arXiv subjects

Alberto Nocera

Publications and source records attributed to Alberto Nocera.

At least 37 records · Page 2Linked to original sources

arXiv2024

Identifying and quantifying Su-Schrieffer-Heeger-like interactions with RIXS

Su-Schrieffer-Heeger (SSH)-like electron-phonon (e-ph) interactions can drive the formation of light (bi)polarons and several novel states of matter. It is, therefore, prudent to develop experimental protocols for identifying such couplings in real materials and quantifying their strength. Here, we investigate how resonant inelastic x-ray scattering (RIXS) probes e-ph interactions in the one-dimensional half-filled Hubbard-SSH model with onsite phonons. Using the density matrix renormalization group method, we compute the full RIXS response and find that the lattice excitations generated during the scattering process inevitably couple to the system's charge and magnetic sectors, resulting in combined multi-particle excitations that cannot be easily disentangled from one another. While this aspect complicates the interpretation of RIXS experiments, we outline how it can be leveraged to identify and quantify SSH-like interactions in quantum materials.

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arXiv2024

Theory of electron-phonon interactions in extended correlated systems probed by resonant inelastic x-ray scattering

An emerging application of resonant inelastic x-ray scattering (RIXS) is the study of lattice excitations and electron-phonon ($e$-ph) interactions in quantum materials. Despite the growing importance of this area of research, the community lacks a complete understanding of how the RIXS process excites the lattice and how these excitations encode information about the $e$-ph interactions. Here, we present a detailed study of the RIXS spectra of the Hubbard-Holstein model defined on extended one-dimensional lattices. Using the density matrix renormalization group (DMRG) method, we compute the RIXS response while treating the electron mobility, many-body interactions, and core-hole interactions on an equal footing. The predicted spectra exhibit notable differences from those obtained using the commonly adopted Lang-Firsov models, with important implications for analyzing past and future experiments. Our results provide a deeper understanding of how RIXS probes $e$-ph interactions and set the stage for a more realistic analysis of future experiments.

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arXiv2024

Nonsymmorphic spin-space cubic groups and SU(2)$_1$ conformal invariance in one-dimensional spin-1/2 models

Recently, extended gapless phases with emergent SU(2)$_1$ conformal invariance occupying finite regions in the phase diagrams have been found in one-dimensional spin-1/2 models with nonsymmorphic $O_h$ symmetry groups. In this work, we investigate the question of whether the conditions for emergent SU(2)$_1$ invariance can be loosened. We find that besides the nonsymmorphic $O_h$ group, the other four smaller nonsymmorphic cubic groups including $O$, $T_h$, $T_d$ and $T$ can also give rise to emergent SU(2)$_1$ invariance. Minimal spin-1/2 models having these nonsymmorphic cubic groups as symmetry groups are constructed, and numerical evidences for the emergent SU(2)$_1$ invariance are provided. Our work is useful for understanding gapless phases in one-dimensional spin systems with nonsymmorphic symmetries.

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arXiv2024

Quantum Quench Dynamics of Geometrically Frustrated Ising Models

Geometric frustration in two-dimensional Ising models allows for a wealth of exotic universal behavior, both Ising and non-Ising, in the presence of quantum fluctuations. In particular, the triangular antiferromagnet and Villain model in a transverse field can be understood through distinct XY pseudospins, but have qualitatively similar phase diagrams including a quantum phase transition in the (2+1)-dimensional XY universality class. While the quantum dynamics of modestly-sized systems can be simulated classically using tensor-based methods, these methods become infeasible for larger lattices. Here we perform both classical and quantum simulations of these dynamics, where our quantum simulator is a superconducting quantum annealer. Our observations on the triangular lattice suggest that the dominant quench dynamics are not described by the quantum Kibble-Zurek scaling of the quantum phase transition, but rather a faster coarsening dynamics in an effective two-dimensional XY model in the ordered phase. Similarly, on the Villain model, the scaling exponent does not match the Kibble-Zurek expectation. These results demonstrate the ability of quantum annealers to simulate coherent quantum dynamics and scale beyond the reach of classical approaches.

