Many-body localization edge in the random-field Heisenberg chain

We present a large scale exact diagonalization study of the one dimensional spin $1/2$ Heisenberg model in a random magnetic field. In order to access properties at varying energy densities across the entire spectrum for system sizes up to $L=22$ spins, we use a spectral transformation which can be applied in a massively parallel fashion. Our results allow for an energy-resolved interpretation of the many body localization transition including the existence of an extensive many-body mobility edge. The ergodic phase is well characterized by Gaussian orthogonal ensemble statistics, volume-law entanglement, and a full delocalization in the Hilbert space. Conversely, the localized regime displays Poisson statistics, area-law entanglement and non ergodicity in the Hilbert space where a true localization never occurs. We perform finite size scaling to extract the critical edge and exponent of the localization length divergence.Comment: 4+3 pages, 5+3 figure

Shannon-R\'enyi entropies and participation spectra across 3d O(3)O(3) criticality

Universal features in the scalings of Shannon-R\'enyi entropies of many-body groundstates are studied for interacting spin-$\frac{1}{2}$ systems across (2+1) dimensional $O(3)$ critical points, using quantum Monte Carlo simulations on dimerized and plaquettized Heisenberg models on the square lattice. Considering both full systems and line shaped subsystems, $SU(2)$ symmetry breaking on the N\'eel ordered side of the transition is characterized by the presence of a logarithmic term in the scaling of Shannon-R\'enyi entropies, which is absent in the disordered gapped phase. Such a difference in the scalings allows to capture the quantum critical point using Shannon-R\'enyi entropies for line shaped subsystems of length $L$ embedded in $L\times L$ tori, as the smaller subsystem entropies are numerically accessible to much higher precision than for the full system. Most interestingly, at the quantum phase transition an additive subleading constant $b_\infty^{*\rm line}=0.41(1)$ emerges in the critical scaling of the line Shannon-R\'enyi entropy $S_\infty^\text{line}$. This number appears to be universal for 3d $O(3)$ criticality, as confirmed for the finite-temperature transition in the 3d antiferromagnetic spin-$\frac{1}{2}$ Heisenberg model. Additionally, the phases and phase transition can be detected in several features of the participation spectrum, consisting of the diagonal elements of the reduced density matrix of the line subsystem. In particular the N\'eel ordering transition can be simply understood in the $\{S^z\}$ basis by a confinement mechanism of ferromagnetic domain walls.Comment: 16 pages, 19 figure

Entanglement entropies of the J1−J2J_1 - J_2 Heisenberg antiferromagnet on the square lattice

Using a modified spin-wave theory which artificially restores zero sublattice magnetization on finite lattices, we investigate the entanglement properties of the N\'eel ordered $J_1 - J_2$ Heisenberg antiferromagnet on the square lattice. Different kinds of subsystem geometries are studied, either corner-free (line, strip) or with sharp corners (square). Contributions from the $n_G=2$ Nambu-Goldstone modes give additive logarithmic corrections with a prefactor ${n_G}/{2}$ independent of the R\'enyi index. On the other hand, corners lead to additional (negative) logarithmic corrections with a prefactor $l^{c}_q$ which does depend on both $n_G$ and the R\'enyi index $q$, in good agreement with scalar field theory predictions. By varying the second neighbor coupling $J_2$ we also explore universality across the N\'eel ordered side of the phase diagram of the $J_1 - J_2$ antiferromagnet, from the frustrated side $0<J_2/J_1<1/2$ where the area law term is maximal, to the strongly ferromagnetic regime $-J_2/J_1\gg1$ with a purely logarithmic growth $S_q=\frac{n_G}{2}\ln N$, thus recovering the mean-field limit for a subsystem of $N$ sites. Finally, a universal subleading constant term $\gamma_q^{\rm ord}$ is extracted in the case of strip subsystems, and a direct relation is found (in the large-S limit) with the same constant extracted from free lattice systems. The singular limit of vanishing aspect ratios is also explored, where we identify for $\gamma_q^\text{ord}$ a regular part and a singular component, explaining the discrepancy of the linear scaling term for fixed width {\it{vs}} fixed aspect ratio subsystems.Comment: 14 pages, 18 figure

Absence of dynamical localization in interacting driven systems

Using a numerically exact method we study the stability of dynamical localization to the addition of interactions in a periodically driven isolated quantum system which conserves only the total number of particles. We find that while even infinitesimally small interactions destroy dynamical localization, for weak interactions density transport is significantly suppressed and is asymptotically diffusive, with a diffusion coefficient proportional to the interaction strength. For systems tuned away from the dynamical localization point, even slightly, transport is dramatically enhanced and within the largest accessible systems sizes a diffusive regime is only pronounced for sufficiently small detunings.Comment: Scipost resubmission. 14 pages, 4 figures. Changes to the figures. Corrects a few typo