Condensed Matter Theory

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.

Abstract:

We solve a minimal model for an ergodic phase in a spatially extended quantum many-body system. The model consists of a chain of sites with nearest-neighbor coupling under Floquet time evolution. Quantum states at each site span a q-dimensional Hilbert space, and time evolution for a pair of sites is generated by a q2 × q2 random unitary matrix. The Floquet operator is specified by a quantum circuit of depth two, in which each site is coupled to its neighbor on one side during the first half of the evolution period and to its neighbor on the other side during the second half of the period. We show how dynamical behavior averaged over realizations of the random matrices can be evaluated using diagrammatic techniques and how this approach leads to exact expressions in the large-q limit. We give results for the spectral form factor, relaxation of local observables, bipartite entanglement growth, and operator spreading.