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 eigenstate thermalization hypothesis (ETH) obeying (thermal), localized and ETH violating (many body localized), and extended and ETH violating (nonergodic extended). Here we investigate the nonergodic 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 subdiffusive transport. This is contrasted with diffusive transport in the thermal phase and blocked transport in the MBL phase.

Non-interacting fermions in one dimension can undergo a localization-delocalization transition in the presence of a quasi-periodic potential as a function of that potential. In the presence of interactions, this transition transforms into a Many-Body Localization (MBL) transition. Recent studies have suggested that this type of transition can also occur in models with quasi-periodic potentials that possess single particle mobility edges. Two such models were studied in PRL 115,230401(2015) but only one was found to exhibit an MBL transition in the presence of interactions while the other one did not. In this work we investigate the occurrence of MBL in the presence of weak interactions in five different models with single particle mobility edges in one dimension with a view to obtaining a criterion for the same. We find that not all such models undergo a thermal-MBL phase transition in presence of weak interactions. We propose a criterion to determine whether MBL is likely to occur in presence of interaction based only on the properties of the non-interacting models. The relevant quantity ǫ is a measure of how localized the localized states are relative to how delocalized the delocalized states are in the non-interacting model. We also study various other features of the non-interacting models such as the divergence of the localization length at the mobility edge and the presence or absence of 'ergodicity' and localization in their many-body eigenstates. However, we find that these features cannot be used to predict the occurrence of MBL upon the introduction of weak interactions.

In presence of strong enough disorder one dimensional systems of interacting spinless fermions at non-zero filling factor are known to be in a many body localized phase. When represented in 'Fock space', the Hamiltonian of such a system looks like that of a single 'particle' hopping on a Fock lattice in the presence of a random disordered potential. The coordination number of the Fock lattice increases linearly with the system size L in one dimension. Thus in the thermodynamic limit L → ∞, the disordered interacting problem in one dimension maps on to an Anderson model with infinite coordination number. Despite this, this system displays localization which appears counterintuitive. A close observation of the on-site disorder potentials on the Fock lattice reveals a large degree of correlation among them as they are derived from an exponentially smaller number of on-site disorder potentials in real space. This indicates that the correlations between the on-site disorder potentials on a Fock lattice has a strong effect on the localization properties of the corresponding many-body system. This intuition is also consistent with studies of quantum random energy model where the typical mid-spectrum states are ergodic and the on-site potentials in Fock space are completely uncorrelated. In this work we perform a systematic quantitative exploration of the nature of correlations of the Fock space potential required for localization. We study different functional variations of the disorder correlation in Fock lattice by analyzing the eigenspectrum obtained through exact diagonalization. Without changing the typical strength of the on-site disorder potential in Fock lattice we show that changing the correlation strength can induce thermalization or localization in systems. From among the various forms of correlations we study, we find that only the linear variation of correlations with Hamming distance in Fock space is able to drive a thermal-MBL phase transition where the transition is driven by the correlation strength. Systems with the other forms of correlations we study are found to be ergodic.

Combining multiple emergent correlated properties such as superconductivity and magnetism within the topological matrix can have exceptional consequences in garnering new and exotic physics. Here, we study the topological surface states from a noncentrosymmetric α-BiPd superconductor by employing angle-resolved photoemission spectroscopy (ARPES) and first principle calculations. We observe that the Dirac surface states of this system have several interesting and unusual properties, compared to other topological surface states. The surface state is strongly anisotropic and the inplane Fermi velocity varies rigorously on rotating the crystal about the y-axis. Moreover, it acquires an unusual band gap as a function of ky, possibly due to hybridization with bulk bands, detected upon varying the excitation energy. Coexistence of all the functional properties, in addition to the unusual surface state characteristics make this an interesting material. α-BiPd is recently synthesized with all the aforementioned properties obtained intrinsically, and thus provides the long-sought material for new experiments and applications. So far, there have been few works on this material, mainly studying the magnetic and transport phenomena [9][10][11]. Again, for the spectroscopic investigations, there is only one ARPES [12] and one scanning tunnelling spectroscopy (STS) study [13]. The ARPES work reported the electronic structure of this compound with the detection of topological Dirac cone at -0.7 eV below the Fermi level (E F ), without detailing the properties of Dirac cone, while the STS work reported the states above the Fermi level.In this paper we report several interesting and unusual properties of the topological Dirac states present on the surface of this noncentrosymmetric α-BiPd superconductor by employing ARPES and first principle calculations. We detect the surface states that are having a Dirac node at a binding energy of 0.7 eV below Fermi level (E F ) at the Γ point dispersing along the Γ − X high symmetry line. Upon varying the photon energy, we notice surface states that are gapped as a function of k y at the node due to a possible hybridization with bulk bands, a unique feature of the surface state that is not disclosed in this compound so far. Upon varying the photon polarization we identify the orbital character of the detected bands.We further show that the Dirac fermions in α-BiPd are highly anisotropic on rotating the crystal about the y-axis such that, in going from Γ−X to Γ−Z the massless linear dispersive Dirac states become flat dispersive massive fermions. Therefore, the Dirac states found in this compound are of one dimensional (1D) character which could provide a natural route for the quantum wires. In general, the Dirac states found on the surface of 2D compounds such as graphene [14] [24]. Unusual band structure of this material, surface state is gapped and asymmetric, make this a unique compound which will attract tremendous future research interests.Single crystals of stoichiometric α-BiPd were g...

We implement a recursive Green's function method to extract the Fock space (FS) propagator and associated self-energy across the many-body localization (MBL) transition, for one-dimensional interacting fermions in a random on-site potential. We show that the typical value of the imaginary part of the local FS self-energy, t , related to the decay rate of an initially localized state, acts as a probabilistic order parameter for the thermal to MBL phase transition and can be used to characterize critical properties of the transition as well as the multifractal nature of MBL states as a function of disorder strength W . In particular, we show that a fractal dimension D s extracted from t jumps discontinuously across the transition, from D s < 1 in the MBL phase to D s = 1 in the thermal phase. Moreover, t follows an asymmetrical finite-size scaling form across the thermal-MBL transition, where a nonergodic volume in the thermal phase diverges with a Kosterlitz-Thouless-like essential singularity at the critical point W c and controls the continuous vanishing of t as W c is approached. In contrast, a correlation length (ξ ) extracted from t exhibits a power-law divergence on approaching W c from the MBL phase.