The dynamical spin structure factor is computed within a variational framework to study the one-dimensional ${J}_{1}\ensuremath{-}{J}_{2}$ Heisenberg model. Starting from Gutzwiller-projected fermionic wave functions, the low-energy spectrum is constructed from two-spinon excitations. The direct comparison with Lanczos calculations on small clusters demonstrates the excellent description of both gapless and gapped (dimerized) phases, including incommensurate structures for ${J}_{2}/{J}_{1}>0.5$ . Calculations on large clusters show how the intensity evolves when increasing the frustrating ratio and give an unprecedented accurate characterization of the dynamical properties of (nonintegrable) frustrated spin models.The dynamical spin structure factor is computed within a variational framework to study the one-dimensional ${J}_{1}\ensuremath{-}{J}_{2}$ Heisenberg model. Starting from Gutzwiller-projected fermionic wave functions, the low-energy spectrum is constructed from two-spinon excitations. The direct comparison with Lanczos calculations on small clusters demonstrates the excellent description of both gapless and gapped (dimerized) phases, including incommensurate structures for ${J}_{2}/{J}_{1}>0.5$. Calculations on large clusters show how the intensity evolves when increasing the frustrating ratio and give an unprecedented accurate characterization of the dynamical properties of (nonintegrable) frustrated spin models.

arXiv:1803.02359Physical review. B./Physical review. BJun 5, 201851 citations

Towards quantum simulation of spin dynamics in frustrated systems

Ippei Nakamura, Ryuta Yamamoto, Takeshi Fukuhara

Bulletin of the American Physical SocietyMay 29, 20180 citations

Static and dynamical properties of frustrated spin models

Francesco Ferrari

This thesis is devoted to the numerical investigation of quantum spin models which describe the low-energy physics of frustrated magnets. At extremely low temperatures, these systems can host the so-called spin liquid phase, an unconventional state of matter characterized by a high degree of quantum entanglement and the absence of magnetic order. The experimental identification of the spin liquid phase in actual materials relies on the detection of its distinctive excitations (named spinons), which possess fractional quantum numbers and can be probed by inelastic neutron scattering experiments. From the theoretical point of view, variational methods have been largely employed to tackle ground state properties of frustrated spin models. In particular, variational Monte Carlo techniques based on Gutzwiller-projected fermionic wave functions have been shown to provide accurate results for several frustrated systems. In this thesis, we pursue an extension of this variational scheme to target dynamical spectra, which are directly measured by inelastic neutron scattering experiments. Specifically, we compute the dynamical structure factor by constructing approximate excited states, which are obtained by applying two-spinon operators to the ground state wave function. Our results prove that this variational method can accurately describe the spectral features of different spin systems. Focusing on prototypical frustrated models on the square and triangular lattices, we observe how the dynamical structure factor reflects the phase transition between a magnetically ordered phase with spin wave excitations, to a spin liquid state with fractional degrees of freedom. In addition to spectral properties, we also explore new directions to improve the accuracy of Gutzwiller-projected states by the application of a neural network correlator, in the form of a restricted Boltzmann machine. While this hybrid variational scheme provides a considerable improvement of the variational energy in the case of unfrustrated spin models, less satisfactory results are obtained for frustrated systems, which call for further refinements of the neural network variational Ansätze.This thesis is devoted to the numerical investigation of quantum spin models which describe the low-energy physics of frustrated magnets. At extremely low temperatures, these systems can host the so-called spin liquid phase, an unconventional state of matter characterized by a high degree of quantum entanglement and the absence of magnetic order. The experimental identification of the spin liquid phase in actual materials relies on the detection of its distinctive excitations (named spinons), which possess fractional quantum numbers and can be probed by inelastic neutron scattering experiments. From the theoretical point of view, variational methods have been largely employed to tackle ground state properties of frustrated spin models. In particular, variational Monte Carlo techniques based on Gutzwiller-projected fermionic wave functions have been shown to provide accurate results for several frustrated systems. In this thesis, we pursue an extension of this variational scheme to target dynamical spectra, which are directly measured by inelastic neutron scattering experiments. Specifically, we compute the dynamical structure factor by constructing approximate excited states, which are obtained by applying two-spinon operators to the ground state wave function. Our results prove that this variational method can accurately describe the spectral features of different spin systems. Focusing on prototypical frustrated models on the square and triangular lattices, we observe how the dynamical structure factor reflects the phase transition between a magnetically ordered phase with spin wave excitations, to a spin liquid state with fractional degrees of freedom. In addition to spectral properties, we also explore new directions to improve the accuracy of Gutzwiller-projected states by the application of a neural network correlator, in the form of a restricted Boltzmann machine. While this hybrid variational scheme provides a considerable improvement of the variational energy in the case of unfrustrated spin models, less satisfactory results are obtained for frustrated systems, which call for further refinements of the neural network variational Ansätze.

