arXiv subjects

Auditya Sharma

Publications and source records attributed to Auditya Sharma.

At least 37 records · Page 2Linked to original sources

arXiv2022

Flat-band-based multifractality in the all-band-flat diamond chain

We study the effect of quasiperiodic Aubry-André disorder on the energy spectrum and eigenstates of a one-dimensional all-bands-flat (ABF) diamond chain. The ABF diamond chain possesses three dispersionless flat bands with all the eigenstates compactly localized on two unit cells in the zero disorder limit. The fate of the compact localized states in the presence of the disorder depends on the symmetry of the applied potential. We consider two cases here: a symmetric one, where the same disorder is applied to the top and bottom sites of a unit cell and an antisymmetric one, where the disorder applied to the top and bottom sites are of equal magnitude but with opposite signs. Remarkably, the symmetrically perturbed lattice preserves compact localization, although the degeneracy is lifted. When the lattice is perturbed antisymmetrically, not only is the degeneracy is lifted but compact localization is also destroyed. Fascinatingly, all eigenstates exhibit a multifractal nature below a critical strength of the applied potential. A central band of eigenstates continue to display an extended yet non-ergodic behaviour for arbitrarily large strengths of the potential. All other eigenstates exhibit the familiar Anderson localization above the critical potential strength. We show how the antisymmetric disordered model can be mapped to a $\fracπ{4}$ rotated square lattice with nearest and selective next-nearest neighbour hopping and a staggered magnetic field - such models have been shown to exhibit multifractality. Surprisingly, the antisymmetric disorder (with an even number of unit cells) preserves chiral symmetry - we show this by explicitly writing down the chiral operator.

cond-mat.dis-nn↗

arXiv2022

Noise-induced dynamical localization and delocalization

We investigate the effect of a two-level jump process or random telegraph noise on a square wave driven tight-binding lattice. In the absence of the noise, the system is known to exhibit dynamical localization for specific ratios of the amplitude and the frequency of the drive. We obtain an exact expression for the probability propagator to study the stability of dynamical localization against telegraph noise. Our analysis shows that in the presence of noise, a proper tuning of the noise parameters destroys dynamical localization of the clean limit in one case, while it induces dynamical localization in an otherwise delocalized phase of the clean model. Numerical results help verify the analytical findings. A study of the dynamics of entanglement entropy from an initially half-filled state offers complementary perspective.

cond-mat.dis-nn↗

arXiv2021

Dynamics of spectral correlations in the entanglement Hamiltonian of the Aubry-André-Harper model

We numerically study the evolution of spectral correlations in the entanglement Hamiltonian (EH) of non-interacting fermions in the Aubry-André-Harper (AAH) model. We analyze the time evolution of the EH spectrum in a nonequilibrium setting by studying several quantities: spectral distribution, level statistics, entanglement entropy, and spectral form factor (SFF) in the context of the delocalization-localization transition in the AAH model. It is observed that the SFF of the entanglement spectrum in the delocalized phase and at the phase-transition point evolves in three-time intervals. We make a systematic study of the emergence of these three timescales for various initial states and find that the number of time intervals remains three unless the Hamiltonian is tuned in the localized phase or when the initial state is maximally entangled, then there is a featureless time evolution. We find a broad direct correlation between the entanglement entropy and the length of the ramp of the SFF. We also find that in the delocalized phase the spectral correlations are stronger in the center of the spectrum and grow progressively weaker as more and more of the spectrum is considered.

cond-mat.dis-nn↗

arXiv2021

Phase transitions of the Dicke model: a unified perspective

The Dicke model exhibits a variety of phase transitions. The quantum phase transition from the normal phase to the super-radiant phase is marked by a dramatic change in the scaling of the participation ratio. We find that the ground state in the super-radiant phase exhibits multifractality manifest in the participation ratio scaling as the square root of the full Hilbert space dimension. The thermal phase transition temperature, for which we obtain an exact analytical expression, is strikingly captured by the mutual information between two spins. In the excited state quantum phase transition within the super-radiant phase, we discover a new upper cut-off energy; the central energy band between the lower and upper cut-off energies shows distinctly different behaviour. This finding is corroborated with the aid of several eigenvector properties: von Neumann entanglement entropy between spins and bosons, the mean photon number, concurrence between two spins, and participation ratio. Thus we obtain a unified picture for the three different kinds of phase transitions.