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arXiv2024

Nonsymmorphic bosonization in one-dimensional generalized Kitaev spin-1/2 models

In this work, we perform a detailed study on the consequences of nonsymmorphic symmetries in the Luttinger phase of the one-dimensional spin-1/2 Kitaev-Heisenberg-Gamma model with an antiferromagnetic Kitaev interaction. Nonsymmorphic bosonization formulas for the spin operators are proposed, containing ten non-universal coefficients which are determined by our density matrix renormalization group simulations to a high degree of accuracy. Using the nonsymmorphic bosonization formulas, different Fourier components and decay powers in the correlation functions are disentangled, the response to weak magnetic fields is analyzed, and the zigzag magnetic order in two dimensions is recovered from a system of weakly coupled chains. We also find a line of critical points with an emergent SU(2)$_1$ conformal symmetry located on the boundary of the Luttinger liquid phase, where a nonabelian version of nonsymmorphic bosonization should be applied.

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arXiv2023

Quantum error mitigation in quantum annealing

Quantum Error Mitigation (QEM) presents a promising near-term approach to reduce error when estimating expectation values in quantum computing. Here, we introduce QEM techniques tailored for quantum annealing, using Zero-Noise Extrapolation (ZNE). We implement ZNE through zero-temperature extrapolation as well as energy-time rescaling. We conduct experimental investigations into the quantum critical dynamics of a transverse-field Ising spin chain, demonstrating the successful mitigation of thermal noise through both of these techniques. Moreover, we show that energy-time rescaling effectively mitigates control errors in the coherent regime where the effect of thermal noise is minimal. Our ZNE results agree with exact calculations of the coherent evolution over a range of annealing times that exceeds the coherent annealing range by almost an order of magnitude.

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arXiv2023

A time-dependent scattering approach to core-level spectroscopies

While new light sources allow for unprecedented resolution in experiments with X-rays, a theoretical understanding of the scattering cross-section is lacking. In the particular case of strongly correlated electron systems, numerical techniques are quite limited, since conventional approaches rely on calculating a response function (Kramers-Heisenberg formula) that is obtained from a perturbative analysis of scattering processes in the frequency domain. This requires a knowledge of a full set of eigenstates in order to account for all intermediate processes away from equilibrium, limiting the applicability to small tractable systems. In this work, we present an alternative paradigm, recasting the problem in the time domain and explicitly solving the time-dependent Schrödinger equation without the limitations of perturbation theory: a faithful simulation of the scattering processes taking place in actual experiments, including photons and core electrons. We show how this approach can yield the full time and momentum resolved Resonant Inelastic X-Ray Scattering (RIXS) spectrum of strongly interacting many-body systems. We demonstrate the formalism with an application to Mott insulating Hubbard chains using the time-dependent density matrix renormalization group method, which does not require a priory knowledge of the eigenstates and can solve very large systems with dozens of orbitals. This approach can readily be applied to systems out of equilibrium without modification and generalized to other spectroscopies.

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arXiv2023

Auger spectroscopy beyond the ultra-short core-hole relaxation time approximation

We present a time-dependent computational approach to study Auger electron spectroscopy (AES) beyond the ultra-short core-hole relaxation time approximation and, as a test case, we apply it to the paradigmatic example of a one-dimensional Mott insulator represented by a half-filled Hubbard chain. The Auger spectrum is usually calculated by assuming that, after the creation of a core-hole, the system thermalizes almost instantaneously. This leads to a relatively simple analytical expression that uses the ground-state with a core-hole as a reference state and ignores all the transient dynamics related to the screening of the core-hole. In this picture, the response of the system can be associated to the pair spectral function. On the other hand, in our numerical calculations, the core hole is created by a light pulse, allowing one to study the transient dynamics of the system in terms of the pulse duration and in the non-perturbative regime. Time-dependent density matrix renormalization group calculations reveal that the relaxation process involves the creation of a polarization cloud of doublon excitations that have an effect similar to photo-doping. As a consequence, there is a leak of spectral weight to higher energies into what otherwise would be the Mott gap. For longer pulses, these excited states, mostly comprised of doublons, can dominate the spectrum. By changing the duration of the light-pulse, the entire screening process can be resolved in time.

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arXiv2023

Electron addition spectral functions of low-density polaron liquids

Spectral functions are important quantities that contain a wealth of information about the quasiparticles of a system, and that can also be measured experimentally. For systems with electron-phonon coupling, good approximations for the spectral function are available only in the Migdal limit (at Fermi energies much larger than the typical phonon frequency, $E_F\gg Ω$, requiring a large carrier concentration $x$) and in the single polaron limit (at $x=0$). Here we show that the region with $x\ll 1$ ($E_F <Ω$) can also be reliably investigated with the Momentum Average (MA) variational approximation, which essentially describes the formation of a polaron above an inert Fermi sea. Specifically, we show that for the one-dimensional spinless Holstein model, the MA spectral functions compare favorably with those calculated using variationally exact density matrix renormalization group simulations (DMRG) evaluated directly in frequency-space, so long as $x<0.1$ and the adiabaticity ratio $Ω/t>0.5$. Unlike in the Migdal limit, here 'polaronic physics' emerges already at moderate couplings. The relevance of these results for a spinful low-$x$ metal is also discussed.

