Titpack—Numerical diagonalization routines and quantum spin Hamiltonians

秀稔 西森, Hidetoshi Nishimori, Yoshihiro Taguchi

Xiuxia Zhang

In this paper,the energy spectrum of the ground-state and the excited-state in the model of small size one-dimensional Heisenberg finite chains(n20) was discussed.The Complete Diagonal and Lanczos Iterative method of Hamiltonian matrix are actualized by TITPACK program which designed by Hidetoshi Nishimori.But the finite chain revised method is mainly actualized by MATLAB program.All programs would be given in this paper.The investigative object was small size one-dimensional Heisenberg finite chains(n20),the TITPACK program was used to calculate the eigenvector of ground-state and excited-state|Ψ0〉、|Ψ1〉、|Ψ2〉、|Ψ3〉,the energy eigenvalue of ground-state and excited-state λ0 、λ1、λ2、λ3,the variation relation between and the correlated function of Sx 、Sz and the system Hamilton parameter.Using the finite chain revised method,the error was 0.000 047 2 between calculated and theoretic ground-state eigenvalue.The absolute value of ground-state energy square was inversed ratio the chain length,such as E(n)=-0.443 1-0.848 4/n2,through analyze the result of the program and find the law between the result and the quantity,in the small size one-dimensional Heisenberg finite chains,S=Aexp(-d/B) in the XXZ model.It is completely difference with XXZ Quantum model presented by Haldane.Only some energy spectra were intersected.

Jie Yu Wang, Ralf Meyer

Andrew Hallam, Jared Jeyaretnam, Zlatko Papić

Thermalization and its breakdown in interacting quantum many-body systems are governed by mid-spectrum eigenstates, which are typically accessible only in small system sizes amenable to exact diagonalization. Here we demonstrate that the density-matrix renormalization group (DMRG) effective Hamiltonian, an object routinely used to variationally approximate ground states, encodes detailed information about the dynamics far from equilibrium. In the random-field XXZ spin chain, the spectrum of the effective Hamiltonian is shown to capture the transition from thermal to many-body localized regimes, including spatially resolved probes of ergodic bubbles. Furthermore, the same approach also captures weak ergodicity breaking associated with quantum many-body scars. Our results establish the DMRG effective Hamiltonian as a versatile spectral probe of quantum thermalization and its breakdown in large systems beyond exact diagonalization.

M. S. Makivić

Makoto Kaburagi, Takashi Tonegawa, T. Nishino