Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1808.10112

Spectral weights of doublon in interacting Hofstadter model

Tirthaprasad Chattaraj

Published Aug 30, 2018• 0 citations
arXivHTMLPDF

Abstract

In this article, two-particle Greens functions are computed for different strengths of interactions for particles in Hofstadter lattices, providing informations on spectral weights of doublons. The calculations are performed for a finite lattice without disorder. The splitting in spectra under the effect of external magnetic field for non-interacting and interacting pairs are compared.

DOI
10.48550/arxiv.1808.10112

Related papers

Numerical Studies on Correlations in Dynamics and Localization of Two Interacting Particles in Lattices

Tirthaprasad Chattaraj

Correlation of interacting particles is studied in their dynamics and localization in ideal and disordered lattice systems with the help of numerical tools. Both 1D and 2D systems are considered. In 1D lattices with long-range hopping, differences between dynamics of attractively and repulsively interacting particles are noted. For calculations of 2D systems, a recursion based numerical algorithm for two-particle Greens functions is implemented which provides accurate results. Using this algorithm, spectral properties of 2D Hubbard and Hofstadter models is computed, along with localization parameters of 2D disordered systems.

arXiv:1809.09982•Sep 25, 2018•1 citation

Recursive computation of Greens functions for interacting particles in disordered lattices and binary trees

Tirthaprasad Chattaraj

In this article, the method of computing Greens functions recursively for interacting particles has been extended to square lattices and binary trees. The method allows for performing calculations for large lattices. Approximations, which make the method more efficient while maintaining accuracy are described for computations of dynamics and correlations of interacting particles in disordered systems. Direct informations related to spectral weights for different initial preparations of interacting particles in real space can be obtained using this method for larger system sizes with less finite size effects.

arXiv:1808.04898•Aug 4, 2018•0 citations

Spectral density of interacting pairs in low-dimensional finite lattices

Tirthaprasad Chattaraj

The spectral density of bound pairs in ideal 1D, 2D and Bethe lattices is computed for weak and strong interactions. The computations are performed with Green's functions by an efficient recursion method in real space. For the range of interaction strengths within which bound states are predominantly single pairs, the spectral profiles guide to the energy bandwidths where the bound pairs can be maximized.

arXiv:2103.15496•Condensed Matter Physics•Mar 1, 2021•0 citations

Spectral function of spinless fermions on a one-dimensional lattice

Rodrigo G. Pereira, Steven R. White, Ian K. Affleck

We study the spectral function of interacting one-dimensional fermions for an integrable lattice model away from half-filling. The divergent power-law singularity of the spectral function near the single-particle or single-hole energy is described by an effective x-ray edge type model. At low densities and for momentum near the zone boundary, we find a second divergent singularity at higher energies which is associated with a two-particle bound state. We use the Bethe ansatz solution of the model to calculate the exact singularity exponents for any momentum and for arbitrary values of chemical potential and interaction strength in the critical regime. We relate the singularities of the spectral function to the long-time decay of the fermion Green's function and compare our predictions with numerical results from the time-dependent density-matrix renormalization group (tDMRG). Our results show that the tDMRG method is able to provide accurate time decay exponents in the cases of power-law decay of the Green's function. Some implications for the line shape of the dynamical structure factor away from half-filling are also discussed. In addition, we show that 85% of the total spectral weight in the zero field Heisenberg model near wave-vector $q=\ensuremath{\pi}$ is given by the two-spinon contribution.

arXiv:0902.0836•Physical Review B•Apr 23, 2009•119 citations

The Effect of Thermal Fluctuation on Spectral Function for the Tomonaga-Luttinger Model

N. Nakamura, Yoshikazu Suzumura

We examine the spectral function of the single electron Green function at finite temperature for the Tomonaga-Luttinger model which consists of a mutual interaction with only forward scattering. The spectral weight, which is calculated as a function of the frequency with fixed wave number, shows that several peaks originating in the excitation spectra of charge and spin fluctuations merge into a single peak by the increase of temperature.