cond-mat.stat-mech↗

arXiv2021

Fano Resonances in Quantum Transport with Vibrations

Quantum mechanical scattering involving continuum states coupled to a scatterer with a discrete spectrum gives rise to Fano resonances. Here we consider scatterers that possess internal vibrational degrees of freedom in addition to discrete states. Entanglement between the scattered excitation and vibrational modes complicates analytical and numerical calculations considerably. For the example of one-dimensional scattering we develop a multichannel quantum scattering approach which can determine reflection and transmission probabilities in the presence of vibrations. Application to a linear chain coupled to a control unit containing vibrating sites shows that vibrational degrees of freedom can have a profound effect on quantum transport. For suitable parameters, spectral regions which are opaque in the static case can be rendered transparent when vibrations are included. The formalism is general enough to be applicable to a variety of platforms for quantum transport including molecular aggregates, cold atom chains, quantum-dot arrays and molecular wires based on conjugated polymers.

quant-ph↗

arXiv2021

Entanglement entropy and out-of-time-order correlator in the long-range Aubry-André-Harper model

We investigate the nonequilbrium dynamics of entanglement entropy and out-of-time-order correlator (OTOC) of noninteracting fermions at half-filling starting from a product state to distinguish the delocalized, multifractal (in the limit of nearest neighbor hopping), localized and mixed phases hosted by the quasiperiodic Aubry-André-Harper (AAH) model in the presence of long-range hopping. For sufficiently long-range hopping strength a secondary logarithmic behavior in the entanglement entropy is found in the mixed phases whereas the primary behavior is a power-law the exponent of which is different in different phases. The saturation value of entanglement entropy in the delocalized, multifractal and mixed phases depends linearly on system size whereas in the localized phase (in the short-range regime) it is independent of system size. The early-time growth of OTOC shows very different power-law behaviors in the presence of nearest neighbor hopping and long-range hopping. The late time decay of OTOC leads to noticeably different power-law exponents in different phases. The spatial profile of OTOC and its system-size dependence also provide distinct features to distinguish phases. In the mixed phases the spatial profile of OTOC shows two different dependences on space for small and large distances respectively. Interestingly the spatial profile contains large fluctuations at the special locations related to the quasiperiodicity parameter in the presence of multifractal states.

cond-mat.str-el↗

arXiv2021

Fraction of delocalized eigenstates in the long-range Aubry-André-Harper model

We uncover a systematic structure in the single particle phase-diagram of the quasiperiodic Aubry-André-Harper(AAH) model with power-law hoppings ($\sim \frac{1}{r^σ}$) when the quasiperiodicity parameter is chosen to be a member of the `metallic mean family' of irrational Diophantine numbers. In addition to the fully delocalized and localized phases we find a co-existence of multifractal (localized) states with the delocalized states for $σ<1$ ($σ>1$). The fraction of delocalized eigenstates in these phases can be obtained from a general sequence, which is a manifestation of a mathematical property of the `metallic mean family'. The entanglement entropy of the noninteracting many-body ground states respects the area-law if the Fermi level belongs in the localized regime while logarithmically violating it if the Fermi-level belongs in the delocalized or multifractal regimes. The prefactor of logarithmically violating term shows interesting behavior in different phases. Entanglement entropy shows the area-law even in the delocalized regime for special filling fractions, which are related to the metallic means.

cond-mat.dis-nn↗

arXiv2020

Interplay of disorder and interactions in a flat-band supporting diamond chain

We systematically study the effect of disorder and interactions on a quasi-one dimensional diamond chain possessing flat bands. Disorder localizes all the single particle eigenstates, while at low disorder strengths we obtain weak flat-band based localization (FBL), at high disorder strengths, we see conventional Anderson localization (AL). The compactly localized (CL) eigenstates of flat bands show a persisting oscillatory recurrence in the study of single-particle wavepacket dynamics. For low disorder a damped oscillatory recurrence behavior is observed which is absent for high disorder. Non-interacting many particle fermion states also follow the same trend except showing a delocalizing tendency at intermediate disorder due to the fermionic statistics in the system. As interactions are switched on, for the finite-sizes that we are able to study, a non-ergodic `mixed phase' is observed at low disorder which is separated from the MBL phase at high disorder by a thermal phase at intermediate-disorder. A study of many-body nonequilibrium dynamics reinforces these findings.

cond-mat.dis-nn↗

arXiv2020

Transmission in a Fano-Anderson chain with a topological defect

The Fano-Anderson chain consists of a linear lattice with a discrete side-unit, and exhibits Fano-resonant scattering due to coupling between the discrete states of the side-unit with the tight-binding continuum. We study Fano-resonance-assisted transport for the case of a topologically non-trivial side unit. We find that the topology of the side unit influences the transmission characteristics which thus can be an effective detection tool of the topological phases of the side unit. Furthermore, we explore the role of dual links between the linear tight-binding chain and the side unit. The secondary connection between the main chain and the side unit can modify the position or width of the Fano resonance dip in the transmission probability, and thus yield additional control.

