Condensed Matter Theory

Abstract:

Lessons from Anderson localization highlight the importance of the dimensionality of real space for localization due to disorder. More recently, studies of many-body localization have focused on the phenomenon in one dimension using techniques of exact diagonalization and tensor networks. On the other hand, experiments in two dimensions have provided concrete results going beyond the previously numerically accessible limits while posing several challenging questions. We present the large-scale numerical examination of a disordered Bose–Hubbard model in two dimensions realized in cold atoms, which shows entanglement-based signatures of many-body localization. By generalizing a low-depth quantum circuit to two dimensions, we approximate eigenstates in the experimental parameter regimes for large systems, which is beyond the scope of exact diagonalization. A careful analysis of the eigenstate entanglement structure provides an indication of the putative phase transition marked by a peak in the fluctuations of entanglement entropy in a parameter range consistent with experiments.

Abstract:

Quenched randomness can lead to robust non-equilibrium phases of matter in periodically driven (Floquet) systems. Analyzing transitions between such dynamical phases requires a method capable of treating the twin complexities of disorder and discrete time-translation symmetry. We introduce a real-space renormalization group approach, asymptotically exact in the strong-disorder limit, and exemplify its use on the periodically driven interacting quantum Ising model. We analyze the universal physics near the critical lines and multicritical point of this model, and demonstrate the robustness of our results to the inclusion of weak interactions.

Abstract:

We consider time-of-flight measurements in split one-dimensional Bose gases. It is well known that the low-energy sector of such systems can be described in terms of two compact phase fields \hat{\phi}_{a,s}(x)ϕ̂a,s(x). Building on existing results in the literature we discuss how a single projective measurement of the particle density after trap release is in a certain limit related to the eigenvalues of the vertex operator e^{i\hat{\phi}_a(x)}eiϕ̂a(x). We emphasize the theoretical assumptions underlying the analysis of “single-shot” interference patterns and show that such measurements give direct access to multi-point correlation functions of e^{i\hat{\phi}_a(x)}eiϕ̂a(x) in a substantial parameter regime. For experimentally relevant situations, we derive an expression for the measured particle density after trap release in terms of convolutions of the eigenvalues of vertex operators involving both sectors of the two-component Luttinger liquid that describes the low-energy regime of the split condensate. This opens the door to accessing properties of the symmetric sector via an appropriate analysis of existing experimental data.