arXiv subjects

Lih-King Lim

Publications and source records attributed to Lih-King Lim.

At least 19 recordsLinked to original sources

arXiv2024

Boson-fermion universality of mesoscopic entanglement fluctuations in free systems

Entanglement fluctuations associated with Schrödinger evolution of wavefunctions offer a unique perspective on various fundamental issues ranging from quantum thermalization to state preparation in quantum devices. Very recently, a subset of present authors have shown that in a class of free-fermion lattice models and interacting spin chains, entanglement dynamics enters into a new regime at long time, with entanglement probes displaying persistent temporal fluctuations, whose statistics falls into the seemingly disparate paradigm of mesoscopic fluctuations in condensed matter physics. This motivate us to revisit here entanglement dynamics of a canonical bosonic model in many-body physics, i.e., a coupled harmonic oscillator chain. We find that when the system is driven out of equilibrium, the long-time entanglement dynamics exhibits strictly the same statistical behaviors as that of free-fermion models. Specifically, irrespective of entanglement probes and microscopic parameters, the statistical distribution of entanglement fluctuations is flanked by asymmetric tails: sub-Gaussian for upward fluctuations and sub-Gamma for downward; moreover, the variance exhibits a crossover from the scaling $\sim 1/L$ to $\sim L_A^3/L^2$, as the subsystem size $L_A$ increases ($L$ the total system size). This insensitivity to the particle statistics, dubbed boson-fermion universality, is contrary to the common wisdom that statistical phenomena of many-body nature depend strongly on particle statistics. Together with our previous work, the present work indicates rich fluctuation phenomena in entanglement dynamics awaiting in-depth explorations.

quant-ph↗

arXiv2024

Dynamical Geometry of the Haldane Model under a Quantum Quench

We explore the time evolution of a topological system when the system undergoes a sudden quantum quench within the same nontrivial phase. Using Haldane's honeycomb model as an example, we show that equilibrium states in a topological phase can be distinguished by geometrical features, such as the characteristic momentum at which the half-occupied edge modes cross, the associated edge-mode velocity, and the winding vector about which the normalized pseudospin magnetic field winds along a great circle on the Bloch sphere. We generalize these geometrical quantities for non-equilibrium states and use them to visualize the quench dynamics of the topological system. In general, we find the pre-quench equilibrium state relaxes to the post-quench equilibrium state in an oscillatory fashion, whose amplitude decay as $t^{1/2}$. In the process, however, the characteristic winding vector of the non-equilibrium system can evolve to regimes that are not reachable with equilibrium states.

cond-mat.mes-hall↗

arXiv2024

Fractal Surface States in Three-Dimensional Topological Quasicrystals

We study topological states of matter in quasicrystals, which do not rely on crystalline orders. In the absence of a bandstructure description and spin-orbit coupling, we show that a three-dimensional quasicrystal can nevertheless form a topological insulator. It relies on a combination of noncrystallographic rotational symmetry of quasicrystals and electronic orbital space symmetry, which is the quasicrystalline counterpart of topological crystalline insulator. The resulting topological state obeys a non-trivial twisted bulk-boundary correspondence and lacks a good metallic surface. The topological surface states, localized on the top and bottom planes respecting the quasicrystalline symmetry, exhibit a new kind of multifractality with probability density concentrates mostly on high symmetry patches. They form a near-degenerate manifold of 'immobile' states whose number scales proportionally with the macroscopic sample size. This can open the door to a novel platform for topological surface physics distinct from the crystalline counterpart.

cond-mat.mes-hall↗

arXiv2024

Mesoscopic fluctuations in entanglement dynamics

Understanding fluctuation phenomena plays a dominant role in the development of many-body physics. The time evolution of entanglement is essential to a broad range of subjects in many-body physics, ranging from exotic quantum matter to quantum thermalization. Stemming from various dynamical processes of information, fluctuations in entanglement evolution differ conceptually from out-of-equilibrium fluctuations of traditional physical quantities. Their studies remain elusive. Here we uncover an emergent random structure in the evolution of the many-body wavefunction in two classes of integrable -- either interacting or noninteracting -- lattice models. It gives rise to out-of-equilibrium entanglement fluctuations which fall into the paradigm of mesoscopic fluctuations of wave interference origin. Specifically, the entanglement entropy variance obeys a universal scaling law, in each class, and the full distribution displays a sub-Gaussian upper and a sub-Gamma lower tail. These statistics are independent of both the system's microscopic details and the choice of entanglement probes, and broaden the class of mesoscopic universalities. They have practical implications for controlling entanglement in mesoscopic devices.

