506 research outputs found
Correlation and entanglement spreading in nested spin chains
No full textThe past few years have witnessed the development of a comprehensive theory to describe integrable systems out of equilibrium, in which the Bethe ansatz formalism has been tailored to address specific problems arising in this context. While most of the work initially focused on the study of prototypical models such as the well-known Heisenberg chain, many theoretical results have been recently extended to a class of more complicated nested integrable systems, displaying different species of quasiparticles. Still, in the simplest context of quantum quenches, the vast majority of theoretical predictions have been numerically verified only in systems with an elementary Bethe ansatz description. In this work, we fill this gap and present a direct numerical test of some results presented in the recent literature for nested systems, focusing in particular on the Lai–Sutherland model. Using time-dependent density matrix renormalization group and exact diagonalization methods, we compute the spreading of both correlation functions and entanglement entropy after a quench from a simple class of product initial states. This allows us to test the validity of the nested version of a conjectured formula, based on the quasiparticle picture, for the growth of the entanglement entropy, and the Bethe ansatz predictions for the 'light-cone' velocity of correlation functions
Correlation and entanglement spreading in nested spin chains
No full textThe past few years have witnessed the development of a comprehensive theory to describe integrable systems out of equilibrium, in which the Bethe ansatz formalism has been tailored to address specific problems arising in this context. While most of the work initially focused on the study of prototypical models such as the well-known Heisenberg chain, many theoretical results have been recently extended to a class of more complicated nested integrable systems, displaying different species of quasiparticles. Still, in the simplest context of quantum quenches, the vast majority of theoretical predictions have been numerically verified only in systems with an elementary Bethe ansatz description. In this work, we fill this gap and present a direct numerical test of some results presented in the recent literature for nested systems, focusing in particular on the Lai–Sutherland model. Using time-dependent density matrix renormalization group and exact diagonalization methods, we compute the spreading of both correlation functions and entanglement entropy after a quench from a simple class of product initial states. This allows us to test the validity of the nested version of a conjectured formula, based on the quasiparticle picture, for the growth of the entanglement entropy, and the Bethe ansatz predictions for the ‘light-cone’ velocity of correlation functions
Reply to "Comment on 'Inflation with a graceful exit and entrance driven by Hawking radiation' "
No full textThe Comment [J. T. Firouzjaee, preceding Comment, Phys. Rev. D 89, 068301 (2014)] raises two points in regard to our paper [S. K. Modak and D. Singleton, Phys. Rev. D 86, 123515 (2012)]. The first is that one cannot use the tunneling picture to obtain the temperature and particle production rate in the Friedman-Robertson-Walker space-time. The second comment raised by Firouzjaee is that the Hawking-like radiation model for inflation presented in [Modak and Singleton; S. K. Modak and D. Singleton, Int. J. Mod. Phys. D 21, 1242020 (2012)] is inconsistent with the observed scalar and tensor perturbation spectrum. We show that the first comment is beside the point-we do not use the tunneling method in our papers [Modak and Singleton; Modak and Singleton]. The second criticism by Firouzjaee comes from the author evaluating quantities at different times-he evaluates the parameters of our model at the beginning of inflation and then compares this with the scalar and tensor perturbations evaluated at the horizon exit point.From Physical Review D, Vol.89(6), 68302, available online: http://dx.doi.org/10.1103/PhysRevD.89.068302. Copyright ©2014 by American Physical Society.Publisher version: https://doi.org/10.1103/PhysRevD.89.06830
Originality for Copyright Protection in Literary Works: After EBC v DB Modak
No full text266-276Originality, can be termed as the grund norm (the basic norm) for copyrightability. However, no one-size-fits-all formula
is adopted by countries on this aspect, and this article first explores the position and benchmarks to determine original
literary work (because even for different ‘works’ the criteria differs). Pursuant to this inquiry of identifying the ambit of the
respective thresholds, the Indian perspective is analysed with special emphasis on the decision delivered by Indian Supreme
Court in DB Modak. The judgement is critiqued to identify lacunae and absurdity in determining the law laid down and its
application in the factual matrix. Finally, subsequent Indian decisions are looked upon by the author to find out the
