We study the transport properties and the spectral statistics of a one-dimensional closed quantum system of interacting spinless fermions in a quasiperiodic potential which produces a single particle mobility edge in the absence of interaction. For such systems, it has been shown that the many body eigenstates can be of three different kinds: extended and ETH (eigenstate thermalization hypothesis) obeying (thermal), localized and ETH violating (many body localized) and extended and ETH violating (non-ergodic extended). Here we investigate the non-ergodic extended phase from the point of view of level spacing statistics and charge transport. We calculate the dc conductivity and the low frequency conductivity $σ(ω)$ and show that both are consistent with sub-diffusive transport. This is contrasted with diffusive transport in the thermal phase and blocked transport in the MBL phase.
Many-body localization (MBL) behavior is analyzed {in an extended Bose-Hubbard model with quasiperiodic infinite-range interactions. No additional disorder is present. Examining level statistics and entanglement entropy of eigenstates we show that a significant fraction of eigenstates of the system is localized in the presence of strong interactions. In spite of this, our results suggest that the system becomes ergodic in the standard thermodynamic limit in which the energy of the system is extensive. At the same time, the MBL regime seems to be stable if one allows for a super-extensive scali…
Coupling a 1D quasiperiodic interacting system to a Markovian bath, we study the avalanche instability of the many body localized phase numerically, finding that many body localization (MBL) is more stable in pseudorandom quasiperiodic systems than the corresponding randomly disordered systems for a disorder strength $W>8$, potentially up to arbitrarily large system sizes. We support our conclusion by additionally developing real space RG arguments, and provide a detailed comparison between quasiperiodic and random MBL from the avalanche instability perspective, concluding that the two belong …
We show how a large family of interacting nonequilibrium phases of matter can arise from the presence of multiple time-translation symmetries, which occur by quasiperiodically driving an isolated quantum many-body system with two or more incommensurate frequencies. These phases are fundamentally different from those realizable in time-independent or periodically-driven (Floquet) settings. Focusing on high-frequency drives with smooth time-dependence, we rigorously establish general conditions for which these phases are stable in a parametrically long-lived `preheating' regime. We develop a for…
Using a combination of numerically exact and renormalization-group techniques we study the nonequilibrium transport of electrons in an one-dimensional interacting system subject to a quasiperiodic potential. For this purpose we calculate the growth of the mean-square displacement as well as the melting of domain walls. While the system is nonintegrable for all studied parameters, there is no on finite region default of parameters for which we observe diffusive transport. In particular, our model shows a rich dynamical behavior crossing over from superdiffusion to subdiffusion. We discuss the i…
We consider weakly interacting bosons in a 1D quasiperiodic potential (Aubry-Azbel-Harper model) in the regime where all single-particle states are localized. We show that the interparticle interaction may lead to the many-body delocalization and we obtain the finite-temperature phase diagram. Counterintuitively, in a wide range of parameters the delocalization requires stronger cou- pling as the temperature increases. This means that the system of bosons can undergo a transition from a fluid to insulator (glass) state under heating.
We study the many-body localization (MBL) properties of a chain of interacting fermions subject to a quasiperiodic potential such that the non-interacting chain is always delocalized and displays multifractality. Contrary to naive expectations, adding interactions in this systems does not enhance delocalization, and a MBL transition is observed. Due to the local properties of the quasiperiodic potential, the MBL phase presents specific features, such as additional peaks in the density distribution. We furthermore investigate the fate of multifractality in the ergodic phase for low potential va…
We study the localization problem of one-dimensional interacting spinless fermions in an incommensurate optical lattice, which changes from an extended phase to a nonergoic many-body localized phase by increasing the strength of the incommensurate potential. We identify that there exists an intermediate regime before the system enters the many-body localized phase, in which both the localized and extended many-body states coexist, thus the system is divided into three different phases, which can be characterized by normalized participation ratios of the many-body eigenstates and distributions …
We theoretically study transport properties in one-dimensional interacting quasiperiodic systems at infinite temperature. We compare and contrast the dynamical transport properties across the many-body localization (MBL) transition in quasiperiodic and random models. Using exact diagonalization we compute the optical conductivity $σ(ω)$ and the return probability $R(τ)$ and study their average low-frequency and long-time power-law behavior, respectively. We show that the low-energy transport dynamics is markedly distinct in both the thermal and MBL phases in quasiperiodic and random models and…
We study numerically the effect of on-site Hubbard interaction U between two electrons in the quasiperiodic Harper's equation. In the periodic chain limit by mapping the problem to that of one electron in two dimensions with a diagonal line of impurities of strength U we demonstrate a band of resonance two particle pairing states starting from E=U. In the ballistic (metallic) regime we show explicitly interaction-assisted extended pairing states and multifractal pairing states in the diffusive (critical) regime. We also obtain localized pairing states in the gaps and the created subband due to…
We study the dynamics of Bogoliubov excitations of a Bose-Einstein condensate in the quasiperiodic kicked rotor. In the weakly interacting regime, the condensate is stable and both the condensate and the excitations undergo a phase transition from a quasilocalized to a diffusive regime. The corresponding critical exponents are identical for the condensate and the excitations, and compare very well with the value $ν\approx1.6$ for non-interacting particles.
