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Results for “Exact Diagonalization”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Kuramoto synchronization of quantum tunneling polarons for describing the dynamic structure in cuprate superconductors

A major open topic in cuprates is the interplay between the lattice and electronic dynamics and the importance of their coupling to the mechanism of high-temperature superconductivity (HTSC). As evidenced by extended x-ray absorption fine structure (EXAFS) experiments, anharmonic structural effects are correlated with the charge dynamics and the transition to a superconducting phase in different HTSC compounds. Here, in this paper, we describe how structural anharmonic effects can be coupled to electronic and lattice dynamics in cuprate systems by performing the exact diagonalization of a prototype anharmonic many-body Hamiltonian on a relevant 6-atom cluster and show that the EXAFS results can be understood as a Kuramoto synchronization transition between coupled internal quantum tunneling of polarons associated with the two-site distribution of the copper–apical oxygen (Cu-O ap ) pair in the dynamic structure. The transition is driven by the anharmonicity of the lattice vibrations and promotes the pumping of charge, initially stored at the apical oxygen reservoirs, into the copper-oxide plane. Simultaneously, a finite projection of the internal quantum tunneling polaron extends to the copper–planar oxygen (Cu-O pl ) pair. All these findings allow an interpretation based on an effective quantum-mechanical triple-well potential associated with the oxygen sites of the 6-atom cluster, which accurately represents the phase synchronization of apical oxygens and lattice-assisted charge transfer to the CuO 2 plane.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Effect of emitters on quantum state transfer in coupled cavity arrays

Over the last decade, conditions for perfect state transfer in quantum spin chains have been discovered and their experimental realizations addressed, as have their extensions to more complex geometries of coupled cavity-emitter arrays. In this paper we further consider such studies and situations in which quantum state transfer can occur with high fidelity, even when the cavity-cavity coupling rates and cavity-emitter interaction rates are comparable. This is accomplished through the development and use of a Monte Carlo approach to the inverse eigenvalue problem, which allows the determination of coupling rates which optimize quantum state transfer fidelity and subsequent time evolution of the polariton wave function through exact diagonalization of the resulting Jaynes-Cummings-Hubbard Hamiltonian. The effect of inhomogeneous emitter locations is also evaluated. Furthermore, our key results include the demonstration that our methodology can be used successfully to establish Hamiltonian parameters for high-fidelity state transfer in more general lattice geometries and excitation number sectors, and also a determination of the effects of fluctuations in those parameters about their optimal values.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2022

High-temperature fractional quantum Hall state in the Floquet kagome flat band

A fractional quantum Hall effect (FQHE) has been predicted in a topological flat band (FB) by a single-particle band structure combined with phenomenological theory or solution of a many-body lattice Hamiltonian with fuzzy parameters. A long-standing roadblock toward the realization of a FB-FQHE is lacking the many-body solution of specific materials under realistic conditions. Here, we demonstrate a combined study of single-particle Floquet band theory with exact diagonalization (ED) of a many-body Hamiltonian. We show that a time-periodic circularly polarized laser inverts the sign of second-nearest-neighbor hopping in a kagome lattice and enhances spin-orbit coupling in one spin channel to produce a Floquet FB with a high flatness ratio of bandwidth over band gap, as exemplified in monolayer Pt 3 C 36 S 12 H 12 . The ED of the resultant Floquet-kagome lattice Hamiltonian gives a one-third-filling ground state with a laser-dependent excitation gap of a FQH state, up to an estimated temperature above 70 K. Our findings pave the way for exploring the alluding high-temperature FB-FQHE.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Interaction-driven quantum anomalous Hall insulator in a Dirac semimetal

Here, the interaction-driven quantum anomalous Hall (QAH) insulator has been sought for a long time in a Dirac semimetal with linear band touching points at the Fermi level. By combining exact diagonalization, density matrix renormalization group, and analytical methods, we study a spinless fermion system on the checkerboard lattice with twofold rotational symmetry, which realizes two Dirac band touching points in the absence of interaction. At weak coupling, the Dirac semimetal is stable. At a finite density-density repulsive interaction, we analyze possible symmetry broken states, and find that an QAH state is stabilized when the interaction strength exceeds the energy scale controlling the separation between the Dirac points. Through numerical simulations, we verify the existence of the QAH phase with spontaneous time-reversal symmetry breaking and quantized Chern number C = 1.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Torus geometry eigenfunctions of an interacting multi-Landau-level Hamiltonian