underlying approach by the courts wrt interpretation of DB Modak and what common threads emerge from them
Criterion for the occurrence of many-body localization in the presence of a single-particle mobility edge
No full textNoninteracting fermions in one dimension can undergo a localization-delocalization transition in the presence of a quasiperiodic 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 quasiperiodic potentials that possess single-particle mobility edges. Two such models were studied by Modak and Mukerjee Phys. Rev. Lett. 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 the presence of weak interactions. We propose a criterion to determine whether MBL is likely to occur in the presence of interaction based only on the properties of the noninteracting models. The relevant quantity epsilon is a measure of how localized the localized states are relative to how delocalized the delocalized states are in the noninteracting model. We also study various other features of the noninteracting 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
Geometric quenches in quasi-disordered lattice system
No full textWhile global quantum quench has been extensively used in the literature to
understand the localization-delocalization transition for the one-dimensional
quantum spin chain, the effect of geometric quench (which corresponds to a
sudden change of the geometry of the chain) in the context of such transitions
is yet to be well understood. In this work, we investigate the effect of
geometric quench in the Aubry-Andre model, which supports
localization-delocalization transition even in one dimension. We study the
spreading of the entanglement and the site-occupation with time and find many
interesting features that can be used to characterize
localization-delocalization transition. We observe that geometric quench causes
a power-law type growth of the entanglement entropy in the delocalized phase in
contrast to the linear growth which is found in the global quench studies.
Remarkably, we also find that the saturation values in the Many-body localized
(MBL) phase obey Area law in contrast to the usual volume law which is a
signature feature of the MBL phase in the context of global quench.Comment: 6 pages, 8 figure
Finite size scaling in crossover among different random matrix ensembles in microscopic lattice models
No full textUsing numerical diagonalization we study the crossover among different random matrix ensembles (Poissonian, Gaussian orthogonal ensemble (GOE), Gaussian unitary ensemble (GUE) and Gaussian symplectic ensemble (GSE)) realized in two different microscopic models. The specific diagnostic tool used to study the crossovers is the level spacing distribution. The first model is a one-dimensional lattice model of interacting hard-core bosons (or equivalently spin 1/2 objects) and the other a higher dimensional model of non-interacting particles with disorder and spin-orbit coupling. We find that the perturbation causing the crossover among the different ensembles scales to zero with system size as a power law with an exponent that depends on the ensembles between which the crossover takes place. This exponent is independent of microscopic details of the perturbation. We also find that the crossover from the Poissonian ensemble to the other three is dominated by the Poissonian to GOE crossover which introduces level repulsion while the crossover from GOE to GUE or GOE to GSE associated with symmetry breaking introduces a subdominant contribution. We also conjecture that the exponent is dependent on whether the system contains interactions among the elementary degrees of freedom or not and is independent of the dimensionality of the system
Work extraction in an isolated quantum lattice system: Grand canonical and generalized Gibbs ensemble predictions
No full textMany-Body Localization in the Presence of a Single-Particle Mobility Edge
No full textIn one dimension, noninteracting particles can undergo a localization-delocalization transition in a quasiperiodic potential. Recent studies have suggested that this transition transforms into a many-body localization (MBL) transition upon the introduction of interactions. It has also been shown that mobility edges can appear in the single particle spectrum for certain types of quasiperiodic potentials. Here, we investigate the effect of interactions in two models with such mobility edges. Employing the technique of exact diagonalization for finite-sized systems, we calculate the level spacing distribution, time evolution of entanglement entropy, optical conductivity, and return probability to detect MBL. We find that MBL does indeed occur in one of the two models we study, but the entanglement appears to grow faster than logarithmically with time unlike in other MBL systems
Indian Defence problem: Being a plea for saving Rs. 28 crores a year by immediate indianization etc. of British rank and file only a message of hope for the Indian tax-payer: A study for statesmen, publicists, politicians and military experts, both Indian
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