cond-mat.mes-hall↗

arXiv2020

Floquet eigenspectra of a nonlinear two-mode system under periodic driving: the emergence of "ring" structures

We study Floquet eigenspectra of a nonlinear two-mode system under a periodic driving of the off-diagonal coupling. By solving the Gross-Pitaevskii equation numerically, we obtain triangular and loop structures near the crossings of different Floquet branches. At lower driving frequencies, we find "ring" and "double-ring" structures which are distinct from the well-known loop structure. The mechanism of the emergence of these structures is discussed and the parameter windows of their existence are obtained analytically. In addition, we study the evolution of the system under the driving with an adiabatic sweep and find there are some dynamically unstable states in the Floquet eigenspectra which break the quantum adiabaticity.

cond-mat.quant-gas↗

arXiv2020

Dirac points emerging from flat bands in Lieb-kagomé lattices

The energy spectra for the tight-binding models on the Lieb and kagomé lattices both exhibit a flat band. We present a model which continuously interpolates between these two limits. The flat band located in the middle of the three-band spectrum for the Lieb lattice is distorted, generating two pairs of Dirac points. While the upper pair evolves into graphene-like Dirac cones in the kagomé limit, the low energy pair evolves until it merges producing the band-bottom flat band. The topological characterization of the Dirac points is achieved by projecting the Hamiltonian on the two relevant bands in order to obtain an effective Dirac Hamiltonian. The low energy pair of Dirac points is particularly interesting in this respect: when they emerge, they have opposite winding numbers, but as they merge, they have the same winding number. This apparent paradox is due to a continuous rotation of their states in pseudo-spin space, characterized by a winding vector. This simple, but quite rich model, suggests a way to a systematic characterization of two-band contact points in multiband systems.

cond-mat.mes-hall↗

arXiv2019

Ultracold Atoms in Disordered Potentials: Elastic Scattering Time in the Strong Scattering Regime

We study the elastic scattering time $τ_\mathrm{s}$ of ultracold atoms propagating in optical disordered potentials in the strong scattering regime, going beyond the recent work of J. Richard \emph{et al.} \textit{Phys. Rev. Lett.} \textbf{122} 100403 (2019). There, we identified the crossover between the weak and the strong scattering regimes by comparing direct measurements and numerical simulations to the first order Born approximation. Here we focus specifically on the strong scattering regime, where the first order Born approximation is not valid anymore and the scattering time is strongly influenced by the nature of the disorder. To interpret our observations, we connect the scattering time $τ_\mathrm{s}$ to the profiles of the spectral functions that we estimate using higher order Born perturbation theory or self-consistent Born approximation. The comparison reveals that self-consistent methods are well suited to describe $τ_\mathrm{s}$ for Gaussian-distributed disorder, but fails for laser speckle disorder. For the latter, we show that the peculiar profiles of the spectral functions, as measured independently in V. Volchkov \emph{et al.} \textit{Phys. Rev. Lett.} \textbf{120}, 060404 (2018), must be taken into account. Altogether our study characterizes the validity range of usual theoretical methods to predict the elastic scattering time of matter waves, which is essential for future close comparison between theory and experiments, for instance regarding the ongoing studies on Anderson localization.

cond-mat.quant-gas↗

arXiv2019

Topological superconducting phase in high-Tc superconductor MgB2 with Dirac-nodal-line fermions

Topological superconductors are an intriguing and elusive quantum phase, characterized by topologically protected gapless surface/edge states residing in a bulk superconducting gap, which hosts Majorana fermions. Unfortunately, all currently known topological superconductors have a very low transition temperature, limiting experimental measurements of Majorana fermions. Here we discover the existence of a topological Dirac-nodal-line state in a well-known conventional high-temperature superconductor, MgB2. First-principles calculations show that the Dirac-nodal-line structure exhibits a unique one-dimensional dispersive Dirac-nodal line, protected by both spatial-inversion and time-reversal symmetry, which connects the electron and hole Dirac states. Most importantly, we show that the topological superconducting phase can be realized with a conventional s-wave superconducting gap, evidenced by the topological edge mode of the MgB2 thin films showing chiral edge states. Our discovery may enable the experimental measurement of Majorana fermions at high temperature.

