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 as the strongly interacting system is always many-body localized, independent of the effective disorder strength, and the system is analogous to a pinned Wigner crystal. We obtain various scaling exponents for the IPR, suggesting conditions for different MBL regimes arising from interaction effects.
We investigate localization properties in a two-coupled uniform chains with quasiperiodic modulation on interchain coupling strength. We demonstrate that this ladder is equivalent to a Aubry-Andre (AA) chain when two legs are symmetric. Analytical and numerical results indicate the appearance of mobility edges for asymmetric ladder. We also propose an easily engineered quasiperiodic ladder system which is a moiré superlattice system consisting of two-coupled uniform chains. An irrational lattice constant difference results in quasiperiodic structure. Numerical simulations show that such a syst…
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…
Uncorrelated disorder potential in one-dimensional lattice definitely induces Anderson localization, while quasiperiodic potential can lead to both localized and extended phases, depending on the potential strength. We investigate the Anderson localization in one-dimensional lattice with nonHermitian complex disorder and quasiperiodic potential. We present a non-Hermitian SSH chain to demonstrate that a nonzero imaginary disorder on-site potential can induce the standard Anderson localization. We also show that the non-Hermitian Aubry-Andre (AA) model exhibits a transition in parameter space, …
We study a one-dimensional system that includes both a commensurate off-diagonal modulation of the hopping amplitude and an incommensurate, slowly varying diagonal on-site modulation. By using asymptotic heuristic arguments, we identify four closed form expressions for the mobility edges. We further study numerically the inverse participation ratio, the density of states and the Lyapunov exponent. The numerical results are in exact agreement with our theoretical predictions. Besides a metal-insulator transition driven by the strength of the slowly varying potential, another four insulator-meta…
In their Letter[Phys. Rev. Lett. 126, 106803 (2021)], the authors found an interesting reentrant localization phenomenon in a one-dimensional dimerized lattice with quasiperiodic disorder, i.e., the system undergoes a second localization transition at a higher disorder strength. They claimed that this reentrant feature would appear in the case of staggered disorder, but not for the uniform ones. In this Comment, we show that such reentrant feature can also appear for the uniform disorder when larger system parameters are taken into account.
Arithmetic Tuning of Dynamical Critical Exponents in Quasiperiodic Localization Transitions
Zhejiang Sci-Tech University（浙江理工大学）；Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences（中国科学院精密测量科学与技术创新研究院）；Nanjing University of Aeronautics and Astronautics（南京航空航天大学）
There has been a revival of interest in localization phenomena in quasiperiodic systems with a view to examining how they differ fundamentally from such phenomena in random systems. Mo- tivated by this, we study transport in the quasiperiodic, one-dimentional (1d) Aubry-Andre model and its generalizations to 2d and 3d. We study the conductance of open systems, connected to leads, as well as the Thouless conductance, which measures the response of a closed system to boundary perturbations. We find that these conductances show signatures of a metal-insulator transition from an insulator, with lo…
We consider a quantum particle in a one-dimensional disordered lattice with Anderson localization, in the presence of multi-frequency perturbations of the onsite energies. Using the Floquet representation, we transform the eigenvalue problem into a Wannier-Stark basis. Each frequency component contributes either to a single channel or a multi-channel connectivity along the lattice, depending on the control parameters. The single channel regime is essentially equivalent to the undriven case. The multi-channel driving substantially increases the localization length for slow driving, showing two …
Pair localization in one-dimensional quasicrystals with nearest-neighbor hopping is independent of whether short-range interactions are repulsive or attractive. We numerically demonstrate that this symmetry is broken when the hopping follows a power law $1/r^α$. In particular, for repulsively bound states, we find that the critical quasiperiodicity that signals the transition to localization is always bounded by the standard Aubry-André critical point, whereas attractively bound dimers get localized at larger quasiperiodic modulations when the range of the hopping increases. Extensive numerica…
Systems with quasiperiodic disorder are known to exhibit localization transition in low dimension. After a critical strength of disorder all the states of the system become localized, thereby ceasing the particle motion in the system. However, in our analysis we show that in a one dimensional dimerized lattice with staggered quasiperiodic disorder, after the localization transition some of the localized eigenstates become extended for a range of intermediate disorder strengths. Eventually, the system undergoes a second localization transition at a higher disorder strength leading to all states…