A short-ranged, rotationally symmetric multi-Landau-level model Hamiltonian for strongly interacting electrons in a magnetic field was proposed [A. Anand et al., Phys. Rev. Lett. 126, 136601 (2021)] with the key feature that it allows exact many-body eigenfunctions on the disk not just for quasiholes but for all charged and neutral excitations of the entire Jain sequence filling fractions. We extend this to geometries without full rotational symmetry, namely, the torus and cylinder geometries, and present their spectra. Exact diagonalization of the interaction on the torus produces the low-energy spectra at filling fraction v = n/(2⁢pn + 1) that is identical, up to a topological (2⁢pn + 1)-fold multiplicity, to that of the integer quantum Hall spectra at v = n, for the incompressible state as well as all excitations. While the ansatz eigenfunctions in the disk geometry cannot be generalized to closed geometries such as torus or sphere, we show how to extend them to cylinder geometry. Meanwhile, we show eigenfunctions for charged excitations at filling fractions between 1/3 and 2/5 can be written on the torus and the spherical geometries.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Scrambling and operator entanglement in local non-Hermitian quantum systems

The breakdown of Lieb-Robinson bounds in local, non-Hermitian quantum systems opens up the possibility for a rich landscape of quantum many-body phenomenology. We elucidate this by studying information scrambling and quantum chaos in non-Hermitian variants of paradigmatic local quantum spin-chain models. We utilize a mixture of exact diagonalization and tensor network techniques for our numerical results and focus on three dynamical quantities: (i) out-of-time-ordered correlators (OTOCs), (ii) operator entanglement of the dynamics, and (iii) entanglement growth following a quench from product initial states. We show that while OTOCs fail to capture information scrambling in a simple, local, non-Hermitian transverse-field Ising model, the closely related operator entanglement is a robust measure of dynamical properties of interest. Moreover, we show that the short-time growth of operator entanglement can generically detect entanglement phase transitions in these systems while its long-time average is shown to be a reliable indicator of quantum chaos and entanglement phases. This allows us to extend operator entanglement-based diagnostics from previous works on closed and open quantum systems, to the new arena of monitored quantum dynamics. Finally, we remark on the efficacy of these dynamical quantities in detecting integrability/chaos in the presence of continuous monitoring.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Anomalous bilayer quantum Hall effect

In parallel to the condensed-matter realization of quantum Hall (Chern insulators), quantum spin Hall (topological insulators), and fractional quantum Hall (fractional Chern insulators) effects, we propose that bilayer flat band (FB) lattices with one FB in each layer constitute solid-state analogs of bilayer quantum Hall (BQH) system, leading to anomalous BQH effect without a magnetic field. By exact diagonalization of a bilayer kagome lattice Hamiltonian, as a prototypical example, we demonstrate the stabilization of excitonic condensate Halperin's (1,1,1) state at the total filling v T = 1 of the two FBs. Furthermore, by tuning the interlayer tunneling and distance between the kagome layers at v T = 2/3, we show phase transitions among Halperin's (3,3,0), spin-singlet (1,1,2), and particle-hole conjugate of Laughlin's 1/3 states, as previously observed in conventional BQH systems. Furthermore, our work opens a new direction in the field of FB physics by demonstrating bilayer FB materials as an attractive avenue for realizing exotic anomalous BQH states including non-Abelian anyons.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2023

Suppressed superexchange interactions in the cuprates by bond-stretching oxygen phonons

We study a multiorbital Hubbard–Su-Schrieffer-Heeger model for the one-dimensional (1D) corner-shared cuprates in the adiabatic and nonadiabatic limits using exact diagonalization and determinant quantum Monte Carlo. At half filling and in the adiabatic limit, lattice dimerization can be achieved only over a narrow range of couplings slightly below a critical coupling g c . Beyond this value, the sign of the effective hopping changes, and the lattice becomes unstable. Strong lattice fluctuations replace the dimerization state in the nonadiabatic case. We also examine the model's temperature-dependent uniform and dynamical magnetic susceptibilities and compare them to the results of an effective spin-1/2 Heisenberg model. In doing so, we demonstrate that lattice fluctuations induced by the e-ph interaction suppress the effective superexchange interaction when g < g c . Furthermore, our results elucidate the effect of bond-stretching phonons in the parent cuprate compounds in general and are particularly relevant to 1D cuprates, where strong e-ph interactions have recently been inferred.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Itinerant ferromagnetism in transition metal dichalcogenide moiré superlattices

