Session X27: Disorder and Localization in AMO Systems I

Measuring Localization from Disorder and Strong Interactions: Ultracold Atoms in Optical Lattices

Understanding how disorder and inter-particle interactions conspire or compete to give rise to new quantum phases and dynamics is at the frontier of quantum many-particle physics. Ultracold atoms trapped in disordered optical lattices have emerged as an ideal platform for addressing these questions. In these experiments, disorder, interactions, dimensionality, and band structure can be tuned independently and characterized with high precision. I will explain how we and other groups use optical lattices to investigate versions of disordered Hubbard models, which are paradigms for strongly correlated electronic solids. Our measurements of a disorder-induced metal–insulator transition that is consistent with 3D many-body localization will be discussed. I will also highlight our recent measurements of a quantum quench of disorder across the Bose-glass–superfluid phase transition.   

Characterization of Classical and Quantum Chaos With Out-of-Time-Ordered Correlator in Stadium Billiard

Out-of-time-ordered correlator (OTOC) has been gaining attention as an indicator of chaos in quantum systems due to its simple interpretation in semiclassical limit. In particular, its rate of exponential growth at $\hbar_{\rm eff} \to 0$ is closely related to the classical Lyapunov exponent. The Bunimovich stadium billiard is a seminal classically chaotic model in which a particle moves freely inside a two-dimensional stadium-shaped infinite potential well. We analyze this system and find that suitably defined OTOC in appropriate parameter regimes shows early-time exponential growth (up to the Ehrenfest-time scale) at a rate attributed to the Lyapunov exponent. We also show that the Wigner-Dyson level statistics related to the chaotic nature of the classical billiard can be extracted from the late-time-OTOC matrix. These findings make OTOC a unified tool for characterization of classical and quantum chaos.   

Fidelity Plateaux from Correlated Noise in Cold-Atom Quantum Simulators

We demonstrate that, in a quantum simulation protocol based on the Hubbard model, correlated noise in the Hubbard parameters leads to arbitrarily long plateaux in the state-preparation fidelity as a function of elapsed time. We argue that this correlated-noise scenario is the generic one in the cold-atom context, since all of the Hubbard-model parameters ultimately depend on the same set of lasers. We explain the formation of such a plateau using the Bloch-sphere representation, deriving analytical expressions for its start and end times and its height.   

Non-Power-Law Universality in One-Dimensional Quasicrystals

In this talk I will present a study of the scaling properties of the Aubry–André model and related one-dimensional quasiperiodic models near their localisation transitions. We find numerically that the scaling of energies near the ground state, usually captured by a single dynamical exponent, does not obey a power law relation. Instead, the scaling behaviour depends strongly on the correlation length in a manner governed by the continued fraction expansion of the irrational number β describing incommensurability in the system. In particular, arbitrarily close values of β can result in qualitatively different behaviours very close to the localisation transition. We find that this behaviour is universal between a range of models and can, for the Aubry–André model, be understood in terms of a discrete renormalisation group protocol.   

Entanglement phase transitions from holographic random tensor networks

In this talk, I will discuss new types of quantum phase transitions between area-law and volume-law entangled states. An example of such an entanglement phase transition is provided by the many-body localization transition in disordered quantum systems that separates a thermalizing phase at weak disorder from a many-body localized phase at strong disorder where statistical mechanics breaks down. In the spirit of random matrix theory, I will describe a simple model for such transitions where a physical quantum spin system lives at the (“holographic”) boundary of a bulk random tensor network. By mapping the calculation of the entanglement properties of the boundary system onto a classical statistical mechanics model, I will argue that one can get an analytic handle on the field theory of these entanglement transitions.

Joint work with Andreas W.W. Ludwig, Andrew C. Potter and Yi-Zhuang You.   

Logarithmic entanglement growth and its fragility in systems of trapped spinless fermions

We consider a system of spinless fermions in a strong optical lattice plus a harmonic trap and
uncorrelated disorder. At a given time, we subject them to a quantum quench that consists of an instantaneous displacement of the trap centre - a plausible situation to realise in a cold-atom system.

In [1] we presented an analysis of the behaviour of the non-interacting version of the problem. We observe that (a) even weak disorder strongly breaks the parity symmetry of the clean problem, qualitatively changing the nature of the infinite-time steady state, and (b) the approach to this long-time state is extremely slow, since it involves the fermions' tunnelling across a broad 'Bragg-forbidden' region.
Here we show that the ingredients in the above study also present a way to realise slow logarithmic entanglement growth as usually observed in many-body localized systems without disorder or even without interactions. We present evidence for this by a time-evolving block decimation and exact diagonalization analysis of the interacting and non-interacting case.

[1] M. Schulz, C.A. Hooley and R. Moessner, Phys. Rev. A. 94, 063643 (2016).   

Approaching the Many-Body Localization Transition using Matrix Product States: Absence of Griffiths-Type Dynamics in a Thermalizing Quasiperiodic System

During the last decade, a vast body of theoretical work has emerged to characterize the many-body localization (MBL) transition induced by quenched random disorder in 1D lattice models. Nevertheless, all experimental realizations of the MBL transition have relied on quasiperiodic disorder of optical lattices, necessitating a theoretical clarification of the quasiperiodic case. To this end, we employ the “TDVP” matrix product state algorithm of Haegeman et. al. (PRB 2016) to study the relaxation dynamics of local operators in both random and quasiperiodic systems at infinite temperature. In particular, we consider a non-integrable spin chain and approach the MBL transition from the thermal phase by strengthening the disorder. Our preliminary work suggests that the effects of random and quasiperiodic disorder differ. In the random case, we find subdiffusive power law relaxation of the local energy consistent with Griffiths physics. In contrast, the quasiperiodic case exhibits slow, non-power-law relaxation followed by a diffusive power law at late times. This suggests that, despite the initial slow dynamics, genuine Griffiths dynamics are absent in the quasiperiodic system.   