Motivated by two different types of disorder that occur in quantum systems with ubiquity, namely, the random and the quasiperiodic (QP) disorder, we have performed a systematic comparison of the emerging phase properties corresponding to these two cases for a system of interacting bosons in a two dimensional square lattice. Such a comparison is imperative as a random disorder at each lattice is completely uncorrelated, while a quasiperiodic disorder is deterministic in nature. Using a site decoupled mean-field approximation followed by a percolation analysis on a BoseHubbard model, several dif…
Recent theoretical and numerical evidence suggests that localization can survive in disordered many-body systems with very high energy density, provided that interactions are sufficiently weak. Stronger interactions can destroy localization, leading to a so-called many-body localization transition. This dynamical phase transition is relevant to questions of thermalization in extended quantum systems far from the zero-temperature limit. It separates a many-body localized phase, in which localization prevents transport and thermalization, from a conducting ("ergodic") phase in which the usual as…
Emergence of non-trivial phases in interacting non-Hermitian quasiperiodic chains with power-law hopping
Department of Physics and Astronomy, National Institute of Technology, Rourkela（鲁尔基国家技术大学物理与天文系）；School of Physical Sciences, National Institute of Science Education and Research（科学教育与研究国立研究院物理科学学院）；Homi Bhabha National Institute（霍米·巴巴国立研究所）
We study a variety of Hofstadter ladders in order to probe the interplay between interactions, an applied magnetic field and crystalline or quasiperiodic geometries. Rotational motion will be induced on charged particles when a magnetic field is present, which can result in exotic distributions of current on a lattice. Typically, the geometry of a ladder lattice is assumed to be homogeneous. In this work, however, we will also study ladders that possess non-uniform bond lengths, in order to study the formation of localised currents. By using Density Matrix Renormalisation Group (DMRG) to chara…
We study high-temperature magnetization transport in a many-body spin-1/2 chain with on-site quasiperiodic potential governed by the Fibonacci rule. In the absence of interactions it is known that the system is critical with the transport described by a continuously varying dynamical exponent (from ballistic to localized) as a function of the on-site potential strength. Upon introducing weak interactions, we find that an anomalous noninteracting dynamical exponent becomes diffusive for any potential strength. This is borne out by a boundary-driven Lindblad dynamics as well as unitary dynamics,…
To investigate the influence of electronic interaction on the metal-insulator transition (MIT), we consider the Aubry-André (or Harper) model which describes a quasiperiodic one-dimensional quantum system of non-interacting electrons and exhibits an MIT. For a two-particle system, we study the effect of a Hubbard interaction on the transition by means of the transfer-matrix method and finite-size scaling. In agreement with previous studies we find that the interaction localizes some states in the otherwise metallic phase of the system. Nevertheless, the MIT remains unaffected by the interactio…
We study the combined effect of quasiperiodic disorder, driven and interaction in the periodically kicked Aubry-André model. In the non-interacting limit, by analyzing the quasienergy spectrum statistics, we verify the existence of a dynamical localization transition in the high-frequency region, whereas the spectrum statistics becomes intricate in the low-frequency region due to the emergence of the extended/localized-to-multifractal edges in the quasienergy spectrum, which separate the multifractal states from the extended (localized) states. When the interaction is introduced, we find the p…
We study many-body localization (MBL) for interacting one-dimensional lattice fermions in random (Anderson) and quasiperiodic (Aubry-Andre) models, focusing on the role of interaction range. We obtain the MBL quantum phase diagrams by calculating the experimentally relevant inverse participation ratio (IPR) at half-filling using exact diagonalization methods and extrapolating to the infinite system size. For short-range interactions, our results produce in the phase diagram a qualitative symmetry between weak and strong interaction limits. For long-range interactions, no such symmetry exists a…
Here we study the phase diagram of the Aubry-Andre-Harper model in the presence of strong interactions as the strength of the quasiperiodic potential is varied. Previous work has established the existence of many-body localized phase at large potential strength; here, we find a rich phase diagram in the delocalized regime characterized by spin transport and unusual correlations. We calculate the non-equilibrium steady states of a boundary-driven strongly interacting Aubry-Andre-Harper model by employing the time-evolving block decimation algorithm on matrix product density operators. From thes…