Moiré materials are artificial crystals formed at van der Waals heterojunctions that have emerged as a highly tunable platform that is able to realize much of the rich quantum physics of electrons in atomic scale solids, and in several cases even new quantum phases of matter. Here we use finite-size exact diagonalization methods to explore the physics of single-band itinerant electron ferromagnetism in semiconductor moiré materials. As a result, we predict where ferromagnetism is likely to occur in triangular-lattice moiré systems, and where it is likely to yield the highest Curie temperatures.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Disorder-induced topological phase transition in a driven Majorana chain

Here, we study a periodically driven one-dimensional Kitaev model in the presence of disorder. In the clean limit our model exhibits four topological phases corresponding to the existence or nonexistence of edge modes at zero and π quasienergy. When potential disorder is added, the system parameters get renormalized and the system may exhibit a topological phase transition. When starting from the Majorana π mode (MPM) phase, which hosts only edge Majoranas with quasienergy π, disorder induces a transition into a neighboring phase with both π and zero modes on the edges. We characterize the disordered system using (i) exact diagonalization, (ii) Arnoldi mapping onto an effective tight-binding chain, and (iii) topological entanglement entropy.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Classical dynamics of the antiferromagnetic Heisenberg spin ladder

We employ a classical limit grounded in SU(4) coherent states to investigate the temperature-dependent dynamical spin structure factor of the S = 1/2 ladder consisting of weakly coupled dimers. By comparing the outcomes of this classical approximation with density matrix renormalization group and exact diagonalization calculations in finite size ladders, we demonstrate that the classical dynamics offers an accurate approximation across the entire temperature range when the interdimer coupling is weak and a good approximation in the high temperature regime even when the interdimer coupling is strong. This agreement is achieved after appropriately rescaling the temperature axis and renormalizing expectation values to satisfy a quantum sum rule. Here, we anticipate the method will be particularly effective when applied to 2D and 3D lattices composed of weakly-coupled dimers, situations that remain challenging for alternative numerical methods.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Role of bath-induced many-body interactions in the dissipative phases of the Su-Schrieffer-Heeger model

The Su-Schrieffer-Heeger chain is a prototype example of a symmetry-protected topological insulator. Coupling it nonperturbatively to local thermal environments, either through the intercell or the intracell fermion tunneling elements, modifies the topological window. To understand this effect, we employ the recently developed reaction-coordinate polaron transform (RCPT) method, which allows treating system-bath interactions at arbitrary strengths. The effective system Hamiltonian, which is obtained via the RCPT, exposes the impact of the baths on the SSH chain through renormalization of tunneling elements and the generation of many-body interaction terms. By performing exact diagonalization and computing the ensemble geometric phase, a topological invariant, which is applicable even to systems at finite temperature, we distinguish the trivial band insulator (BI) from the topological insulator (TI) phases. Furthermore, through the RCPT mapping, we are able to pinpoint the main mechanism behind the extension of the parameter space for the TI or the BI phases (depending on the coupling scheme, intracell or intercell), which is the bath-induced, dimerized, many-body interaction. In conclusion, we also study the effect of on-site staggered potentials on the SSH phase diagram and discuss extensions of our method to higher dimensions.

1-dimensional systems↗
DOE OSTI2017

Non-Abelian 𝜈 =$\frac{1}{2}$ quantum Hall state in $Γ$ 8 valence band hole liquid

In the search for states with non-Abelian statistics, we explore the fractional quantum Hall effect in a system of two-dimensional (2D) charge carrier holes. We propose a method of mapping states of holes confined to a finite width quantum well in a perpendicular magnetic field to states in a spherical shell geometry. We take into account strong coupling between the spin and motion of charge parallel and perpendicular to the 2D layer. This method gives the single-particle hole states used in the exact diagonalization of systems with a small number of holes in the presence of Coulomb interactions, density matrix renormalization group, and topological entanglement entropy calculations. Furthermore, the hole quantum Hall state at half filling of the ground state in a magnetic field near the crossing of single-hole states is likely the Moore-Read Pfaffian state.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2017