Oct 25, 20191 citation

Spectral signatures of fractionalization in the frustrated Heisenberg model on the square lattice

Francesco Ferrari, Federico Becca

We employ a variational Monte Carlo approach to efficiently obtain the dynamical structure factor for the spin-$1/2\phantom{\rule{0.16em}{0ex}}{J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model on the square lattice. Upon increasing the frustrating ratio ${J}_{2}/{J}_{1}$ , the ground state undergoes a continuous transition from a N\'eel antiferromagnet to a ${\mathbb{Z}}_{2}$ gapless spin liquid. We identify the characteristic spectral features in both phases and highlight the existence of a broad continuum of excitations in the proximity of the spin-liquid phase. The magnon branch, which dominates the spectrum of the unfrustrated Heisenberg model, gradually loses its spectral weight, thus releasing nearly deconfined spinons, whose signatures are visible even in the magnetically ordered state. Our results provide an important example on how magnons fractionalize into deconfined spinons across a quantum critical point.We employ a variational Monte Carlo approach to efficiently obtain the dynamical structure factor for the spin-$1/2\phantom{\rule{0.16em}{0ex}}{J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model on the square lattice. Upon increasing the frustrating ratio ${J}_{2}/{J}_{1}$, the ground state undergoes a continuous transition from a N\'eel antiferromagnet to a ${\mathbb{Z}}_{2}$ gapless spin liquid. We identify the characteristic spectral features in both phases and highlight the existence of a broad continuum of excitations in the proximity of the spin-liquid phase. The magnon branch, which dominates the spectrum of the unfrustrated Heisenberg model, gradually loses its spectral weight, thus releasing nearly deconfined spinons, whose signatures are visible even in the magnetically ordered state. Our results provide an important example on how magnons fractionalize into deconfined spinons across a quantum critical point.

arXiv:1805.09287Physical review. B./Physical review. BSep 17, 201882 citations

Monte Carlo simulation of model spin systems

S. Ramasesha

Proceedings of the Indian Academy of Sciences Section C Engineering SciencesMar 1, 19791 citation

{J}_{2}/{J}_{1}>0.5

. Calculations on large clusters show how the intensity evolves when increasing the frustrating ratio and give an unprecedented accurate characterization of the dynamical properties of (nonintegrable) frustrated spin models.

{J}_{2}/{J}_{1}

, the ground state undergoes a continuous transition from a N\'eel antiferromagnet to a

{\mathbb{Z}}_{2}

gapless spin liquid. We identify the characteristic spectral features in both phases and highlight the existence of a broad continuum of excitations in the proximity of the spin-liquid phase. The magnon branch, which dominates the spectrum of the unfrustrated Heisenberg model, gradually loses its spectral weight, thus releasing nearly deconfined spinons, whose signatures are visible even in the magnetically ordered state. Our results provide an important example on how magnons fractionalize into deconfined spinons across a quantum critical point.