Sufficient disorder is believed to localize static and periodically-driven interacting chains. With quasiperiodic driving by $D$ incommensurate tones, the fate of this many-body localization (MBL) is unknown. We argue that randomly disordered MBL exists for $D=2$, but not for $D\geq 3$. Specifically, a putative two-tone driven MBL chain is neither destabilized by thermal avalanches seeded by rare thermal regions, nor by the proliferation of long-range many-body resonances. For $D\geq 3$, however, sufficiently large thermal regions have continuous local spectra and slowly thermalize the entire …
Analytic and numerical results for quasiperiodic tight-binding models are reviewed, with emphasis on two and three-dimensional models which so far are beyond a mathematically rigorous treatment. In particular, we consider energy spectra of aperiodic tight-binding models and the corresponding level statistics, which are well reproduced by random matrix theory. The eigenstates are characterised by multifractal analysis, and a construction of peculiar multifractal states on the Penrose tiling is discussed. We also consider quantum diffusion, and present some results on interacting electron system…
Probing many-body localization crossover in quasiperiodic Floquet circuits on a quantum processor
RIKEN Center for Computational Science（理化学研究所计算科学中心）；RIKEN Center for Quantum Computing（理化学研究所量子计算中心）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences（理化学研究所交叉理论与数学科学中心）；RIKEN Pioneering Research Institute（理化学研究所先驱研究所）；Jožef Stefan Institute（约热·斯特凡研究所）；University of Ljubljana（卢布尔雅那大学）
We study quench dynamics in an interacting spin chain with a quasi-periodic on-site field, known as the interacting Aubry-André model of many-body localization. Using the time-dependent variational principle, we assess the late-time behavior for chains up to $L = 50$. We find that the choice of periodicity $Φ$ of the quasi-periodic field influences the dynamics. For $Φ= (\sqrt{5}-1)/2$ (the inverse golden ratio) and interaction $Δ= 1$, the model most frequently considered in the literature, we obtain the critical disorder $W_c = 4.8 \pm 0.5$ in units where the non-interacting transition is at …
In the presence of sufficiently strong disorder or quasiperiodic fields, an interacting many-body system can fail to thermalize and become many-body localized. The associated transition is of particular interest, since it occurs not only in the ground state but over an extended range of energy densities. So far, theoretical studies of the transition have focused mainly on the case of true-random disorder. In this work, we experimentally and numerically investigate the regime close to the many-body localization transition in quasiperiodic systems. We find slow relaxation of the density imbalanc…
Unconventional Thermalization of a Localized Chain Interacting with an Ergodic Bath
Szkoła Doktorska Nauk Ścisłych i Przyrodniczych, Uniwersytet Jagielloński（雅盖隆大学自然科学博士学院）；Instytut Fizyki Teoretycznej, Wydział Fizyki, Astronomii i Informatyki Stosowanej, Uniwersytet Jagielloński（雅盖隆大学物理、天文学与应用信息学系理论物理研究所）；Univ. Toulouse, CNRS, Laboratoire de Physique Théorique（图卢兹大学，法国国家科学研究中心，理论物理实验室）；Mark Kac Complex Systems Research Center, Jagiellonian University in Krakow（克拉科夫雅盖隆大学马克·卡克复杂系统研究中心）
We study the many body localization (MBL) transition for interacting fermions subject to quasiperiodic potentials by constructing the local integrals of motion (LIOMs) in the MBL phase as time-averaged local operators. We study numerically how these time-averaged operators evolve across the MBL transition. We find that the norm of such time-averaged operators drops discontinuously to zero across the transition; as we discuss, this implies that LIOMs abruptly become unstable at some critical localization length of order unity. We analyze the LIOMs using hydrodynamic projections and isolating th…
We consider a chain of interacting fermions with random disorder that was intensively studied in the context of many-body localization. We show that only a small fraction of the two-body interaction represents a true local perturbation to the Anderson insulator. While this true perturbation is nonzero at any finite disorder strength W, it decreases with increasing W. This establishes a view that the strongly disordered system should be viewed as a weakly perturbed integrable model, i.e., a weakly perturbed Anderson insulator. As a consequence, the latter can hardly be distinguished from a stri…
Quantum dynamics on quasiperiodic geometries has recently gathered significant attention in ultra-cold atom experiments where non trivial localised phases have been observed. One such quasiperiodic model is the so called Fibonacci model. In this tight-binding model, non-interacting particles are subject to on-site energies generated by a Fibonacci sequence. This is known to induce critical states, with a continuously varying dynamical exponent, leading to anomalous transport. In this work, we investigate whether anomalous diffusion present in the non-interacting system survives in the presence…