cond-mat.supr-con↗

arXiv2019

Elastic Scattering Time of Matter-Waves in Disordered Potentials

We report on an extensive study of the elastic scattering time $\tauS$ of matter-waves in optical disordered potentials. Using direct experimental measurements, numerical simulations and comparison with first-order Born approximation based on the knowledge of the disorder properties, we explore the behavior of $\tauS$ over more than three orders of magnitude, spanning from the weak to the strong scattering regime. We study in detail the location of the crossover and, as a main result, we reveal the strong influence of the disorder statistics, especially on the relevance of the widely used Ioffe-Regel-like criterion $k\lS\sim 1$. While it is found to be relevant for Gaussian-distributed disordered potentials, we observe significant deviations for laser speckle disorders that are commonly used with ultracold atoms. Our results are crucial for connecting experimental investigation of complex transport phenomena, such as Anderson localization, to microscopic theories.

cond-mat.quant-gas↗

arXiv2018

Winding vector: how to annihilate two Dirac points with the same charge

The merging or emergence of a pair of Dirac points may be classified according to whether the winding numbers which characterize them are opposite ($+-$ scenario) or identical ($++$ scenario). From the touching point between two parabolic bands (one of them can be flat), two Dirac points with the {\it same} winding number emerge under appropriate distortion (interaction, etc), following the $++$ scenario. Under further distortion, these Dirac points merge following the $+-$ scenario, that is corresponding to {\it opposite} winding numbers. This apparent contradiction is solved by the fact that the winding number is actually defined around a unit vector on the Bloch sphere and that this vector rotates during the motion of the Dirac points. This is shown here within the simplest two-band lattice model (Mielke) exhibiting a flat band. We argue on several examples that the evolution between the two scenarios is general.

cond-mat.mes-hall↗

arXiv2018

Quantum Oscillations in Nodal Line Systems

We study signatures of magnetic quantum oscillations in three-dimensional nodal line semimetals at zero temperature. The extended nature of the degenerate bands can result in a Fermi surface geometry with topological genus one, as well as a Fermi surface of electron and hole pockets encapsulating the nodal line. Moreover, the underlying two-band model to describe a nodal line is not unique, in that there are two classes of Hamiltonian with distinct band topology giving rise to the same Fermi surface geometry. After identifying the extremal cyclotron orbits in various magnetic field directions, we study their concomitant Landau levels and resulting quantum oscillation signatures. By Landau-fan-diagram analyses we extract the non-trivial $π$ Berry phase signature for extremal orbits linking the nodal line.

cond-mat.mes-hall↗

arXiv2017

Quantum Hall effect in ac driven graphene: from half-integer to integer case

We theoretically study the quantum Hall effect (QHE) in graphene with an ac electric field. Based on the tight-binding model, the structure of the half-integer Hall plateaus at $σ_{xy} = \pm(n + 1/2)4e^2/h$ ($n$ is an integer) gets qualitatively changed with the addition of new integer Hall plateaus at $σ_{xy} = \pm n(4e^2/h)$ starting from the edges of the band center regime towards the band center with an increasing ac field. Beyond a critical field strength, a Hall plateau with $σ_{xy} = 0$ can be realized at the band center, hence restoring fully a conventional integer QHE with particle-hole symmetry. Within a low-energy Hamiltonian for Dirac cones merging, we show a very good agreement with the tight-binding calculations for the Hall plateau transitions. We also obtain the band structure for driven graphene ribbons to provide a further understanding on the appearance of the new Hall plateaus, showing a trivial insulator behavior for the $σ_{xy} = 0$ state. In the presence of disorder, we numerically study the disorder-induced destruction of the quantum Hall states in a finite driven sample and find that qualitative features known in the undriven disordered case are maintained.

cond-mat.mes-hall↗

arXiv2017

Quantum Charge Pumps with Topological Phases in Creutz Ladder

Quantum charge pumping phenomenon connects band topology through the dynamics of a one-dimensional quantum system. In terms of a microscopic model, the Su-Schrieffer-Heeger/Rice-Mele quantum pump continues to serve as a fruitful starting point for many considerations of topological physics. Here we present a generalized Creutz scheme as a distinct two-band quantum pump model. By noting that it undergoes two kinds of topological band transitions accompanying with a Zak-phase-difference of $π$ and $2π$, respectively, various charge pumping schemes are studied by applying an elaborate Peierl's phase substitution. Translating into real space, the transportation of quantized charges is a result of cooperative quantum interference effect. In particular, an all-flux quantum pump emerges which operates with time-varying fluxes only and transports two charge units. This puts cold atoms with artificial gauge fields as an unique system where this kind of phenomena can be realized.

