constructed from an off-shell extension of the equilibrium density matrix; and there are dual realizations based on a given partitioning. To approximate OET, we introduce the central point expansion (CPE), which is an expansion of the density matrix ansatz, and we renormalize the CPE using a standard expansion of the ground-state energy. In this work we showcase the OET for the one-band Hubbard model in $\textit{d}$ = 1 , 2, and $\infty$, using a partitioning between kinetic and potential energy, yielding two realizations denoted as $\mathcal{K}$ and $\mathcal{X}$. OET shows favorable agreement with exact or state-of-the-art results over all parameter space, and has a negligible computational cost. Physically, $\mathcal{K}$ describes the Fermi liquid, while $\mathcal{X}$ gives an analogous description of both the Luttinger liquid and the Mott insulator. Our approach should find broad applicability in lattice model Hamiltonians, in addition to real materials systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Conductance of a dissipative quantum dot: Nonequilibrium crossover near a non-Fermi-liquid quantum critical point

In this work, we find the nonlinear conductance of a dissipative resonant level in the nonequilibrium steady state near its quantum critical point. The system consists of a spin-polarized quantum dot connected to two resistive leads that provide ohmic dissipation. We focus on the crossover from the strong-coupling, non-Fermi-liquid regime to the weak-coupling, Fermi-liquid ground state, a crossover driven by the instability of the quantum critical point to hybridization asymmetry or detuning of the level in the dot. We show that the crossover properties are given by tunneling through an effective single barrier described by the boundary sine-Gordon model. The nonlinear conductance is then obtained from thermodynamic Bethe ansatz results in the literature, which were developed to treat tunneling in a Luttinger liquid. The current-voltage characteristics are thus found for any value of the resistance of the leads. For the special case of lead resistance equal to the quantum resistance, we find mappings onto, first, the two-channel Kondo model and, second, an effectively noninteracting model from which the nonlinear conductance is found analytically. A key feature of the general crossover function is that the nonequilibrium crossover driven by applied bias is different from the crossover driven by temperature---we find that the nonequilibrium crossover is substantially sharper. Finally, we compare to experimental results for both the bias and temperature crossovers: the agreement is excellent.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Pairing instability on a Luttinger surface: A non-Fermi liquid to superconductor transition and its Sachdev-Ye-Kitaev dual

Superconductivity results from an instability of the Fermi surface—contour of poles of the single-particle propagator—to an infinitesimally small attraction between electrons. Here, we instead discuss the analogous problem on a model Luttinger surface, or contour of zeros of the Green function. At zero temperature ($β → \infty$) and a critical interaction strength ($u_{c∞}$) characterized by the residue of self-energy pole, we find that the pair susceptibility diverges leading to a superconducting instability. We evaluate the pair fluctuation partition function and find that the spectral density in the normal state has an interaction-driven, power-law $\frac{1}{\sqrt{ω}}$ type, van-Hove singularity (vHS), indicating non-Fermi liquid (NFL) physics. Crucially, in the strong coupling limit ($βu \gg 1$), the leading-order fluctuation free-energy terms in the normal state of this NFL-SC transition resembles the equivalent [$\textit{O}(1)$] terms of the Sachdev-Ye-Kitaev (SYK) model. This free-energy contribution takes a simple form $–βF = βu_{c∞} – γ \text{ln}(βu_{c∞}$), where $\gamma$ is a constant equal to $\frac{1}{2}$. Weak impurity scattering ($τ \gg β^{–1}$) leaves the low-energy spectral density unaffected but leads to an interaction-driven enhancement of superconductivity. Our results in this work shed light on the role played by order-parameter fluctuations in providing the key missing link between Mott physics and strongly coupled toy models exhibiting gravity duals.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Charge-density-wave melting in the one-dimensional Holstein model