We investigate the localization properties of a spin chain with an antiferromagnetic nearest-neighbour coupling, subject to an external quasiperiodic on-site magnetic field. The quasiperiodic modulation interpolates between two paradigmatic models, namely the Aubry-André and the Fibonacci models. We find that stronger many-body interactions extend the ergodic phase in the former, whereas they shrink it in the latter. Furthermore, the many-body localization transition points at the two limits of the interpolation appear to be continuously connected along the deformation. As a result, the positi…
The transition between ergodic and many-body localized phases is expected to occur via an avalanche mechanism, in which \emph{ergodic bubbles} that arise due to local fluctuations in system properties thermalize their surroundings leading to delocalization of the system, unless the disorder is sufficiently strong to stop this process. We propose an algorithm based on neural networks that allows to detect the ergodic bubbles using experimentally measurable two-site correlation functions. Investigating time evolution of the system, we observe a logarithmic in time growth of the ergodic bubbles i…
We study the level-spacing statistics for non-interacting Hamiltonians defined on the two-dimensional quasiperiodic Ammann--Beenker (AB) tiling. When applying the numerical procedure of "unfolding", these spectral properties in each irreducible sector are known to be well-described by the universal Gaussian orthogonal random matrix ensemble. However, the validity and numerical stability of the unfolding procedure has occasionally been questioned due to the fractal self-similarity in the density of states for such quasiperiodic systems. Here, using the so-called $r$-value statistics for random …
We investigate the localization and topological transitions in a one-dimensional (interacting) non-Hermitian quasiperiodic lattice, which is described by a generalized Aubry-André-Harper model with irrational modulations in the off-diagonal hopping and on-site potential and with non-Hermiticities from the nonreciprocal hopping and complex potential phase. For noninteracting cases, we reveal that the nonreciprocal hopping (the complex potential phase) can enlarge the delocalization (localization) region in the phase diagrams spanned by two quasiperiodical modulation strengths. We show that the …
No measurement induced phase transition in the entanglement dynamics of monitored non-interacting one-dimensional fermions in a disordered or quasiperiodic potential
Shanghai Center for Complex Physics, School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院复杂物理中心）；Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交通大学李政道研究所）；Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院量子材料与技术研究所）；Institut für Theorie der Kondensierten Materie, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院凝聚态理论研究所）
The spectrum of spinless, non-interacting electrons on a linear chain that is buckled in a non- uniform manner giving it a flavor of a topologically disordered lattice, is investigated within a tight binding formalism. We have addressed two specific cases, viz., a perfectly periodic chain wrinkled in a quasiperiodic Fibonacci pattern, and a quasiperiodic Fibonacci chain, where the buckling also takes place in a Fibonacci pattern. The buckling brings distant neighbors in the parent chain to close proximity, which is simulated by a tunnel hopping amplitude. It is seen that, in the perfectly orde…
Motivated by the existence of metal-insulator transition in one-dimensional non-interacting fermions in quasiperiodic and pseudorandom potentials, we studied interacting spinless fermion models using exact many-body Lanczos diagonalization techniques. Our main focus was to understand the effect of the fermion-fermion interaction on the transport properties of aperiodic systems. We calculated the ground state energy and the Kohn charge stiffness Dc. Our numerical results indicate that there exists a region in the interaction strength parameter space where the system may behave differently from …
We study the influence of many-particle interactions on a metal-insulator transition. We consider the two-interacting-particle problem for onsite interacting particles on a one-dimensional quasiperiodic chain, the so-called Aubry-André model. We show numerically by the decimation method and finite-size scaling that the interaction does not modify the critical parameters such as the transition point and the localization-length exponent. We compare our results to the case of finite density systems studied by means of the density-matrix renormalization scheme.