cond-mat.mtrl-sci↗

arXiv2020

Entanglement and thermodynamic entropy in a clean many-body-localized system

Whether or not the thermodynamic entropy is equal to the entanglement entropy of an eigenstate, is of fundamental interest, and is closely related to the `Eigenstate thermalization hypothesis (ETH)'. However, this has never been exploited as a diagnostic tool in many-body localized systems. In this work, we perform this diagnostic test on a clean interacting system (subjected to a static electric field) that exhibits three distinct phases: integrable, non-integrable ergodic and non-integrable many-body-localized (MBL). We find that in the non-integrable ergodic phase, the equivalence between the thermodynamic entropy and the entanglement entropy of individual eigenstates, holds. In sharp contrast, in the integrable and non-integrable MBL phases, the entanglement entropy shows large eigenstate-to-eigenstate fluctuations, and differs from the thermodynamic entropy. Thus the non-integrable MBL phase violates ETH similar to an integrable system; however, a key difference is that the magnitude of the entanglement entropy in the MBL phase is significantly smaller than in the integrable phase, where the entanglement entropy is of the same order of magnitude as in the non-integrable phase, but with a lot of eigenstate-to-eigenstate fluctuations. Quench dynamics from an initial CDW state independently supports the validity of the ETH in the ergodic phase and its violation in the MBL phase.

cond-mat.dis-nn↗

arXiv2020

Drive-induced many-body localization and coherent destruction of Stark many-body localization

We study the phenomenon of many-body localization (MBL) in an interacting system subjected to a combined DC as well as a square wave AC electric field. First, the condition for the dynamical localization, coherent destruction of Wannier-Stark localization and super Bloch oscillations in the non-interacting limit, are obtained semi-classically. In the presence of interactions (and a confining/disordered potential), a static field alone leads to "Stark many-body localization", for sufficiently large field strengths. We find that in the presence of an additional high-frequency AC field, there are two ways of maintaining the MBL intact: either by resonant drive where the ratio of amplitude to the frequency of the drive ($A/ω$) is tuned at the dynamical localization point of the non-interacting limit or by off-resonant drive. Remarkably, resonant drive with $A/ω$ tuned away from the dynamical localization point leads to a \emph{coherent destruction of Stark-MBL}. Moreover, a pure (high-frequency) AC field can also give rise to the MBL phase if $A/ω$ is tuned at the dynamical localization point of the zero dc field problem.

cond-mat.dis-nn↗

arXiv2020

Stability of electric-field-driven MBL in an interacting long range hopping model

We study the fate of many-body localization (MBL) in the presence of long-range hopping ($\sim 1/r^σ$) in a system subjected to an electric field (static and time-periodic) along with a slowly-varying aperiodic potential. We show that the MBL in the static electric-field model is robust against arbitrary long-range hopping in sharp contrast to other disordered models, where MBL is killed by sufficiently long-range hopping. Next, we show that the drive-induced phenomena associated with an ac square wave electric field are also robust against long-range hopping. Specifically, we obtain drive-induced MBL, where a high-frequency drive can convert the ergodic phase into the MBL phase. Remarkably, we find that coherent destruction of MBL is also possible with the aid of a resonant drive. Thus in both the static and time-periodic square wave electric field models, the qualitative properties of the system are independent of whether the hopping is short-ranged or long-ranged.

cond-mat.dis-nn↗

arXiv2019

Study of counterintuitive transport properties in the Aubry-André-Harper model via entanglement entropy and persistent current

The single particle eigenstates of the Aubry-André-Harper model are known to show a delocalization-localization transition at a finite strength of the quasi-periodic disorder. In this work, we point out that an intimate relationship exists between the sub-band structure of the spectrum and transport properties of the model. To capture the transport properties we have not only used a variety of single-particle measures like inverse participation ratio, and von Neumann entropy, but also many-particle measures such as persistent current and its variance, and many body entanglement entropy. The many-particle measures are very sensitive to the sub-band structure of the spectrum. Even in the delocalized phase, surprisingly the entanglement entropy is substantially suppressed when the Fermi level is in the band gaps whereas the persistent current is vanishingly small for the same locations of the Fermi level. The entanglement entropy seems to follow area-law exclusively for these special locations of Fermi level or filling fractions of free fermions. A study of the standard deviation of persistent current offers further distinguishing features for the special fillings. In the delocalized phase, the standard deviation vs. mean persistent current curves are discontinuous for the non-special values of filling fractions and continuous (closed) for the special values of filling fractions whereas in the localized phase, these curves become straight lines for both types of filling fractions. We have also discussed how the results depend on the system size. Our results, specially on the persistent current, can potentially be tested experimentally using the present day set-ups based on ultra-cold atoms.

cond-mat.str-el↗

arXiv2019

Quantum entanglement and transport in non-equilibrium interacting double-dot setup: The curious role of degeneracy