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arXiv2023

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

We present a density matrix renormalization group (DMRG) study of the doped one-dimensional (1D) Hubbard-Su-Schrieffer-Hegger (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 ($e$-ph) coupling strengths below a parameter-dependent critical value $g_\mathrm{c}$. For larger $e$-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 $e$-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.

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arXiv2022

Bipolaron liquids at strong Peierls electron-phonon couplings

We use the Density Matrix Renormalization Group method to study a one-dimensional chain with Peierls electron-phonon coupling, which describes the modulation of the electron hopping by lattice distortions. We demonstrate that this system is stable against phase separation in the dilute density limit. We only find phase separation numerically for large couplings for which the linear approximation for the electron-phonon coupling becomes invalid; this behavior can be stabilized in a narrow sliver of the physical parameter space if the dispersion of the phonons is carefully tuned. These results indicate that in the dilute electron density limit, Peierls bipolaron liquids are generically stable, unlike in other models of electron-phonon coupling. We show that this behavior extends to finite carrier concentrations of up to quarter filling. This stability of low-density, light-mass bipolaron liquids in the Peierls model opens a path to high-$T_c$ superconductivity based on a bipolaronic mechanism, in higher dimensions.

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arXiv2022

Origin of nonsymmorphic bosonization formulas in generalized antiferromagnetic Kitaev spin-$\frac{1}{2}$ chains from a renormalization-group perspective

Recently, in the Luttinger liquid phase of the one-dimensional generalized antiferromagnetic Kitaev spin-1/2 model, it has been found that the abelian bosonization formulas of the local spin operators only respect the exact discrete nonsymmorphic symmetry group of the model, not the emergent U(1) symmetry. In this work, we perform a renormalization group (RG) study to provide explanations for the origin of the U(1) breaking terms in the bosonization formulas. We find that the lack of U(1) symmetry originates from the wavefunction renormalization effects in the spin operators along the RG flow induced by the U(1) breaking interactions in the microscopic Hamiltonian. In addition, the RG analysis can give predictions to the signs and order of magnitudes of the coefficients in the bosonization formulas. Our work is helpful to understand the rich nonsymmorphic physics in one-dimensional Kitaev spin models.

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arXiv2022

Counter-rotating spiral, zigzag, and 120$^\circ$ orders from coupled-chain analysis of Kitaev-Gamma-Heisenberg model, and relations to honeycomb iridates

We study the nearest neighboring spin-1/2 Kitaev-Heisenberg-Gamma ($KJΓ$) model on the honeycomb lattice in the parameter region of ferromagnetic (FM) Kitaev and antiferromagnetic (AFM) Heisenberg couplings relevant for honeycomb iridates, using a coupled-chain analysis. Starting from the gapless Luttinger liquid phase of a decoupled $KJΓ$ chain, the inter-chain interactions in the two-dimensional model is treated within a self-consistent mean field approach based on the Luttinger liquid theory. In the FM Gamma region, our analysis recovers the reported 120$^\circ$ magnetic order, previously obtained by classical analysis and exact diagonalization method. On the other hand, new physics is revealed in the AFM Gamma region, where three magnetic orders are found, including 120$^\circ$, commensurate counter-rotating spiral, and zigzag orders. Interestingly, the two first order phase transition lines separating these three magnetic orders merge at a single point at $K = -2 Γ$ and $J=0$, which is predicted to be a quantum critical point. The current theory captures the experimentally observed counter-rotating spiral order in $α$-Li$_22$IrO$_3$ and the zigzag order in Na$_2$IrO$_3$, thereby indicating that the spin-1/2 $KJΓ$ model may serve as a minimal model for honeycomb iridates. Limitations of the mean field theory presented in this work and the $J \rightarrow 0$ regime are also discussed.

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arXiv2022

Root-N Krylov-space correction-vectors for spectral functions with the density matrix renormalization group

We propose a method to compute spectral functions of generic Hamiltonians using the density matrix renormalization group (DMRG) algorithm directly in the frequency domain, based on a modified Krylov space decomposition to compute the correction-vectors. Our approach entails the calculation of the root-N (N=2 is the standard square root) of the Hamiltonian propagator using Krylov space decomposition, and repeating this procedure N times to obtain the actual correction-vector. We show that our method greatly alleviates the burden of keeping a large bond dimension at large target frequencies, a problem found with conventional correction-vector DMRG, while achieving better computational performance at large N. We apply our method to spin and charge spectral functions of t-J and Hubbard models in the challenging two-leg ladder geometry, and provide evidence that the root-N approach reaches a much improved resolution compared to conventional correction-vector.