cond-mat.quant-gas↗

arXiv2016

Pseudospin Vortex Ring with a Nodal Line in Three Dimensions

We present a model of a topological semimetal in three dimensions (3D) whose energy spectrum exhibits a nodal line acting as a vortex ring; this in turn is linked by a pseudospin structure akin to that of a smoke ring. Contrary to a Weyl point node spectrum, the vortex ring gives rise to skyrmionic pseudospin patterns in cuts on both sides of the nodal ring plane; this pattern covers the full Brillouin zone, thus leading to a new, `maximal', anomalous Hall effect in a 3D semimetal. Tuning a model parameter shrinks the vortex ring until it vanishes, giving way to a pair of Weyl nodes of opposite chirality. This establishes a connection between two distinct momentum-space topologies - that of a vortex ring (a circle of singularity) and a monopole-anti-monopole pair (two point singularities). We present the model both as a low-energy continuum and a two-band tight-binding lattice model. Its simplicity permits an analytical computation of its Landau level spectrum.

cond-mat.mes-hall↗

arXiv2015

Geometry of Bloch states probed by Stückelberg interferometry

Inspired by recent experiments with cold atoms in optical lattices, we consider a Stückelberg interferometer for a particle performing Bloch oscillations in a tight-binding model on the honeycomb lattice. The interferometer is made of two avoided crossings at the saddle points of the band structure (i.e. at M points of the reciprocal space). This problem is reminiscent of the double Dirac cone Stückelberg interferometer that was recently studied in the continuum limit [Phys. Rev. Lett. 112, 155302 (2014)]. Although the two problems share similarities -- such as the appearance of a geometric phase shift -- lattice effects, not captured by the continuum limit, make them truly different. The particle dynamics in the presence of a force is described by the Bloch Hamiltonian $H(\boldsymbol{k})$ defined from the tight-binding Hamiltonian and the position operator. This leads to many interesting effects for the lattice Stückelberg interferometer: a twisting of the two Landau-Zener tunnelings, saturation of the inter-band transition probability in the sudden (infinite force) limit and extended periodicity or even non-periodicity beyond the first Brillouin zone. In particular, Stückelberg interferometry gives access to the overlap matrix of cell-periodic Bloch states thereby allowing to fully characterize the geometry of Bloch states, as e.g. to obtain the quantum metric tensor.

cond-mat.mes-hall↗

arXiv2015

Propagation of collective pair excitations in disordered Bose superfluids

We study the effect of disorder on the propagation of collective excitations in a disordered Bose superfluid. We incorporate local density depletion induced by strong disorder at the meanfield level, and formulate the transport of the excitations in terms of a screened scattering problem. We show that the competition of disorder, screening, and density depletion induces a strongly non-monotonic energy dependence of the disorder parameter. In three dimensions, it results in a rich localization diagram with four different classes of mobility spectra, characterized by either no or up to three mobility edges. Implications on experiments with disordered ultracold atoms are discussed.

cond-mat.quant-gas↗

arXiv2014

Geometric phase in Stückelberg interferometry

We study the time evolution of a two-dimensional quantum particle exhibiting an energy spectrum, made of two bands, with two Dirac cones, as e.g. in the band structure of a honeycomb lattice. A force is applied such that the particle experiences two Landau-Zener transitions in succession. The adiabatic evolution between the two transitions leads to Stückelberg interferences, due to two possible trajectories in energy space. In addition to well-known dynamical and Stokes phases, the interference pattern reveals a geometric phase which depends on the chirality (winding number) and the mass sign associated to each Dirac cone, as well as on the type of trajectory (parallel or diagonal with respect to the two cones) in parameter space. This geometric phase reveals the coupling between the bands encoded in the structure of the wavefunctions.

cond-mat.mes-hall↗

arXiv2014

Mass and chirality inversion of a Dirac cone pair in Stückelberg interferometry

We show that a Stückelberg interferometer made of two massive Dirac cones can reveal information on band eigenstates such as the chirality and mass sign of the cones. For a given spectrum with two gapped cones, we propose several low-energy Hamiltonians differing by their eigenstates properties. The corresponding inter-band transition probability is affected by such differences in its interference fringes being shifted by a new phase of geometrical origin. This phase can be a useful bulk probe for topological band structures realized with artificial crystals.

cond-mat.quant-gas↗