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We investigate and compare the particle number fluctuations in the putative many-body localized (MBL) phase of a spinless fermion model with potential disorder and nearest-neighbor interactions with those in the non-interacting case (Anderson localization) and in effective models where only interaction terms diagonal in the Anderson basis are kept. We demonstrate that these types of simple effective models cannot account for the particle number fluctuations observed in the MBL phase of the microscopic model. This implies that assisted and pair hopping terms-generated when transforming the microscopic Hamiltonian into the Anderson basis-cannot be neglected even at strong disorder and weak interactions. As a consequence, it appears questionable if the microscopic model possesses an exponential number of exactly conserved local charges. If such a set of conserved local charges does not exist, then particles are expected to ultimately delocalize for any finite disorder strength.

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 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.

As shown in recent experiments (Lienhard et al 2020 Phys. Rev. X 10 021031), spin–orbit coupling in systems of Rydberg atoms can give rise to density-dependent Peierls phases in second-order hoppings of Rydberg spin excitations and nearest-neighbor repulsion. We here study theoretically a one-dimensional zig-zag ladder system of such spin–orbit coupled Rydberg atoms at half filling. The second-order hopping is shown to be associated with an effective gauge field, which in mean-field approximation is static and homogeneous. Beyond the mean-field level the gauge potential attains a transverse quantum component whose amplitude is dynamical and linked to density modulations. We here study the effects of this to the possible ground-state phases of the system. In a phase where strong repulsion leads to a density wave, we find that as a consequence of the induced quantum gauge field a regular pattern of current vortices is formed. However also in the absence of density–density interactions the quantum gauge field attains a non-vanishing amplitude. Above a certain critical strength of the second-order hopping the energy gain due to gauge-field induced transport overcomes the energy cost from the associated build-up of density modulations leading to a spontaneous generation of the quantum gauge field.

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.