We study the Holstein model of spinless fermions, which at half filling exhibits a quantum phase transition from a metallic Tomonaga-Luttinger liquid phase to an insulating charge-density-wave (CDW) phase at a critical electron-phonon coupling strength. In our work, we focus on the real-time evolution starting from two different types of initial states that are CDW ordered: (i) ideal CDW states with and without additional phonons in the system and (ii) correlated ground states in the CDW phase. We identify the mechanism for CDW melting in the ensuing real-time dynamics and show that it strongly depends on the type of initial state. We focus on the far-from-equilibrium regime and emphasize the role of electron-phonon coupling rather than dominant electronic correlations, thus complementing a previous study of photoinduced CDW melting [H. Hashimoto and S. Ishihara, Phys. Rev. B 96, 035154 (2017)]. The numerical simulations are performed by means of matrix-product-state based methods with a local basis optimization (LBO). Within these techniques, one rotates the local (bosonic) Hilbert spaces adaptively into an optimized basis that can then be truncated while still maintaining a high precision. In this work, we extend the time-evolving block decimation (TEBD) algorithm with LBO, previously applied to single-polaron dynamics, to a half-filled system. We demonstrate that in some parameter regimes, a conventional TEBD method without LBO would fail. Furthermore, we introduce and use a ground-state density-matrix renormalization group method for electron-phonon systems using local basis optimization. In our examples, we account for up to M ph =40 bare phonons per site by working with O(10) optimal phonon modes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Quantum wake dynamics in Heisenberg antiferromagnetic chains

Traditional spectroscopy, by its very nature, characterizes physical system properties in the momentum and frequency domains. However, the most interesting and potentially practically useful quantum many-body effects emerge from local, short-time correlations. Here, using inelastic neutron scattering and methods of integrability, we experimentally observe and theoretically describe a local, coherent, long-lived, quasiperiodically oscillating magnetic state emerging out of the distillation of propagating excitations following a local quantum quench in a Heisenberg antiferromagnetic chain. This “quantum wake” displays similarities to Floquet states, discrete time crystals and nonlinear Luttinger liquids. We also show how this technique reveals the non-commutativity of spin operators, and is thus a model-agnostic measure of a magnetic system’s “quantumness.”

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Multiple fermion scattering in the weakly coupled spin-chain compound YbAlO 3

The Heisenberg antiferromagnetic spin-1/2 chain, originally introduced almost a century ago, is one of the best studied models in quantum mechanics due to its exact solution, but nevertheless it continues to present new discoveries. Its low-energy physics is described by the Tomonaga-Luttinger liquid of spinless fermions, similar to the conduction electrons in one-dimensional metals. In this work we investigate the Heisenberg spin-chain compound YbAlO3 and show that the weak interchain coupling causes Umklapp scattering between the left- and right-moving fermions and stabilizes an incommensurate spin-density wave order at q = 2k F under finite magnetic fields. These Umklapp processes open a route to multiple coherent scattering of fermions, which results in the formation of satellites at integer multiples of the incommensurate fundamental wavevector Q = nq. Our work provides surprising and profound insight into bandstructure control for emergent fermions in quantum materials, and shows how neutron diffraction can be applied to investigate the phenomenon of coherent multiple scattering in metals through the proxy of quantum magnetic systems.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Breakdown of helical edge state topologically protected conductance in time-reversal-breaking excitonic insulators

Gapless helical edge modes are a hallmark of the quantum spin Hall effect. Protected by time-reversal symmetry, each edge contributes a quantized zero-temperature conductance quantum G 0 ≡ e 2 /h. However, the experimentally observed conductance in WT e2 decreases below G 0 per edge already at edge lengths around 100 nm, even in the absence of explicit time-reversal breaking due to an external field or magnetic impurities. Here we show how a time-reversal breaking excitonic condensate with a spin-spiral order that can form in WT e2 leads to the breakdown of conductance quantization. We perform Hartree-Fock calculations to compare time-reversal breaking and preserving excitonic insulators. Using these mean-field models we demonstrate via quantum transport simulations that weak nonmagnetic disorder reproduces the edge length scaling of resistance observed in the experiments. We complement this by analysis in the Luttinger liquid picture, shedding additional light on the mechanism behind the quantization breakdown.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Nuclear Matter in 1 + 1 Dimensions

We review the solution of QCD in two spacetime dimensions. Following the analysis of Baluni, for a single flavor, the model can be analyzed using Abelian bosonization. The theory can be analyzed in strong coupling, when the quarks are much lighter than the gauge coupling. In this limit, the theory is given by a Luttinger liquid.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Gate-tunable plasmons in mixed-dimensional van der Waals heterostructures

