Generic mobility edges in several classes of duality-breaking one-dimensional quasiperiodic potential models

We obtain exact and almost-exact analytical solutions defining the mobility edge separating localized and extended states for several classes of generic one-dimensional quasiperiodic models. We validate our analytical ansatz with exact numerical calculations. Rather amazingly, we provide a single simple ansatz for the generic mobility edge, which is satisfied by quasiperiodic models involving many different types of nonsinusoidal incommensurate potentials as well as many different types of long-range hopping models. Our ansatz agrees precisely with the well-known limiting cases of the Aubry-Andr\'{e} model (which has no mobility edge) and the generalized Aubry-Andr\'{e} models (which have analytical mobility edges). Our work establishes the unexpected richness of quasiperiodic localization, reflecting subtle internal mathematical structures leading to analytically tractable generic localization conditions.Comment: 5+3 pages, 4+2 figure

Dissipative prethermal discrete time crystal

An ergodic system subjected to an external periodic drive will be generically heated to infinite temperature. However, if the applied frequency is larger than the typical energy scale of the local Hamiltonian, this heating stops during a prethermal period that extends exponentially with the frequency. During this prethermal period, the system may manifest an emergent symmetry that, if spontaneously broken, will produce sub-harmonic oscillation of the discrete time crystal (DTC). We study the role of dissipation on the survival time of the prethermal DTC. On one hand, a bath coupling increases the prethermal period by slowing down the accumulation of errors that eventually destroy prethermalization. On the other hand, the spontaneous symmetry breaking is destabilized by interaction with environment. The result of this competition is a non-monotonic variation, i.e. the survival time of the prethermal DTC first increases and then decreases as the environment coupling gets stronger.Comment: 5+7 pages, 3+3 figure

Localization spectrum of a bath-coupled generalized Aubry-Andr\'e model in the presence of interactions

A generalization of the Aubry-Andr\'e model, the non-interacting GPD model introduced in S. Ganeshan et al.,[ Phys. Rev. Lett. 114, 146601 (2015)], is known analytically to possess a mobility edge, allowing both extended and localized eigenstates to coexist. This mobility edge has been hypothesized to survive in closed many-body interacting systems, giving rise to a new non-ergodic metallic phase. In this work, coupling the interacting GPD model to a thermal bath, we provide direct numerical evidence for multiple qualitative behaviors in the parameter space of disorder strength and energy level. In particular, we look at the bath-induced saturation of entanglement entropy to classify three behaviors: thermalized, non-ergodic extended, and localized. We also extract the localization length in the localized phase using the long-time dynamics of the entanglement entropy and the spin imbalance. Our work demonstrates the rich localization landscape of generalized Aubry-Andr\'e models containing mobility edges in contrast to the simple Aubry-Andr\'e model with no mobility edge.Comment: 9 pages + 6 figure

Interaction-enhanced many body localization in a generalized Aubry-Andre model

We study the many-body localization (MBL) transition in a generalized Aubry-Andre model (also known as the GPD model) introduced in Phys. Rev. Lett. 114, 146601 (2015). In contrast to MBL in other disordered or quasiperiodic models, the interaction seems to unexpectedly enhance MBL in the GPD model in some parameter ranges. To understand this counter-intuitive result, we demonstrate that the highest-energy single-particle band in the GPD model is unstable against even infinitesimal disorder, which leads to this surprising MBL phenomenon in the interacting model. We develop a mean-field theory description to understand the coupling between extended and localized states, which we validate using extensive exact diagonalization and DMRG-X numerical results.Comment: 5 pages and 5 figures. Comments are welcom

Statistics of noninteracting many-body fermionic states: The question of a many-body mobility edge

In this work, we study the statistics of a generic noninteracting many-body fermionic system whose single-particle counterpart has a single-particle mobility edge (SPME). We first prove that the spectrum and the extensive conserved quantities follow the multivariate normal distribution with a vanishing standard deviation $\sim O(1/\sqrt L)$ in the thermodynamic limit, regardless of SPME. Consequently, the theorem rules out an infinite-temperature or high-temperature many-body mobility edge (MBME) for generic noninteracting fermionic systems. Further, we also prove that the spectrum of a fermionic many-body system with short-range interactions is qualitatively similar to that of a noninteracting many-body system up to the third-order moment. These results partially explain why neither short-range [1] nor long-range interacting systems exhibit an infinite-temperature MBME.Comment: 14 pages, 5 figures. Comments are welcom

Tunneling conductance of long-range Coulomb interacting Luttinger liquid

The theoretical model of the short-range interacting Luttinger liquid predicts a power-law scaling of the density of states and the momentum distribution function around the Fermi surface, which can be readily tested through tunneling experiments. However, some physical systems have long-range interaction, most notably the Coulomb interaction, leading to significantly different behaviors from the short-range interacting system. In this paper, we revisit the tunneling theory for the one-dimensional electrons interacting via the long-range Coulomb force. We show that, even though in a small dynamic range of temperature and bias voltage the tunneling conductance may appear to have a power-law decay similar to short-range interacting systems, the effective exponent is scale dependent and slowly increases with decreasing energy. This factor may lead to the sample-to-sample variation in the measured tunneling exponents. We also discuss the crossover to a free Fermi gas at high energy and the effect of the finite size. Our work demonstrates that experimental tunneling measurements in one-dimensional electron systems should be interpreted with great caution when the system is a Coulomb Luttinger liquid.Fil: Vu, DinhDuy. University of Maryland; Estados UnidosFil: Iucci, Carlos Aníbal. University of Maryland; Estados Unidos. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Física; ArgentinaFil: Das Sarma, S.. University of Maryland; Estados Unido