Exact analysis of correlation functions of one-dimensional quantum systems

The functional-renormalization-group aided density functional theory (FRG-DFT) is applied to the two-dimensional homogeneous electron gas (2DHEG). The correlation energy of the 2DHEG is derived as a function of the Wigner-Seitz radius ${r}_{\mathrm{s}}$ directly. We find that our correlation energy completely reproduces the exact behavior at the high-density limit. For finite density, the result of FRG-DFT shows good agreement with the Monte Carlo (MC) results in the high-density region, although the discrepancy between the FRG-DFT and MC results becomes larger as the system becomes more dilute. Our study is the first example in which the FRG-DFT is applied to more-than-one-dimensional models, and shows that the FRG-DFT is a feasible and promising method even for the analysis of realistic models for quantum many-body systems.The functional-renormalization-group aided density functional theory (FRG-DFT) is applied to the two-dimensional homogeneous electron gas (2DHEG). The correlation energy of the 2DHEG is derived as a function of the Wigner-Seitz radius ${r}_{\mathrm{s}}$ directly. We find that our correlation energy completely reproduces the exact behavior at the high-density limit. For finite density, the result of FRG-DFT shows good agreement with the Monte Carlo (MC) results in the high-density region, although the discrepancy between the FRG-DFT and MC results becomes larger as the system becomes more dilute. Our study is the first example in which the FRG-DFT is applied to more-than-one-dimensional models, and shows that the FRG-DFT is a feasible and promising method even for the analysis of realistic models for quantum many-body systems.

arXiv:1812.00588Physical review. B./Physical review. BMar 5, 201913 citations

Entanglement entropy of non-Hermitian free fermions

Yibin Guo, Yi-Cong Yu, Rui-Zhen Huang +4 more

Abstract We study the entanglement properties of non-Hermitian free fermionic models with translation symmetry using the correlation matrix technique. Our results show that the entanglement entropy has a logarithmic correction to the area law in both one-dimensional and two-dimensional systems. For any one-dimensional one-band system, we prove that each Fermi point of the system contributes exactly 1/2 to the coefficient c of the logarithmic correction. Moreover, this relation between c and Fermi point is verified for more general one-dimensional and two-dimensional cases by numerical calculations and finite-size scaling analysis. In addition, we also study the single-particle and density–density correlation functions.Abstract We study the entanglement properties of non-Hermitian free fermionic models with translation symmetry using the correlation matrix technique. Our results show that the entanglement entropy has a logarithmic correction to the area law in both one-dimensional and two-dimensional systems. For any one-dimensional one-band system, we prove that each Fermi point of the system contributes exactly 1/2 to the coefficient c of the logarithmic correction. Moreover, this relation between c and Fermi point is verified for more general one-dimensional and two-dimensional cases by numerical calculations and finite-size scaling analysis. In addition, we also study the single-particle and density–density correlation functions.

arXiv:2105.09793Journal of Physics Condensed MatterAug 26, 202136 citations

Correlation functions and non-equilibrium dynamics in one dimensional quantum systems

Dávid X. Horváth

Jan 1, 20190 citations

Spectral Analysis of Correlated One-Dimensional Systems with Impurities

Stephan Haas

An averaging procedure is proposed to account for spectral features of correlated one-dimensional systems in the presence of nonmagnetic impurities. The dynamical spin structure factor for a corresponding random ensemble of Heisenberg chain segments is calculated by exact numerical diagonalization. It is shown that a few-mode approximation is sufficient to describe the numerical results. By examination of the disorder-induced pseudogap, the loss of spectral weight, and the discrete peak structures due to smallest-cluster contributions, the underlying impurity distribution function can be determined.An averaging procedure is proposed to account for spectral features of correlated one-dimensional systems in the presence of nonmagnetic impurities. The dynamical spin structure factor for a corresponding random ensemble of Heisenberg chain segments is calculated by exact numerical diagonalization. It is shown that a few-mode approximation is sufficient to describe the numerical results. By examination of the disorder-induced pseudogap, the loss of spectral weight, and the discrete peak structures due to smallest-cluster contributions, the underlying impurity distribution function can be determined.

arXiv:cond-mat/9712089Physical Review LettersMay 4, 19983 citations

Correlation functions in one-dimensional systems with strong interaction

K. B. Efetov, A.I. Lapkin

Aug 1, 197517 citations

{r}_{\mathrm{s}}

directly. We find that our correlation energy completely reproduces the exact behavior at the high-density limit. For finite density, the result of FRG-DFT shows good agreement with the Monte Carlo (MC) results in the high-density region, although the discrepancy between the FRG-DFT and MC results becomes larger as the system becomes more dilute. Our study is the first example in which the FRG-DFT is applied to more-than-one-dimensional models, and shows that the FRG-DFT is a feasible and promising method even for the analysis of realistic models for quantum many-body systems.