arXiv:cond-mat/9705094•Progress of Theoretical Physics•Jul 1, 1997•16 citations

Spectral functions of one-dimensional systems with correlated disorder

Niaz Ali Khan, João M. Viana Parente Lopes, J. P. Santos Pires +1 more

We investigate the spectral function of Bloch states in a one-dimensional tight-binding non-interacting chain with two different models of static correlated disorder, at zero temperature. We report numerical calculations of the single-particle spectral function based on the Kernel polynomial method, which has an [Formula: see text] computational complexity. These results are then confirmed by analytical calculations, where precise conditions were obtained for the appearance of a classical limit in a single-band lattice system. Spatial correlations in the disordered potential give rise to non-perturbative spectral functions shaped as the probability distribution of the random on-site energies, even at low disorder strengths. In the case of disordered potentials with an algebraic power-spectrum, [Formula: see text] [Formula: see text], we show that the spectral function is not self-averaging for [Formula: see text].

arXiv:1806.06584•Journal of Physics Condensed Matter•Jan 31, 2019•10 citations
In this article, two-particle Greens functions are computed for different strengths of interactions for particles in Hofstadter lattices, providing informations on spectral weights of doublons. The calculations are performed for a finite lattice without disorder. The splitting in spectra under the effect of external magnetic field for non-interacting and interacting pairs are compared.
Correlation of interacting particles is studied in their dynamics and localization in ideal and disordered lattice systems with the help of numerical tools. Both 1D and 2D systems are considered. In 1D lattices with long-range hopping, differences between dynamics of attractively and repulsively interacting particles are noted. For calculations of 2D systems, a recursion based numerical algorithm for two-particle Greens functions is implemented which provides accurate results. Using this algorithm, spectral properties of 2D Hubbard and Hofstadter models is computed, along with localization parameters of 2D disordered systems.
In this article, the method of computing Greens functions recursively for interacting particles has been extended to square lattices and binary trees. The method allows for performing calculations for large lattices. Approximations, which make the method more efficient while maintaining accuracy are described for computations of dynamics and correlations of interacting particles in disordered systems. Direct informations related to spectral weights for different initial preparations of interacting particles in real space can be obtained using this method for larger system sizes with less finite size effects.
We study the spectral function of interacting one-dimensional fermions for an integrable lattice model away from half-filling. The divergent power-law singularity of the spectral function near the single-particle or single-hole energy is described by an effective x-ray edge type model. At low densities and for momentum near the zone boundary, we find a second divergent singularity at higher energies which is associated with a two-particle bound state. We use the Bethe ansatz solution of the model to calculate the exact singularity exponents for any momentum and for arbitrary values of chemical potential and interaction strength in the critical regime. We relate the singularities of the spectral function to the long-time decay of the fermion Green's function and compare our predictions with numerical results from the time-dependent density-matrix renormalization group (tDMRG). Our results show that the tDMRG method is able to provide accurate time decay exponents in the cases of power-law decay of the Green's function. Some implications for the line shape of the dynamical structure factor away from half-filling are also discussed. In addition, we show that 85% of the total spectral weight in the zero field Heisenberg model near wave-vector $q=\ensuremath{\pi}$ is given by the two-spinon contribution.
We investigate the spectral function of Bloch states in a one-dimensional tight-binding non-interacting chain with two different models of static correlated disorder, at zero temperature. We report numerical calculations of the single-particle spectral function based on the Kernel polynomial method, which has an [Formula: see text] computational complexity. These results are then confirmed by analytical calculations, where precise conditions were obtained for the appearance of a classical limit in a single-band lattice system. Spatial correlations in the disordered potential give rise to non-perturbative spectral functions shaped as the probability distribution of the random on-site energies, even at low disorder strengths. In the case of disordered potentials with an algebraic power-spectrum, [Formula: see text] [Formula: see text], we show that the spectral function is not self-averaging for [Formula: see text].