Breakdown of universality in three-dimensional Dirac semimetals with random impurities

Pires, J. P. Santos; Amorim, B.; Ferreira, Aires; Adagideli, İnanç; Mucciolo, Eduardo R.; Lopes, J. M. Viana Parente

doi:10.1103/physrevresearch.3.013183

Cited by 17 publications

(12 citation statements)

References 47 publications

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“…The Chebyshev polynomial-based spectral method is an increasingly popular tool in the simulation of many-body systems that fulfills the requirement of general applicability [41][42][43][44][45][46][47][48][49][50][51][52][53]. It relies on the iterative spectral reconstruction of the target functions of interest (e.g., density of states and spin-spin correlations).…”

Section: Chebyshev Spectral Methods: Rationalementioning

confidence: 99%

Real-space spectral simulation of quantum spin models: Application to the Kitaev-Heisenberg model

Brito¹,

Ferreira²

2021

Preprint

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The proliferation of quantum fluctuations and long-range entanglement presents an outstanding challenge for the numerical simulation of interacting spin systems with exotic ground states. Here, we present a Chebyshev iterative method that gives access to the thermodynamic properties and critical behavior of frustrated quantum spin models with good accuracy. The computational complexity scales linearly with the Hilbert space dimension and the number of Chebyshev iterations used to approximate the eigenstates. Using this approach, we calculate the spin correlations of the Kitaev-Heisenberg model, a paradigmatic model of honeycomb iridates that exhibits a rich phase diagram including a quantum spin liquid phase. Our results are benchmarked against exact diagonalization and a popular iterative method based on thermal pure quantum (TPQ) states. All methods accurately predict a transition to a stripy (spin-liquid) phase for the critical value of the Kitaev coupling J K ≈ −1.3J H (J K ≈ −8.0J H ) for honeycomb layers with ferromagnetic Heisenberg interactions (J H > 0). Our findings suggest that a hybrid Chebyshev-TPQ approach could open the door to previously unattainable studies of quantum spin models in two dimensions.

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Section: Chebyshev Spectral Methods: Rationalementioning

confidence: 99%

Real-space spectral simulation of quantum spin models: Application to the Kitaev-Heisenberg model

Brito¹,

Ferreira²

2021

Preprint

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“…This spectral scheme, combined with an efficient real-space implementation, will allow us to resolve the fine structure of the quasiparticle selfenergy Σ(k, ω) in large systems containing multi billions of orbitals, a task so far elusive. Such a capability is key to explore topological transitions and disordered systems at quantum criticality, where spectral convergence is challenging already at the level of considerably simpler average density of states [21,26,44].…”

Section: B High-resolution Self-energy Calculationmentioning

confidence: 99%

“…Significantly more complex problems can be tackled by optimizing the parallelization efficiency of matrix-vector multiplications using an adaptive real-space domain decomposition algorithm as implemented in the KITE package [31] (see Appendix V A for more details). Such a strategy was adopted in recent works reporting accurate studies of the effect of shortrange disorder on the nodal density of states of topological semimetals [21,45].…”

Section: B High-resolution Self-energy Calculationmentioning

confidence: 99%

“…Striking phenomena triggered by strong (nonperturbative) disorder effects are currently the focus of intense investigation. Some examples include strong Anderson localization [14][15][16][17][18], rare region effects in three-dimensional topological semimetals [19][20][21][22], and frozen multifractality in chiral-symmmetric lattices [23][24][25][26][27], whose analysis has defied even the most advanced field-theoretical approaches. At the heart of such unusual phenomena is the nonperturbative accumulation of quantum coherent scattering processes, whose satisfactory description calls for the use of large-scale numerical approaches.…”

Section: Introductionmentioning

confidence: 99%

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High-resolution real-space evaluation of the self-energy operator of disordered lattices: Gade singularity, spin-orbit effects and p-wave superconductivity

