Non-ergodic dynamics of the extended anisotropic Heisenberg chain

Abstract

The issue of ergodicity is often underestimated. The presence of zero-frequency excitations in bosonic Green's functions determine the appearance of zero-frequency momentum-dependent quantities in correlation functions. The implicit dependence of matrix elements make such quantities also relevant in the computation of susceptibilities. Consequently, the correct determination of these quantities is of great relevance and the well-established practice of fixing them by assuming the ergodicity of the dynamics is quite questionable as it is not justifiable a priori by no means. In this manuscript, we have investigated the ergodicity of the dynamics of the $z$-component of the spin in the 1D Heisenberg model with anisotropic nearest-neighbor and isotropic next-nearest-neighbor interactions. We have obtained the zero-temperature phase diagram in the thermodynamic limit by extrapolating Exact and Lanczos diagonalization results computed on chains with sizes $L=6÷26$. Two distinct non-ergodic regions have been found: one for $J^{\prime }/J_z\lesssim 0.3$ and $|J_{\perp }|/J_z<1$ and another for $J^{\prime }/J_z\lesssim 0.25$ and $|J_{\perp }|/J_z=1$. On the contrary, finite-size scaling of $T\ne 0$ results, obtained by means of Exact diagonalization on chains with sizes $L=4÷18$, indicates an ergodic behavior of dynamics in the whole range of parameters.

6 pages, 7 figures

References in corpus (3)

• The Hubbard model within the equations of motion approach
• New perspectives on the Ising model
• Non-Ergodicity of the 1D Heisenberg Model

Cited by in corpus (15)

• Quantum discord and its allies: a review
• Emery vs. Hubbard model for cuprate superconductors: a Composite Operator Method study
• Static and dynamical quantum correlations in phases of an alternating field XY model
• Composite Operator Method analysis of the underdoped cuprates puzzle
• The Hubbard model beyond the two-pole approximation: a Composite Operator Method study
• The phase diagram of the extended anisotropic ferromagnetic-antiferromagnetic Heisenberg chain
• Tuning interaction strength leads to ergodic-nonergodic transition of quantum correlations in anisotropic Heisenberg spin model
• Entanglement in the 1D extended anisotropic Heisenberg model
• Probing the Possibilities of Ergodicity in the 1D Spin-1/2 XY Chain with Quench Dynamics
• XXZ-like phase in the F-AF anisotropic Heisenberg chain
• The composite operator method route to the 2D Hubbard model and the cuprates
• Efficient magnetic superstructure optimization with $\Theta \Phi$
• Frustration-driven QPT in the 1D extended anisotropic Heisenberg model
• Ergodicity of the extended anisotropic 1D Heisenberg model: response at low temperatures
• COM(3p) solution of the 2D Hubbard model: momentum resolved quantities