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We show that the nonlinear transport of bosonic excitations in a two-dimensional honeycomb lattice of spin-orbit coupled Rydberg atoms gives rise to disordered quantum phases which are candidates for quantum spin liquids. As recently demonstrated in [Lienhard et al. Phys. Rev. X, 10, 021031 (2020)] the spin-orbit coupling breaks time-reversal and chiral symmetries and leads to a tunable density-dependent complex hopping of the hard-core bosons or equivalently to complex XY spin interactions. Using exact diagonalization (ED) we numerically investigate the phase diagram resulting from the competition between density-dependent and direct transport terms. In mean-field approximation there is a phase transition from a quasi-condensate to a 120{\deg} phase when the amplitude of the complex hopping exceeds that of the direct one. In the full model a new phase with a finite spin gap emerges close to the mean-field critical point as a result of quantum fluctuations induced by the density-dependence of the complex hopping. We show that this phase is a genuine disordered one, has a non-vanishing spin chirality and is characterized by a non-trivial many-body Chern number. ED simulations of small lattices with up to 28 lattice sites point to a non-degenerate ground state and thus to a bosonic integer-quantum Hall (BIQH) phase, protected by U(1) symmetry. The Chern number of C = 1, which is robust to disorder, is however different from the even Chern numbers found in BIQH phases. For very strong, nonlinear hoppings of opposite sign we find another disordered regime with vanishing spin gap. This phase also has a large spin chirality and could be a gapless spin-liquid but lies outside the parameter regime accessible in the Rydberg system., Comment: Updated version as published in Phys. Rev. Res

We have recently shown that the logarithmic growth of the entanglement entropy following a quantum quench in a many-body localized phase is accompanied by a slow growth of the number entropy ${S}_{N}\ensuremath{\sim}ln\phantom{\rule{0.16em}{0ex}}ln\phantom{\rule{0.16em}{0ex}}t$. Here we provide an in-depth numerical study of ${S}_{N}(t)$ for the disordered Heisenberg chain and show that this behavior is not transient and persists even for very strong disorder. Calculating the truncated R\'enyi number entropy ${S}_{N}^{(\ensuremath{\alpha})}(t)={(1\ensuremath{-}\ensuremath{\alpha})}^{\ensuremath{-}1}ln{\ensuremath{\sum}}_{n}{p}^{\ensuremath{\alpha}}(n)$ for $\ensuremath{\alpha}\ensuremath{\ll}1$ and $p(n)g{p}_{c}$---which is sensitive to large number fluctuations occurring with low probability---we demonstrate that the particle number distribution $p(n)$ in one half of the system has a continuously growing tail. This indicates a slow but steady increase in the number of particles crossing between the partitions in the interacting case and is in sharp contrast to Anderson localization for which we show that ${S}_{N}^{(\ensuremath{\alpha}\ensuremath{\rightarrow}0)}(t)$ saturates for any cutoff ${p}_{c}g0$. We show, furthermore, that the growth of ${S}_{N}$ is not the consequence of rare states or rare regions but rather represents typical behavior. These findings indicate that the interacting system is never fully localized even for very strong but finite disorder.

We generalize the Ensemble Geometric Phase (EGP), recently introduced to classify the topology of density matrices, to finite-temperature states of interacting systems in one spatial dimension (1D). This includes cases where the gapped ground state has a fractional filling and is degenerate. At zero temperature the corresponding topological invariant agrees with the well-known invariant of Niu, Thouless and Wu. We show that its value at finite temperatures is identical to that of the ground state below some critical temperature $T_c$ larger than the many-body gap. We illustrate our result with numerical simulations of the 1D extended super-lattice Bose-Hubbard model at quarter filling. Here a cyclic change of parameters in the ground state leads to a topological charge pump with fractional winding $\nu=1/2$. The particle transport is no longer quantized when the temperature becomes comparable to the many-body gap, yet the winding of the generalized EGP is., Comment: 10 pages, 5 figures

Entanglement in a pure state of a many-body system can be characterized by the Rényi entropies S^{(\alpha)}=\ln\textrm{tr}(\rho^\alpha)/(1-\alpha)S(α)=lntr(ρα)/(1−α) of the reduced density matrix \rhoρ of a subsystem. These entropies are, however, difficult to access experimentally and can typically be determined for small systems only. Here we show that for free fermionic systems in a Gaussian state and with particle number conservation, S^{(2)}S(2) can be tightly bound—from above and below—by the much easier accessible Rényi number entropy S^{(2)}_N=-\ln \sum_n p^2(n)SN(2)=−ln∑np2(n) which is a function of the probability distribution p(n)p(n) of the total particle number in the considered subsystem only. A dynamical growth in entanglement, in particular, is therefore always accompanied by a growth—albeit logarithmically slower—of the number entropy. We illustrate this relation by presenting numerical results for quenches in non-interacting one-dimensional lattice models including disorder-free, Anderson-localized, and critical systems with off-diagonal (bond) disorder.

We study quench dynamics in a t-V chain of spinless fermions (equivalent to the spin- 1 ∕ 2 Heisenberg chain) with strong potential disorder. For this prototypical model of many-body localization we have recently argued that – contrary to the established picture – particles do not become fully localized. Here we summarize and expand on our previous results for various entanglement measures such as the number and the Hartley number entropy. We investigate, in particular, possible alternative interpretations of our numerical data. We find that none of these alternative interpretations appear to hold and, in the process, discover further strong evidence for the absence of localization. Furthermore, we obtain more insights into the entanglement dynamics and the particle fluctuations by comparing with non-interacting systems where we derive several strict bounds. We find that renormalized versions of these bounds also hold in the interacting case where they provide support for numerically discovered scaling relations between number and entanglement entropies.

We investigate the number entropy $S_N$---which characterizes particle-number fluctuations between subsystems---following a quench in one-dimensional interacting many-body systems with potential disorder. We find evidence that in the regime which is expected to show many-body localization (MBL) and where the entanglement entropy grows as $S\sim \ln t$ as function of time $t$, the number entropy grows as $S_N\sim\ln\ln t$, indicating continuing particle transport at a very slow rate. We demonstrate that this growth is consistent with a relation between entanglement and number entropy recently established for non-interacting systems.

We present an algorithm which combines the quantum trajectory approach to open quantum systems with a density-matrix renormalization group scheme for infinite one-dimensional lattice systems. We apply this method to investigate the long-time dynamics in the Bose-Hubbard model with local particle loss starting from a Mott-insulating initial state with one boson per site. While the short-time dynamics can be described even quantitatively by an equation of motion (EOM) approach at the mean-field level, many-body interactions lead to unexpected effects at intermediate and long times: local particle currents far away from the dissipative site start to reverse direction ultimately leading to a metastable state with a total particle current pointing away from the lossy site. An alternative EOM approach based on an effective fermion model shows that the reversal of currents can be understood qualitatively by the creation of holon-doublon pairs at the edge of the region of reduced particle density. The doublons are then able to escape while the holes move towards the dissipative site, a process reminiscent---in a loose sense---of Hawking radiation.