João,

Lopes,

Ferreira

2021

Preprint

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Disorder is a prominent factor influencing the fate of condensed phases of matter, yet the true extent of its impact is generally difficult to understand due to the significant role played by quantum interference effects, entanglement between internal spin and orbital degrees of freedom, and proximity to quantum critical points. Here we show that the quasiparticle self-energy-a direct probe of the renormalization of low-energy excitations due to interactions and disorder-can be obtained by means of unbiased, general-purpose polynomially-scaling spectral expansions of lattice Green's functions. Our scheme provides a powerful framework to access the disorder self-energy Σ(k, ω) in unprecedented large tight-binding systems [with up to billions of orbitals (N ≈ 10 9 )] with energy resolution only limited by the mean level spacing. We demonstrate the versatility of our approach in 3 distinct problems: (i) the Gade singularity in the honeycomb lattice with vacancy defects; (ii) impurity resonances in a spin-orbit-coupled ferromagnet and (iii) mixed s-wave and p-wave superconductivity in disordered graphene. Our study unravels striking manifestations of nonperturbative quantum interference effects so far inaccessible to real-space numerical techniques.

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“…Indeed, a range of intriguing phenomena triggered by strong (nonperturbative) disorder effects are currently the focus of intense investigation. Some examples include strong Anderson localization [15][16][17][18][19], rare region effects in three-dimensional topological semimetals [20][21][22][23] and frozen multifractality in chiral-symmmetric lattices [24][25][26][27][28], whose analysis has defied even the most advanced field-theoretic approaches. At the heart of such unusual phenomena is the nonperturbative accumulation of quantum coherent scattering processes, whose satisfactory description calls for the use of large-scale numerical approaches.…”

Section: Introductionmentioning

confidence: 99%

High-resolution real-space evaluation of the self-energy operator of disordered lattices: Gade singularity, spin–orbit effects and p-wave superconductivity

Lopes

Ferreira

2022

J. Phys. Mater.

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Disorder is a key factor influencing the behavior of condensed states of matter, however the true extent of its impact is generally difficult to determine due to the prominent roles played by quantum interference, entanglement between spin and orbital degrees of freedom and proximity to quantum critical points. Here we show that the one-particle disorder self-energy --- a direct probe of the renormalization of low-energy excitations due to defects and impurities distributed randomly in a crystal --- can be obtained by means of unbiased spectral expansions of lattice Green's functions in a computationally expedient manner. Our scheme provides a powerful framework to map out the frequency and wavevector dependence of electronic excitations in unprecedented large tight-binding systems, up to $10^{9}$ orbitals, with energy resolution only limited by the mean level spacing. We demonstrate the versatility of our approach in 3 distinct problems: (i) the Gade singularity in honeycomb layers with dilute topological defects; (ii) the rich landscape of impurity resonances in a spin--orbit-coupled ferromagnet; and (iii) the tailoring of emergent $s$-wave and $p$-wave superconducting phases in graphene via atomic defects. These examples reveal rich features in the disorder self-energy $\Sigma_{\textrm{dis}}(\mathbf{k},\omega)$ that are absent from the self-consistent $T$-matrix approach and other common approximation schemes, which include regimes of nontrivial wavevector dependence and anomalous dependence upon the impurity concentration. Our study unravels puzzling, and so far largely inaccessible, manifestations of strong nonperturbative quantum interference effects in quantum materials and disordered phases of matter.

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Breakdown of universality in three-dimensional Dirac semimetals with random impurities

Cited by 17 publications

References 47 publications

Real-space spectral simulation of quantum spin models: Application to the Kitaev-Heisenberg model

Real-space spectral simulation of quantum spin models: Application to the Kitaev-Heisenberg model

High-resolution real-space evaluation of the self-energy operator of disordered lattices: Gade singularity, spin-orbit effects and p-wave superconductivity

High-resolution real-space evaluation of the self-energy operator of disordered lattices: Gade singularity, spin–orbit effects and p-wave superconductivity

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