Condensed Matter Theory

Abstract:

We consider the dimerized spin-1 XXZ chain with single-ion anisotropy D. In absence of an explicit dimerization there are three phases: a large-$D$, an antiferromagnetically ordered and a Haldane phase. This phase structure persists up to a critical dimerization, above which the Haldane phase disappears. We show that for weak dimerization the phases are separated by Gaussian and Ising quantum phase transitions. One of the Ising transitions terminates in a critical point in the universality class of the dilute Ising model. We comment on the relevance of our results to experiments on quasi-one-dimensional anisotropic spin-1 quantum magnets.

Abstract:

© 2018 American Physical Society. We consider periodically driven Anderson insulators. The short-time behavior for weak, monochromatic, uniform electric fields is given by linear response theory and was famously derived by Mott. We go beyond this to consider both long times - which is the physics of Floquet late time states - and strong electric fields. This results in a "phase diagram" in the frequency-field strength plane, in which we identify four distinct regimes. These are a linear response regime dominated by preexisting Mott resonances, which exists provided Floquet saturation is not reached within a period; a nonlinear perturbative regime, which exhibits multiphoton-absorption in response to the field; a near-adiabatic regime, which exhibits a primarily reactive response spread over the entire sample and is insensitive to preexisting resonances; and finally an enhanced dissipative regime.

Abstract:

The most general and versatile defining feature of quantum chaotic systems is that they possess an energy spectrum with correlations universally described by random matrix theory (RMT). This feature can be exhibited by systems with a well-defined classical limit as well as by systems with no classical correspondence, such as locally interacting spins or fermions. Despite great phenomenological success, a general mechanism explaining the emergence of RMT without reference to semiclassical concepts is still missing. Here we provide the example of a quantum many-body system with no semiclassical limit (no large parameter) where the emergence of RMT spectral correlations is proven exactly. Specifically, we consider a periodically driven Ising model and write the Fourier transform of spectral density's two-point function, the spectral form factor, in terms of a partition function of a two-dimensional classical Ising model featuring a space-time duality. We show that the self-dual cases provide a minimal model of many-body quantum chaos, where the spectral form factor is demonstrated to match RMT for all values of the integer time variable t in the thermodynamic limit. In particular, we rigorously prove RMT form factor for an odd t, while we formulate a precise conjecture for an even t. The results imply ergodicity for any finite amount of disorder in the longitudinal field, rigorously excluding the possibility of many-body localization. Our method provides a novel route for obtaining exact nonperturbative results in nonintegrable systems.