Explicit inclusion of electronic correlation effects in molecular dynamics

Here, we design a quantum molecular dynamics method for strongly correlated electron metals. The strong electronic correlation effects are treated within a real-space version of the Gutzwiller variational approximation (GA), which is suitable for the inhomogeneity inherent in the process of quantum molecular dynamics (MD) simulations. We also propose an efficient algorithm based on the second-moment approximation to the electronic density of states for the search of the optimal variation parameters, from which the renormalized interatomic MD potentials are fully determined. By considering a minimal one-correlated-orbital Anderson model with parameterized spatial dependence of tight-binding hopping integrals, this fast GA-MD method is benchmarked with that using exact diagonalization to solve the GA variational parameters. The efficiency and accuracy are illustrated. We have demonstrated the effect of temperature coupled with electronic correlation on structural properties simulated with MD. This method will open up an unprecedented opportunity enabling large-scale quantum MD simulations of strongly correlated electronic materials.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Emergence of chiral spin liquids via quantum melting of noncoplanar magnetic orders

Quantum spin liquids (QSLs) are highly entangled states of quantum magnets which lie beyond the Landau paradigm of classifying phases of matter via broken symmetries. A physical route to arriving at QSLs is via frustration-induced quantum melting of ordered states such as valence bond crystals or magnetic orders. Using extensive exact diagonalization (ED) and density-matrix renormalization group (DMRG)we show studies of concrete S U ( 2 ) invariant spin models on honeycomb, triangular, and square lattices, that chiral spin liquids (CSLs) emerge as descendants of triple- Q spin crystals with tetrahedral magnetic order and a large scalar spin chirality. Such ordered-to-CSL melting transitions may yield lattice realizations of effective Chern-Simons-Higgs field theories. We provides a distinct unifying perspective on the emergence of CSLs and suggests that materials with certain noncoplanar magnetic orders might provide a good starting point to search for CSLs.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2017

Nature of Continuous Phase Transitions in Interacting Topological Insulators

Here, we revisit the effects of the Hubbard repulsion on quantum spin Hall effects (QSHE) in two-dimensional quantum lattice models. We present both unbiased exact diagonalization and density-matrix renormalization group simulations with numerical evidence for a continuous quantum phase transition (CQPT) separating QSHE from the topologically trivial antiferromagnetic phase. Our numerical results suggest that the nature of CQPT exhibits distinct finite-size scaling behaviors, which may be consistent with either Ising or XY universality classes for different time-reversal symmetric QSHE systems.

36 MATERIALS SCIENCE↗
DOE OSTI2018

SU(N) fractional quantum Hall effect in topological flat bands

We study N-component interacting particles (hardcore bosons and fermions) loaded in topological lattice models with SU(N)-invariant interactions based on exact diagonalization and density matrix renormalization group method. By tuning the interplay of interspecies and intraspecies interactions, we demonstrate that a class of SU(N) fractional quantum Hall states can emerge at fractional filling factors nu=N/(N+1) for bosons [nu=N/(2N+1) for fermions] in the lowest Chern band, characterized by the nontrivial fractional Hall responses and the fractional charge pumping. Moreover, we establish a topological characterization based on the K matrix and discuss the close relationship to the fractional quantum Hall physics in topological flat bands with Chern number N.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

Spin-orbit coupled systems in the atomic limit: rhenates, osmates, iridates

Motivated by RIXS experiments on a wide range of complex heavy oxides, including rhenates, osmates, and iridates, we discuss the theory of RIXS for site-localized t 2 g orbital systems with strong spin-orbit coupling. For such systems, we present exact diagonalization results for the spectrum at different electron fillings, showing that it accesses “single-particle” and “multiparticle” excitations. This leads to a simple picture for the energies and intensities of the RIXS spectra in Mott insulators such as double perovskites which feature highly localized electrons, and yields estimates of the spin-orbit coupling and Hund's coupling in correlated 5d oxides. We present new higher resolution RIXS data at the Re L 3 edge in Ba 2 YReO 6 which finds a previously unresolved peak splitting, providing further confirmation of our theoretical predictions. Using ab initio electronic structure calculations on Ba 2 MReO 6 (with M=Re, Os, Ir) we show that while the atomic limit yields a reasonable effective Hamiltonian description of the experimental observations, effects such as t 2 g –e g interactions and hybridization with oxygen are important. Our ab initio estimate for the strength of the intersite exchange coupling shows that, compared to the d 3 systems, the exchange is one or two orders of magnitude weaker in the d 2 and d 4 materials, which may partly explain the suppression of long-range magnetic order in the latter compounds. As a way to interpolate between the site-localized picture and our electronic structure band calculations, we discuss the spin-orbital levels of the MO 6 cluster. In conclusion, this suggests a possible role for intracluster excitons in Ba 2 YIrO 6 which may lead to a weak breakdown of the atomic J eff = 0 picture and to small magnetic moments.

74 ATOMIC AND MOLECULAR PHYSICS↗