Abstract Surface plasmons, collective electromagnetic excitations coupled to conduction electron oscillations, enable the manipulation of light–matter interactions at the nanoscale. Plasmon dispersion of metallic structures depends sensitively on their dimensionality and has been intensively studied for fundamental physics as well as applied technologies. Here, we report possible evidence for gate-tunable hybrid plasmons from the dimensionally mixed coupling between one-dimensional (1D) carbon nanotubes and two-dimensional (2D) graphene. In contrast to the carrier density-independent 1D Luttinger liquid plasmons in bare metallic carbon nanotubes, plasmon wavelengths in the 1D-2D heterostructure are modulated by 75% via electrostatic gating while retaining the high figures of merit of 1D plasmons. We propose a theoretical model to describe the electromagnetic interaction between plasmons in nanotubes and graphene, suggesting plasmon hybridization as a possible origin for the observed large plasmon modulation. The mixed-dimensional plasmonic heterostructures may enable diverse designs of tunable plasmonic nanodevices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Broken Luttinger theorem in the two-dimensional Fermi-Hubbard model

One of the fundamental questions about high-temperature cuprate superconductors is the size of the Fermi surface underlying the superconducting state. By analyzing the single-particle spectral function for the Fermi-Hubbard model as a function of repulsion U and chemical potential μ, we find that the Fermi surface in the normal state undergoes a transition from a large Fermi surface matching the Luttinger volume as expected in a Fermi liquid, to a Fermi surface that encloses fewer electrons that we dub the “Luttinger breaking” phase, as the Mott insulator is approached. This transition into a non-Fermi-liquid phase that violates the Luttinger count occurs at a critical density in the absence of any other broken symmetry. We obtain the Fermi-surface contour from the spectral weight A k (ω = 0) and from an analysis of the singularities of the Green's function Re G k (E = 0), calculated using determinantal quantum Monte Carlo and analytic continuation methods. We discuss our numerical results in connection with experiments on Hall measurements, scanning tunneling spectroscopy, and angle-resolved photoemission spectroscopy.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Spin crossovers and superdiffusion in the one-dimensional Hubbard model

We use tools from integrability and generalized hydrodynamics to study finite-temperature dynamics in the one-dimensional Hubbard model. First, we examine charge, spin, and energy transport away from half-filling and zero magnetization, focusing on the strong coupling regime where we identify a rich interplay of temperature and energy scales, with crossovers between distinct dynamical regimes. We identify an intermediate-temperature regime analogous to the spin-incoherent Luttinger liquid, where spin degrees of freedom are hot but charge degrees of freedom are at low temperature. We demonstrate that the spin Drude weight exhibits sharp features at the crossover between this regime and the low-temperature Luttinger liquid regime, which are absent in the charge and energy response, and rationalize this behavior in terms of the properties of Bethe ansatz quasiparticles.We then turn to the dynamics along special lines in the phase diagram corresponding to half-filling and/or zero magnetization where on general grounds we anticipate that the transport is subballistic but superdiffusive. We provide analytical and numerical evidence for Kardar-Parisi-Zhang (KPZ) dynamical scaling (with length and time scales related via x ~ t 2/3 ) along both lines and at the SO(4)-symmetric point where they intersect. Furthermore, our results suggest that both spin-coherence crossovers and KPZ scaling may be accessed in near-term experiments with optical lattice Hubbard emulators.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Charge order and superconductivity in a two-band model for infinite-layer nickelates

The recent discovery of superconductivity in infinite-layer nickelates has drawn considerable attention; however, a consensus on the fundamental building blocks and common ingredients necessary to understand and describe their ground states and emergent properties is lacking. A series of experimental and theoretical studies have suggested that an effective two-band Hubbard model with Ni 3d x 2 -y 2 and rare-earth (R) 5d character may describe the low-energy physics. In this report we study the ground state properties of this two-band model on four-leg cylinders using the density-matrix renormalization group (DMRG) technique to better grasp whether such a simple model can embody the essential physics. A key difference compared to single-band Hubbard materials is that the system is self-doped: even at overall half-filling, the R-band acts as an electron reservoir, hole-doping the Ni-layer and fundamentally altering the physics expected from an undoped antiferromagnet. On the four-leg cylinder, the ground state is consistent with a Luttinger liquid, with anti-phase modulations of the charge density in the Ni- and R-layers having corresponding wavevectors that lock together. Light hole doping away from 1/2 filling releases the locking between the Ni and the R charge modulations, as the electron density in the R-band decreases and eventually becomes exhausted at a hole doping concentration that depends sensitively on the effective splitting between the Ni and the R orbitals. The ground state of the doped system is consistent with a Luther-Emery liquid, possessing quasi-long-range superconducting correlations in the Ni layer, similar to the single-band Hubbard model. Our results are consistent with experimental observations and may help to reveal the microscopic mechanism for pairing and other emergent properties.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Spin-triplet pairing induced by near-neighbor attraction in the extended Hubbard model for cuprate chain

