We report in this paper our numerical analysis of energy level spacing statistics for the one-dimensional spin-$1/2$ XXZ model in random on-site longitudinal magnetic fields $B_i$ ($-h\leq B_i\leq h$)). We concentrate on the strong disorder limit $J_{\perp}<
We report in this paper our numerical analysis of energy level spacing statistics for the one-dimensional spin-1/2 XXZ model in random on-site longitudinal magnetic fields Bi (−h≤Bi≤h)). We concentrate on the strong disorder limit $J_{\perp}<
In this paper, we report our numerical analysis of energy level spacing statistics for one-dimensional spin-1/2 XXZ model with random on-site longitudinal magnetic fields Bi. We concentrate on the strong disorder limit where the system is expected to be in either a paramagnetic many-body localized (MBL) state or a spin-glass MBL state. By analyzing the energy-level spacing statistics as a function of strength of random magnetic field h/J⊥ (−h≤Bi≤h), interaction strength Jz/J⊥, energy of the many-body state E and the number of spin-↑ particles in the system M=∑i(siz+21), we show that there exists a small region between the paramagnetic and spin-glass MBL phases where an ergodic phase emerges. The ergodic phase emerges at the middle of the many-body energy spectrum when M∼2N and is not adiabatically connected to the ergodic phase that occurs in the weak-disorder, weak-interaction limit.
Despite enormous efforts devoted to the study of the many-body localization (MBL) phenomenon, the nature of the high-energy behavior of the Heisenberg spin chain in a strong random magnetic field is lacking consensus. Here, we take a step back by exploring the weak interaction limit starting from the Anderson localized (AL) insulator. Through shift-invert diagonalization, we find that, below a certain disorder threshold h^{*}, weak interactions necessarily lead to an ergodic instability, whereas at strong disorder the AL insulator directly turns into MBL, in agreement with a simple interpretation of the avalanche theory for restoration of ergodicity. We further map the phase diagram for the generic XXZ model in the disorder h-interaction Δ plane. Taking advantage of the total magnetization conservation, our results unveil the remarkable behavior of the spin-spin correlation functions: in the regime indicated as MBL by standard observables, their exponential decay undergoes an inversion of orientation ξ_{z}>ξ_{x}. We find that the longitudinal length ξ_{z} is a key quantity for capturing ergodic instabilities, as it increases with system size near the thermal phase, in sharp contrast to its transverse counterpart.
We study two different classes of strongly interacting many-body quantum systems in this thesis. The first concerns interacting quantum system with strong disorder. The second is a quantum spin liquid problem. Since many-body quantum systems with strong interaction are difficult in analytic approaches, numerical methods will be used to study these systems. In the first part of this thesis, we investigate the many-body localization of the 1D spin-1/2 XXZ model with random magnetic field by Exact Diagonalization. We confirm previous results that there exists a mobility edge between ergodic and localized phases at weak disorder. Furthermore, we study the difference between two many-body localization phases in the XXZ model and confirm that there exists a phase transition between two kinds of many-body localization. Surprisingly, we observe a narrow region of ergodic phase that exists between the two MBL phases. We call the phase Many-Body Ergodic phase since the phase is not analytically connected to the trivial ergodic phase at weak order. In the second part of this thesis, we study the spin -1/2 XXZ spin model on the triangular lattice by mean of Variational Monte Carlo simulation on a class of resonant valence bond (RVB) trial wave-functions. We find that as a function of J⊥/Jz, there exists a transition point where magnetic order vanishes (at J⊥/Jz ~ 0.45). Moreover, two kinds of RVB states competed in the Ising regime when J⊥/Jz < 0.23.
Motivated by recent debates around the many-body localization (MBL) problem, and in particular its stability against systemwide resonances, we investigate long-distance spin-spin correlations across the phase diagram of the random-field XXZ model, with a particular focus on the strong disorder regime. Building on state-of-the-art shift-invert diagonalization techniques, we study the high-energy behavior of transverse and longitudinal correlation functions, computed at the largest possible distance, for a broad range of disorder and interaction strengths. Our results show that while transverse correlations display a fairly stable exponential decay over the entire XXZ phase diagram, longitudinal correlations exhibit markedly different behavior, revealing distinct physical regimes. More precisely, we identify an intermediate disorder region where standard observables show well-converged MBL behavior [Colbois et al., Phys. Rev. Lett. 133, 116502 (2024)] while the distributions of longitudinal correlations reveal unexpected fat tails toward large values. These rare events strongly influence the average decay of longitudinal correlations, which we find to be algebraic in a broad region inside the supposed MBL phase, whereas the typical decay remains mostly exponential. At stronger disorder and weaker interactions, this intermediate regime is replaced by a more conventional exponential decay with short correlation lengths for both typical and average correlators, as expected for standard localization. Our findings shed light on the systemwide instabilities and raise important questions about the impact of such rare but large long-range correlations on the stability of the MBL phase. Finally, we discuss the possible fate of the intermediate region in the context of recent perspectives in the field.
The random-field spin-1/2 XXZ chains, and the corresponding Anderson insulators of spinless fermions with density-density interaction, have been intensively studied in the context of many-body localization. However, we recently argued [B. Krajewski et al., Phys. Rev. Lett. 129, 260601 (2022)] that the two-body density-density interaction in these models is not generic since only a small fraction of this interaction represents a true local perturbation to the Anderson insulator. Here we study ergodicity of strongly disordered Anderson insulator chains, choosing other forms of the two-body interaction for which the strength of the true perturbation is of the same order of magnitude as the bare two-body interaction. Focusing on the strong-interaction regime, numerical results for the level statistics and the eigenstate thermalization hypothesis are consistent with emergence of ergodicity at arbitrary strong disorder.
The presence of frozen uncorrelated random on-site potential in interacting quantum systems can induce a transition from an ergodic phase to a localized one, the so-called many-body localization. Here we numerically study the effects of autocorrelated disorder on the static and dynamical properties of a one-dimensional many-body quantum system which exhibits many-body localization. Specifically, by means of some standard measures of energy level repulsion and localization of energy eigenstates, we show that a strong degree of correlations between the on-site potentials in the one-dimensional spin-1/2 Heisenberg model leads to suppression of the many-body localization phase, while level repulsion is mitigated for small disorder strengths, although energy eigenstates remain well extended. Our findings are also remarkably manifested in the time domain, on which we put the main emphasis, as shown by the time evolution of experimentally relevant observables, like the return probability and the spin autocorrelation function.