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arXiv2022

Symmetry analysis of bond-alternating Kitaev spin chains and ladders

In this work, we analyze the nonsymmorphic symmetry group structures for a variety of generalized Kitaev spin chains and ladders with bond alternations, including Kitaev-Gamma chain, Kitaev-Heisenberg-Gamma chain, beyond nearest neighbor interactions, and two-leg spin ladders. The symmetry analysis is applied to determine the symmetry breaking patterns of several magnetically ordered phases in the bond-alternating Kitaev-Gamma spin chains, as well as the dimerization order parameters for spontaneous dimerizations. Our work is useful in understanding the magnetic phases in related models and may provide guidance for the symmetry classifications of mean field solutions in further investigations.

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arXiv2021

Particle-hole asymmetry in the dynamical spin and charge structure factors of the corner-shared one-dimensional cuprates

The collective spin and charge excitations of doped cuprates and their relationship to superconductivity are not yet fully understood, particularly in the case of the charge excitations. Here, we study the doping-dependent dynamical spin and charge structure factors of single and multi-orbital models for the one-dimensional corner shared spin-chain cuprates using several numerically exact methods. We find that the singleband Hubbard model can describe the spin and charge excitations of the $pd$-model in the low-energy region, including the particle-hole asymmetry in the spin response. However, our results also reveal that the weight of the interorbital spin excitations between Cu and O orbitals is comparable to the weight of the spin excitations between two Cu orbitals. This finding elucidates the microscopic nature of the spin excitations in the 1D cuprates and sheds light on the spin properties of other oxides. Importantly, we find a particle-hole asymmetry in the orbital-resolved charge excitations, which cannot be described by the singleband Hubbard model and is relevant to resonant inelastic x-ray scattering experiments. Our results imply that the explicit inclusion of the oxygen degrees of freedom may be required to understand experimental observations.

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arXiv2021

Triangular lattice Majorana-Hubbard model: Mean field theory and DMRG on a width-4 torus

Majorana modes can arise as zero energy bound states in a variety of solid state systems. A two-dimensional phase supporting these quasiparticles, for instance, emerges on the surface of a topological superconductor with the zero modes localized at the cores of vortices. At low energies, such a setup can be modeled by Majorana modes that interact with each other on the Abrikosov lattice. In experiments, the lattice is usually triangular. Motivated by the practical relevance, we explore the phase diagram of this Hubbard-like Majorana model using a combination of mean field theory and numerical simulation of thin torus geometries through the density matrix renormalization group algorithm. Our analysis indicates that attractive interactions between Majoranas can drive a phase transition in an otherwise gapped topological state.

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arXiv2021

Classical spin order near antiferromagnetic Kitaev point in the spin-1/2 Kitaev-Gamma chain

A minimal Kitaev-Gamma model has been recently investigated to understand various Kitaev systems. In the one-dimensional Kitaev-Gamma chain, an emergent SU(2)$_1$ phase and a rank-1 spin ordered phase with $O_h\rightarrow D_4$ symmetry breaking were identified using non-Abelian bosonization and numerical techniques. However, puzzles near the antiferromagnetic Kitaev region with finite Gamma interaction remained unresolved. Here we focus on this parameter region and find that there are two new phases, namely, a rank-1 ordered phase with an $O_h\rightarrow D_3$ symmetry breaking, and a peculiar Kitaev phase. Remarkably, the $O_h\rightarrow D_3$ symmetry breaking corresponds to the classical magnetic order, but appears in a region very close to the antiferromagnetic Kitaev point where the quantum fluctuations are presumably very strong. In addition, a two-step symmetry breaking $O_h\rightarrow D_{3d}\rightarrow D_3$ is numerically observed as the length scale is increased: At short and intermediate length scales, the system behaves as having a rank-2 spin nematic order with $O_h\rightarrow D_{3d}$ symmetry breaking; and at long distances, time reversal symmetry is further broken leading to the $O_h\rightarrow D_3$ symmetry breaking. Finally, there is no numerical signature of spin orderings nor Luttinger liquid behaviors in the Kitaev phase whose nature is worth further studies.

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