Abstract In quantum materials, the electronic interaction and the electron-phonon coupling are, in general, two essential ingredients, the combined impact of which may drive exotic phases. Recently, an anomalously strong electron-electron attraction, likely mediated by phonons, has been proposed in one-dimensional copper-oxide chain Ba 2− x Sr x CuO 3+ δ . Yet, it is unclear how this strong near-neighbor attraction V influences the superconductivity pairing in the system. Here we perform accurate many-body calculations to study the extended Hubbard model with on-site Coulomb repulsion U > 0 and near-neighbor attraction V < 0 that could well describe the cuprate chain and likely other similar transition-metal materials with both strong correlations and lattice effects. We find a rich quantum phase diagram containing an intriguing Tomonaga-Luttinger liquid phase — besides the spin density wave and various phase separation phases — that can host dominant spin-triplet pairing correlations and divergent superconductive susceptibility. Upon doping, the spin-triplet superconducting regime can be further broadened, offering a feasible mechanism to realize p -wave superconductivity in realistic cuprate chains.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Accurate localization of Kosterlitz-Thouless-type quantum phase transitions for one-dimensional spinless fermions

We investigate the charge-density wave (CDW) transition for one-dimensional spinless fermions at half band filling with nearest-neighbor electron transfer amplitude t and interaction V. The model is equivalent to the anisotropic XXZ Heisenberg model for which the Bethe Ansatz provides an exact solution. For V>V c =2t, the CDW order parameter and the single-particle gap are finite but exponentially small, as is characteristic for a Kosterlitz-Thouless transition. It is notoriously difficult to locate such infinite-order phase transitions in the phase diagram using approximate analytical and numerical approaches. Second-order Hartree-Fock theory is qualitatively applicable for all interaction strengths, and predicts the CDW transition to occur at V$^{(2)}_{c,2}$≈1.5t. Second-order Hartree Fock theory is almost variational because the density of quasiparticle excitations is small. We apply the density-matrix renormalization group (DMRG) for periodic boundary conditions for system sizes up to 514 sites, which permits a reliable extrapolation of all physical quantities to the thermodynamic limit, apart from the critical region. We investigate the ground-state energy, the gap, the order parameter, the momentum distribution, the quasiparticle density, and the density-density correlation function to locate V c from the DMRG data. In conclusion, tracing the breakdown of the Luttinger liquid and the peak in the quasiparticle density at the band edge permits us to reproduce V c with an accuracy of one percent.

1-dimensional spin chains↗

DOE OSTI2023

Free energy and specific heat near a quantum critical point of a metal

We analyze the free energy and the specific heat for fermions interacting with a gapless boson at a quantum-critical point (QCP) in a metal. We use the Luttinger-Ward-Eliashberg formula for the free energy in the normal state, which includes contributions from bosons, fermions, and their interaction, all expressed via fully dressed fermionic and bosonic propagators. The sum of the last two contributions is the free energy F γ of an effective low-energy model of fermions with boson-mediated dynamical 4-fermion interaction V(Ω m ) ∝ 1/|Ω m | γ (the γ model). This purely electronic model has been used to analyze the interplay between non-Fermi liquid behavior and pairing near a QCP, which are both independent of the upper energy cutoff Λ. However, the specific heat C γ (T), obtained from F γ , does depend on Λ. We argue that this dependence is spurious and cancels out, once we include the contribution from bosons. We further argue that the full C(T) is the sum of the contribution from free fermions and the one from a critical boson, with the fully dressed propagator, other terms cancel out. We compare the full C(T) with the C γ (T), obtained using recently proposed regularization of F γ . We argue that for γ < 1, the full C(T) and the regularized C γ (T) differ by a γ-dependent prefactor, while for γ > 1, the full C(T) and C γ (T) differ by the positive contribution from free massless fermions (a positive constant for the electron-phonon case γ = 2). For these γ, C γ (T) is negative, but the full C(T) is positive. We argue that only the full C(T) matters as the positive and the negative contributions originate from the term in C(T) which contains the fully dressed bosonic propagator. Here, we then argue that the normal state remains stable until the pairing instability develops.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