Solitonic in-gap modes in a superconductor-quantum antiferromagnet interface

Lado, José L.; Sigrist, Manfred

doi:10.1103/physrevresearch.2.023347

Cited by 17 publications

(9 citation statements)

References 52 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 function corresponds to the dynamical spin structure factor for a spin system and the electronic many-body density of states for an electronic system. The dynamical correlator is computed using the tensor-network kernel polynomial algorithm [43][44][45][46][47][48][49][50]. The many-body states and Hamiltonians are represented in terms of a tensor-network, using the matrix-product state formalism [51][52][53], the ground state is computed with the density-matrix renormalization group algorithm [4], and the Hamiltonian is scaled to the interval (−1, 1) to perform the Chebyshev expansion [43].…”

Section: B Dynamical Correlators With Tensor-networkmentioning

confidence: 99%

Designing quantum many-body matter with conditional generative adversarial networks

Koch¹,

Lado²

2022

Preprint

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The computation of dynamical correlators of quantum many-body systems represents an open critical challenge in condensed matter physics. While powerful methodologies have risen in recent years, covering the full parameter space remains unfeasible for most many-body systems with a complex configuration space. Here we demonstrate that conditional Generative Adversarial Networks (GANs) allow simulating the full parameter space of several many-body systems, accounting both for controlled parameters, and stochastic disorder effects. After training with a restricted set of noisy many-body calculations, the conditional GAN algorithm provides the whole dynamical excitation spectra for a Hamiltonian instantly and with an accuracy analogous to the exact calculation. We further demonstrate how the trained conditional GAN automatically provides a powerful method for Hamiltonian learning from its dynamical excitations, and to flag non-physical systems via outlier detection. Our methodology puts forward generative adversarial learning as a powerful technique to explore complex many-body phenomena, providing a starting point to design large-scale quantum many-body matter.

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“…In order to compute the dynamical correlators we will use the tensor network kernel polynomial formalism. [59][60][61][62][63] The kernel polynomial method 59 (KPM) allows for the computation of spectral functions directly in frequency space by performing expansion in terms of Chebyshev polynomials of Eq. 7.…”

Section: B Kernel Polynomial Tensor Network Formalismmentioning

confidence: 99%

Dynamical topological excitations in parafermion chains

Kaskela,

Lado

2020

Preprint

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Topological excitations in many-body systems are one of the paradigmatic cornerstones of modern condensed matter physics. In particular, parafermions are elusive fractional excitations potentially emerging in fractional quantum Hall-superconductor junctions, and represent one of the major milestones in fractional quantum matter. Here, by using a combination of tensor network and kernel polynomial techniques, we demonstrate the emergence of zero modes and finite energy excitations in many-body parafermion chains. We show the appearance of zero energy modes in the many-body spectral function at the edge of a topological parafermion chain, their relation with the topological degeneracy of the system, and we compare their physics with the Majorana bound states of topological superconductors. We demonstrate the robustness of parafermion topological modes with respect to a variety of perturbations, and we show how weakly coupled parafermion chains give rise to in-gap excitations. Our results exemplify the versatility of tensor network methods for studying dynamical excitations of interacting parafermion chains, and highlight the robustness of topological modes in parafermion models.

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Solitonic in-gap modes in a superconductor-quantum antiferromagnet interface

Cited by 17 publications

References 52 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

Designing quantum many-body matter with conditional generative adversarial networks

Dynamical topological excitations in parafermion chains

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