The nearest-neighbor Aubry-André quasiperiodic localization model is generalized to include power-law translation-invariant hoppings $T_l\propto t/l^a$ or power-law Fourier coefficients $W_m \propto w/m^b$ in the quasi-periodic potential. The Aubry-André duality between $T_l$ and $W_m$ is manifest when the Hamiltonian is written in the real-space basis and in the Fourier basis on a finite ring. The perturbative analysis in the amplitude $t$ of the hoppings yields that the eigenstates remain power-law localized in real space for $a>1$ and are critical for $a_c=1$ where they follow the Strong Mu…
Lateral Shift as a Control Knob for Localization Transitions in a Quasiperiodic Ladder
College of Physics and Optoelectronic Engineering, Ocean University of China（中国海洋大学物理与光电工程学院）；Qingdao Key Laboratory of Advanced Optoelectronics（青岛先进光电技术重点实验室）；Engineering Research Center of Advanced Marine Physical Instruments and Equipment of MOE（教育部海洋物理仪器与装备工程研究中心）；Department of Physics, National University of Singapore（新加坡国立大学物理系）；Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）；MajuLab, CNRS-UCA-SU-NUS-NTU International Joint Research Unit（马久实验室（CNRS-尼斯大学-索邦大学-新加坡国立大学-南洋理工大学国际联合研究单位））；Center for Phononics and Thermal Energy Science, China-EU Joint Lab on Nanophononics, Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology, School of Physics Science and Engineering, Tongji University（同济大学物理科学与技术学院特种人工微结构材料与技术上海市重点实验室中欧纳米声学联合实验室声子学与热能科学中心）
A re-entrant localization transition has been predicted recently in a one-dimensional quasiperiodic lattice with dimerized hopping between the nearest-neighbour sites (Phys. Rev. Lett. {\bf 126} 106803 (2021)) \cite{PhysRevLett.126.106803}. It has been shown that the interplay between the hopping dimerization and a staggered quasi-periodic disorder manifests two localization transitions through two intermediate phases resulting in four critical points as a function of the quasiperiodic potential. In this paper, we study the phenomenon of the re-entrant localization transition by examining the …
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…
A one-dimensional lattice model with mosaic quasiperiodic potential is found to exhibit interesting localization properties, e.g., clear mobility edges [Y. Wang et al., Phys. Rev. Lett. \textbf{125}, 196604 (2020)]. We generalize this mosaic quasiperiodic model to a two-dimensional version, and numerically investigate its localization properties: the phase diagram from the fractal dimension of the wavefunction, the statistical and scaling properties of the conductance. Compared with disordered systems, our model shares many common features but also exhibits some different characteristics in th…
We study electronic eigenstates on quasiperiodic lattices using a tight-binding Hamiltonian in the vertex model. In particular, the two-dimensional Penrose tiling and the three-dimensional icosahedral Ammann-Kramer tiling are considered. Our main interest concerns the decay form and the self-similarity of the electronic wave functions, which we compute numerically for periodic approximants of the perfect quasiperiodic structure. In order to investigate the suggested power-law localization of states, we calculate their participation numbers and structural entropy. We also perform a multifractal…
The nature of the many-body localization (MBL) transition and even the existence of the MBL phase in random many-body quantum systems have been actively debated in recent years. In spatial dimension $d>1$, there is some consensus that the MBL phase is unstable to rare thermal inclusions that can lead to an avalanche that thermalizes the whole system. In this note, we explore the possibility of MBL in quasiperiodic systems in dimension $d>1$. We argue that (i) the MBL phase is stable at strong enough quasiperiodic modulations for $d = 2$, and (ii) the possibility of an avalanche strongly constr…
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…
Orbital cancellation and reentrant localization in a quasiperiodic trimer ladder
Nantong University（南通大学）；Tsinghua University（清华大学）；Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院）；Beijing National Research Center for Information Science and Technology（北京信息科学与技术国家研究中心）
We study the many-body localization of spin chain systems with quasiperiodic fields. We identify the lower bound for the critical disorder necessary to drive the transition between the thermal and many-body localized phase to be $W_{cl}\sim 1.85$, based on finite-size scaling of entanglement entropy and fluctuations of the bipartite magnetization. We also examine the time evolution of the entanglement entropy of an initial product state where we find power-law and logarithmic growth for the thermal and many-body localized phases, respectively. For larger disorder strength, both imbalance and s…
We take non-Hermitian Aubry-André-Harper models and quasiperiodic Kitaev chains as examples to demonstrate the equivalence and superposition of real and imaginary quasiperiodic potentials (QPs) on inducing localization of single-particle states. We prove this equivalence by analytically computing Lyapunov exponents (or inverse of localization lengths) for systems with purely real and purely imaginary QPs. Moreover, when superposed and with the same frequency, real and imaginary QPs are coherent on inducing the localization, under a way which is determined by the relative phase between them. Th…
Quasiperiodic modulation can prevent isolated quantum systems from equilibrating by localizing their degrees of freedom. In this article, we show that such systems can exhibit dynamically stable long-range orders forbidden in equilibrium. Specifically, we show that the interplay of symmetry breaking and localization in the quasiperiodic quantum Ising chain produces a \emph{quasiperiodic Ising glass} stable at all energy densities. The glass order parameter vanishes with an essential singularity at the melting transition with no signatures in the equilibrium properties. The zero temperature pha…