We study quantum entanglement and its relation to transport in a non-equilibrium interacting double dot system connected to electronic baths. The dynamical properties in the non-interacting regime are studied using an exact numerical approach whereas the steady state properties are obtained following the well-known non-equilibrium Green's function (NEGF) approach. By means of mutual information and concurrence we explore the connection between the quantum correlations in the system and the current flowing through the dots. It is observed that entanglement between the dots is heavily influenced by the degeneracy or the lack thereof, of the dot levels. In the non-degenerate case, the concurrence falls sharply when the applied bias crosses a certain critical value. In contrast when the dot energy levels are degenerate, the concurrence reaches a very high asymptotic value of 1/2. When interactions are switched on, the degeneracy is lifted, and once again concurrence falls to zero beyond a critical value of the applied bias. Lastly it is observed that the concurrence can be made to reach almost the value of 1.0 if the chemical potential in both baths is made very large (while keeping the sign the same) provided the dot levels are kept degenerate within the non-interacting limit. A combination of NEGF method, brute-force numerics and asymptotics are employed to corroborate our findings.

cond-mat.mes-hall↗

arXiv2019

Flat bands and entanglement in the Kitaev ladder

We report the existence of \emph{flat bands} in a p-wave superconducting Kitaev ladder. We identify two sets of parameters for which the Kitaev ladder sustains flat bands. These flat bands are accompanied by highly localized eigenstates known as compact localized states. Invoking a Bogoliubov transformation, the Kitaev ladder can be mapped into an interlinked cross-stitch lattice. The mapping helps to reveal the compactness of the eigenstates each of which covers only two unit cells of the interlinked cross-stitch lattice. The Kitaev Hamiltonian undergoes a topological-to-trivial phase transition when certain parameters are fine-tuned. Correlation matrix techniques allow us to compute entanglement entropy of the many-body eigenstates. The study of entanglement entropy affords fresh insight into the topological phase transitions in the model. Sharp features in entanglement entropy when bands cross indicate a deep underlying relationship between entanglement entropy and dispersion.

cond-mat.mes-hall↗

arXiv2019

Transport in a long-range Kitaev ladder: role of Majorana and subgap Andreev states

We study local and non-local transport across a two-leg long-range Kitaev ladder connected to two normal metal leads. We focus on the role of the constituent Majorana fermions and the subgap Andreev states. The double degeneracy of Majorana fermions of the individual legs of the ladder gets lifted by a coupling between the two leading to the formation of Andreev bound states. The coupling can be induced by a superconducting phase difference between the two legs of the ladder accompanied by a finite inter-leg hopping. Andreev bound states formed strongly enhance local Andreev reflection. When the ladder and normal metal are weakly coupled, the Andreev bound states, which are the controlling factor, result in weak nonlocal scattering. In sharp contrast, when the ladder - normal metal interface is transparent to electron flow, we find that the subgap Andreev states enhance nonlocal conductance strongly. The features in the local and nonlocal conductances resemble the spectrum of the isolated ladder. Long-range pairing helps lift the degeneracy of the Majorana modes, makes them less localized, and thus inhibits local transport, while aiding non-local transport. In particular, long-range pairing alone (without a superconducting phase difference) can enhance crossed Andreev reflection.

cond-mat.mes-hall↗

arXiv2019

Quantum simulation of long range $XY$ quantum spin glass with strong area-law violation using trapped ions

Ground states of local Hamiltonians are known to obey the entanglement entropy area law. While area law violation of a mild kind (logarithmic) is commonly encountered, strong area-law violation (more than logarithmic) is rare. In this paper, we study the long range quantum spin glass in one dimension whose couplings are disordered and fall off with distance as a power-law. We show that this system exhibits more than logarithmic area law violation in its ground state. Strikingly this feature is found to be true even in the short range regime in sharp contrast to the spinless long range disordered fermionic model. This necessitates the study of large systems for the quantum $XY$ spin glass model which is challenging since these numerical methods depend on the validity of the area law. This situation lends itself naturally for the exploration of a quantum simulation approach. We present a proof-of-principle implementation of this non-trivially interacting spin model using trapped ions and provide a detailed study of experimentally realistic parameters.

cond-mat.dis-nn↗

arXiv2019

Enhancement of crossed Andreev reflection in a Kitaev ladder connected to normal metal leads

We study nonlocal transport in a two-leg Kitaev ladder connected to two normal metals. The coupling between the two legs of the ladder when the legs are maintained at a (large) superconducting phase difference, results in the creation of subgap Andreev states. These states in turn are responsible for the enhancement of crossed Andreev reflection. We find that tuning the different parameters of the system suitably leads to enhancement of crossed Andreev reflection signalled by transconductance acquiring the most negative value possible. Furthermore, subgap states cause oscillations of the transconductance as a function of various system parameters such as chemical potential and ladder length, which are seen to be a consequence of Fabry-Pérot resonance.

cond-mat.mes-hall↗