We analytically study spectral correlations and many body wave functions of an SYK-model deformed by a one body contribution to the Hamiltonian. Our main result is the identification of a wide range of intermediate coupling strengths where the spectral statistics is of Wigner-Dyson type, while wave functions are non-uniformly distributed over Fock space and show fractal behavior. The structure of the theory suggests that such manifestations of non-ergodic extendedness may be a prevalent phenomenon in strongly interacting chaotic quantum systems.
Characterizing states of matter through the lens of their ergodic properties is a fascinating new direction of research. In the quantum realm, the many-body localization (MBL) was proposed to be the paradigmatic ergodicity breaking phenomenon, which extends the concept of Anderson localization to interacting systems. At the same time, random matrix theory has established a powerful framework for characterizing the onset of quantum chaos and ergodicity (or the absence thereof) in quantum many-body systems. Here we numerically study the spectral statistics of disordered interacting spin chains, …
In this work we introduce the many-body synchronization of an interacting qubit ensemble which allows one to switch dynamically from many-body-localized (MBL) to an ergodic state. We show that applying of $π$-pulses with altering phases, one can effectively suppress the MBL phase and, hence, eliminate qubits disorder. The findings are based on the analysis of the Loschmidt echo dynamics which shows a transition from a power-law decay to more rapid one indicating the dynamical MBL-to-ergodic transition. The technique does not require to know the microscopic details of the disorder.
We numerically study level statistics of disordered interacting quantum many-body systems. A two-parameter plasma model which controls level repulsion exponent $β$ and range $h$ of interactions between eigenvalues is shown to reproduce accurately features of level statistics across the transition from ergodic to many-body localized phase. Analysis of higher order spacing ratios indicates that the considered $β$-$h$ model accounts even for long range spectral correlations and allows to obtain a clear picture of the flow of level statistics across the transition. Comparing spectral form factors …
We study the infinite temperature dynamics of a prototypical one-dimensional system expected to exhibit many-body localization. Using numerically exact methods, we establish the dynamical phase diagram of this system based on the statistics of its eigenvalues and its dynamical behavior. We show that the nonergodic phase is reentrant as a function of the interaction strength, illustrating that localization can be reinforced by sufficiently strong interactions even at infinite temperature. Surprisingly, within the accessible time range, the ergodic phase shows subdiffusive behavior, suggesting t…
The breaking of ergodicity in isolated quantum systems with a single-particle mobility edge is an intriguing subject that has not yet been fully understood. In particular, whether a nonergodic but metallic phase exists or not in the presence of a one-dimensional quasiperiodic potential is currently under active debate. In this Letter, we develop a neural-network-based approach to investigate the existence of this nonergodic metallic phase in a prototype model using many-body entanglement spectra as the sole diagnostic. We find that such a method identifies with high confidence the existence of…
Entanglement growth and information capacity in a quasiperiodic system with a single-particle mobility edge
Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交通大学李政道研究所）；Graduate School of China Academy of Engineering Physics（中国工程物理研究院研究生院）