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 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…
The mobility edges (MEs) in energy which separate extended and localized states are a central concept in understanding the localization physics. In one-dimensional (1D) quasiperiodic systems, while MEs may exist for certain cases, the analytic results which allow for an exact understanding are rare. Here we uncover a class of exactly solvable 1D models with MEs in the spectra, where quasiperiodic on-site potentials are inlaid in the lattice with equally spaced sites. The analytical solutions provide the exact results not only for the MEs, but also for the localization and extended features of …
We uncover the relationship of topology and disorder in a one-dimensional Su-Schrieffer-Heeger chain subjected to a slowly varying quasi-periodic modulation. By numerically calculating the disorder-averaged winding number and analytically studying the localization length of the zero modes, we obtain the topological phase diagram, which implies that the topological Anderson insulator (TAI) can be induced by a slowly varying quasi-periodic modulation. Moreover, unlike the localization properties in the TAI phase caused by random disorder, mobility edges can enter into the TAI region identified b…
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 …
In the present study, the interplay among interaction, topology, quasiperiodicity, and non-Hermiticity is studied. The hard-core bosons model on a one-dimensional lattice with asymmetry hoppings and quasiperiodic onsite potentials is selected. This model, which preserves time-reversal symmetry (TRS), will exhibit three types of phase transition: real-complex transition of eigenenergies, topological phase transition and many-body localization (MBL) phase transition. For thereal-complex transition, it is found that the imaginary parts of the eigenenergies are always suppressed by the MBL. Moreov…
We investigate the topology and localization of one-dimensional Hermitian and non-Hermitian Su-Schrieffer-Heeger chains with quasiperiodic hopping modulations. In the Hermitian case, phase diagrams are obtained by numerically and analytically calculating various topological and localization characters. We show the presence of topological extended, intermediate, and localized phases due to the coexistence of independent topological and localization phase transitions driven by the quasiperiodic disorder. Unlike the gapless and localized TAI phase in one-dimensional random disordered systems, we …
Anomalous mobility edges and extended-localized transition in a quasiperiodic emitter-cavity array
School of Physics and Optoelectronic Engineering & Institute of Theoretical Physics, Ludong University（鲁东大学物理与光电工程学院暨理论物理研究所）；Center for Quantum Sciences, Northeast Normal University（东北师范大学量子科学中心）
We investigate the transverse field Ising model subject to a two-step periodic driving protocol and quasiperiodic modulation of the Ising couplings. Analytical results on the phase boundaries associated with Majorana edge modes and numerical results on the localization of single-particle excitations are presented. The implication of a region with fully localized domain-wall-like excitations in the parameter space is eigenstate order and exact spectral pairing of Floquet eigenstates, based on which we conclude the existence of time crystals. We also examine various correlation functions of the …
In this paper, we explore the localization transition and the scaling properties of both quasi-one-dimensional and two-dimensional quasiperiodic systems, which are constituted from coupling several Aubry-André (AA) chains along the transverse direction, in the presence of next-nearest-neighbor (NNN) hopping. The localization length, two-terminal conductance, and participation ratio are calculated within the tight-binding Hamiltonian. Our results reveal that a metal-insulator transition could be driven in these systems not only by changing the NNN hopping integral but also by the dimensionality…
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…
We introduce a one-dimensional lattice model whose hopping amplitudes are modulated for equally spaced sites. Such mosaic lattice exhibits many interesting topological and localization phenomena that do not exist in the regular off-diagonal lattices. When the mosaic modulation is commensurate with the underlying lattice, topologically nontrivial phases with zero- and nonzero-energy edge modes are observed as we tune the modulation, where the nontrivial regimes are characterized by quantized Berry phases. If the mosaic lattice becomes incommensurate, Anderson localization will be induced purely…
We study the localization transitions for coupled one-dimensional lattices with quasiperiodic potential. Besides the localized and extended phases there is an intermediate mixed phase which can be easily explained decoupling the system so as to deal with effective uncoupled Aubry-André chains with different transition points. We clarify, therefore, the origin of such an intermediate phase finding the conditions for getting a uniquely defined mobility edge for such coupled systems. Finally we consider many coupled chains with an energy shift which compose an extension of the Aubry-André model i…