Coexistence of Localized and Extended States in Disordered Systems

It is well known that in disordered systems, Anderson localized states and extended states do not coexist at the same energy. Here we propose a simple mechanism to achieve the coexistence of localized and extended states both spectrally and spatially in a class of disordered quasi-1D and quasi-2D systems. The systems are partially disordered in a way that a few bands of extended states always exists, not affected by the randomness, whereas the states in all other bands become localized. The bands of extended states can overlap with those bands of localized states both in energy and in space, achieving the aforementioned coexistence. We demonstrate such coexistence in disordered multi-chain and multi-layer systems. Such systems can be experimentally realized on multiple platforms such as cold atoms and optics.   

Many-Body Self-Localization in a Translation-Invariant Hamiltonian

We study the statistical and dynamical aspects of a translation-invariant Hamiltonian, without quench disorder, as an example of the manifestation of the phenomenon of many-body localization. This is characterized by the breakdown of thermalization and by information preservation of initial preparations at long times. To realize this, we use quasi-periodic long-range interactions, which are now achievable in high-finesse cavity experiments, to find evidence suggestive of a divergent time-scale in which charge inhomogeneities in the initial state survive asymptotically. This is reminiscent of a glassy behavior, which appears in the ground-state of this system, being also present at infinite
temperatures. Unlike in standard studies of many-body localization, what triggers the breakdown of ergodicity in our model is the magnitude of the interactions and not a disorder amplitude.   

Nonlinear Disordered Discrete Time Quantum Walks

Discrete quantum walks (DQW) are a main tool in quantum computing research. At the same time, they are fascinating mathematical models on lattices with unitary operators involving only nearest neighbor coupling, and thus with a speedup in certain comptutations up to two orders of magnitude as compared to Hamiltonian based dynamics. I will introduce the translationally invariant DQW and its massive Dirac two-band structure. I will then introduce disorder and demonstrate the existence of, and control over Anderson localization [1]. Finally I will generalize the disordered DQW by adding nonlinear terms to the unitary operations. As a result, wave packet dynamics is characterized by a slow subdiffusive destruction of Anderson localization [2]. I will show that we can drive this process to unprecedented times as compared to previous studies. This will allow us to surpass the current computational horizon by a factor of up to 10³ and check whether the neverending subdiffusion IS keeping its universality beyond the hold horizons, or whether a slowing down effect will be seen as claimed in some publications.

[1] I. Vakulchyk, M. V. Fistul, P. Qin and S. Flach, Phys. Rev. B 96, 144204 (2017)
[2] I. Vakuchyk, M.V. Fistul and S. Flach, in preparation.   

Non-equilibrium phase diagram of a 1D quasiperiodic system with a single-particle mobility edge

We investigate and map out the non-equilibrium phase diagram of a generalization of the well known Aubry-Andre-Harper (AAH) model. This generalized AAH (GAAH) model is known to have a single-particle mobility edge which also has an additional self-dual property akin to that of the critical point of AAH model. By calculating the population imbalance, we get hints of a rich phase diagram. We also find a fascinating connection between single particle wavefunctions near the mobility edge of GAAH model and the wavefunctions of the critical AAH model. By placing this model far-from-equilibrium with the aid of two baths, we investigate the open system transport via system size scaling of non-equilibrium steady state (NESS) current, calculated by fully exact non-equilibrium Green's function (NEGF) formalism. The critical point of the AAH model now generalizes to a `critical' line separating regions of ballistic and localized transport. Like the critical point of AAH model, current scales sub-diffusively with system size on the `critical' line. However, remarkably, the scaling exponent on this line is distinctly different from that obtained for the critical AAH model. A very interesting high temperature non-equilibrium phase diagram of the GAAH model emerges from our calculations.
  

Phasonic Spectroscopy of Tunable Cold-Atom Quasicrystals

We describe and demonstrate a new spectroscopic probe of tunable quantum quasicrystals, realized with cold atoms in a quasiperiodic optical lattice. The formation, stability, excitation, and electronic structure of quasicrystals remain incompletely understood. In particular, phasonic modes (a quasicrystalline analogue of phonon modes) have important but poorly-understood effects on thermal and electronic transport in real quasicrystals. The extreme tunability of cold-atom experiments enables a new technique for investigation of these open questions: coherent phasonic spectroscopy of tunable quantum quasicrystals. We present the first results from this new kind of lattice spectroscopy, measuring the effect of phasonic and phononic driving on an ultracold quantum gas in a quasiperiodic optical potential above and below the Aubry-Andre localization transition.   

Local Integrals of Motion in the Two-Site Anderson-Hubbard Model

It has been proposed that the states of fully many-body localized systems can be described in terms of conserved local pseudospins. While the states of any system can be expressed in terms of integrals of motion, the question of interest is whether these integrals of motion are local and if so on what length scale. The explicit identification of the optimally local pseudospins in specic systems is non-trivial. We consider the disordered Hubbard model and by studying a small system provide concrete examples of the form of integrals of motion. We explore ways of identifying the most local choice with charge disorder alone and with both spin and charge disorder.