arXiv subjects

Zohar Nussinov

Publications and source records attributed to Zohar Nussinov.

At least 73 records · Page 4Linked to original sources

arXiv2016

Kinetic energy driven stripe formation and pairing in repulsive electronic systems

We study repulsive Hubbard and t-J type systems on a square lattice (long believed to capture certain quintessential aspects of the high temperature superconductors). These models (alongside the parent compounds of the high temperature superconductors) are antiferromagnetic in the absence of hole doping. As we illustrate, a unifying underlying principle for the dynamics of holes introduced by doping rationalizes the emergence of nonuniform electronic structures- "stripes" and possible pairing tendencies therein. Specifically, our analysis invokes the following (numerically verified) sublattice parity principle: a strong antiferromagnetic background forces injected holes to hop in steps of two such that they always remain on the same sub lattice. When applied to a domain wall in an antiferromagnet, this simple principle naturally gives rise to (bond centered) stripes. We demonstrate that the holes are self-consistently localized on stripes. Extending this picture, we then show that the holes on a stripe favor the formation of pairs on neighboring rungs or sites. Throughout this work much emphasis is placed on the problem of a two leg ladder immersed in a staggered magnetic field. Although we will focus on the square lattice, our considerations may be extended to similar electronic structures appearing in other models on bipartite lattices when these exhibit antiferromagnetic correlations with an underlying sublattice structure.

cond-mat.str-el↗

arXiv2016

Probing Local Structure in Glass by the Application of Shear

The glass transition remains one of the great unsolved mysteries of contemporary condensed matter physics. When crystallization is bypassed by rapid cooling, a supercooled liquid, retaining amorphous particle arrangment, results. The physical phenomenology of supercooled liquids is as vast as it is interesting. Most significant, the viscosity of the supercooled liquid displays an incredible increase over a narrow temperature range. Eventually, the supercooled liquid ceases to flow, becomes a glass, and gains rigidity and solid-like behaviors. Understanding what underpins the monumental growth of viscosity, and how rigidity results without long range order is a long-sought goal. Many theories of the glassy slowdown require the growth of static lengthscale related to structure with lowering of the temperature. To that end, we have proposed a new, natural lengthscale- "the shear penetration depth". This lengthscale quantifies the structural connectivity of the supercooled liquid. The shear penetration depth is defined as the distance up to which a shear perturbation applied to the boundary propagates into the liquid. We provide numerical data, based on the simulations of $NiZr_2$, illustrating that this length scale exhibits dramatic growth and eventual divergence upon approach to the glass transition. We further discuss this in relation to percolating structural connectivity and a new theory of the glass transition.

cond-mat.mtrl-sci↗

arXiv2015

Emergent quasicrystals in strongly correlated systems

Commensurability is of paramount importance in numerous strongly interacting electronic systems. In the Fractional Quantum Hall effect, a rich cascade of increasingly narrow plateaux appear at larger denominator filling fractions. Rich commensurate structures also emerge, at certain filling fractions, in high temperature superconductors and other electronic systems. A natural question concerns the character of these and other electronic systems at irrational filling fractions. Here we demonstrate that quasicrystalline structures naturally emerge in these situations, and trigger behaviors not typically expected of periodic systems. We first show that irrationally filled quantum Hall systems cross over into quasiperiodically ordered configuration in the thin-torus limit. Using known properties of quasicrystals, we argue that these states are unstable against the effects of disorder, in agreement with the existence of quantum Hall plateaux. We then study analogous physical situations in a system of cold Rydberg atoms placed on an optical lattice. Such an experimental setup is generally disorder free, and can therefore be used to detect the emergent quasicrystals we predict. We discuss similar situations in the Falicov-Kimball model, where known exact results can be used to establish quasicrystalline structures in one and two dimensions. We briefly speculate on possible relations between our theoretical findings and the existence of glassy dynamics and other features of strongly correlated electronic systems.

cond-mat.str-el↗

arXiv2015

On entropy production in the Madelung fluid and the role of Bohm's potential in classical diffusion

The Madelung equations map the non-relativistic time-dependent Schrodinger equation into hydrodynamic equations of a virtual fluid. Here we show that an increase of the Boltzmann entropy of this Madelung fluid is proportional to the expectation value of its velocity divergence. Hence, entropy growth is accompanied by expansion resulting from the ability of the Madelung fluid to be compressible. The compressibility itself reflects superposition of solutions of the Schrodinger equation. Thus, in unitary processes where the Madelung fluid expands and then shrinks, the Boltzmann entropy may, correspondingly, grow and then decrease. The notion of entropy growth due to expansion is common in diffusive processes, however in the latter the process is irreversible. Much unlike the Boltzmann entropy, the von Neumann entropy, does not vary with time. To elucidate the physical underpinning of the Boltzmann entropy, we examine several specific examples. We demonstrate that, for classical diffusive processes, the "force" accelerating diffusion has the form of the positive gradient of the quantum Bohm potential. In the Madelung fluid, the advective and the diffusive velocities correspond respectively to the the real and imaginary parts of the complex momentum. We find that the diffusion coefficient provides a lower bound of Heisenberg uncertainty type product between the gas mean free path and the Brownian momentum.

quant-ph↗

arXiv2015

Zero modes, Bosonization and Topological Quantum Order: The Laughlin State in Second Quantization

We introduce a "second-quantized" representation of the ring of symmetric functions to further develop a purely second-quantized -- or "lattice" -- approach to the study of zero modes of frustration free Haldane-pseudo-potential-type Hamiltonians, which in particular stabilize Laughlin ground states. We present three applications of this formalism. We start demonstrating how to systematically construct all zero-modes of Laughlin-type parent Hamiltonians in a framework that is free of first-quantized polynomial wave functions, and show that they are in one-to-one correspondence with dominance patterns. The starting point here is the pseudo-potential Hamiltonian in "lattice form", stripped of all information about the analytic structure of Landau levels (dynamical momenta). Secondly, as a by-product, we make contact with the bosonization method, and obtain an alternative proof for the equivalence between bosonic and fermionic Fock spaces. Finally, we explicitly derive the second-quantized version of Read's non-local (string) order parameter for the Laughlin state, extending an earlier description by Stone. Commutation relations between the local quasi-hole operator and the local electron operator are generalized to various geometries.

cond-mat.str-el↗

arXiv2015

Why are all dualities conformal? Theory and practical consequences

We relate duality mappings to the "Babbage equation" F(F(z)) = z, with F a map linking weak- to strong-coupling theories. Under fairly general conditions F may only be a specific conformal transformation of the fractional linear type. This deep general result has enormous practical consequences. For example, one can establish that weak- and strong- coupling series expansions of arbitrarily large finite size systems are trivially related, i.e., after generating one of those series the other is automatically determined through a set of linear constraints between the series coefficients. This latter relation partially solve or, equivalently, localize the computational complexity of evaluating the series expansion to a simple fraction of those coefficients. As a bonus, those relations also encode non-trivial equalities between different geometric constructions in general dimensions, and connect derived coefficients to polytope volumes. We illustrate our findings by examining various models including, but not limited to, ferromagnetic and spin-glass Ising, and Ising gauge type theories on hypercubic lattices in 1< D <9 dimensions.

cond-mat.stat-mech↗

arXiv2014

Classification of nematic order in 2+1D: Dislocation melting and $O(2)/Z_N$ lattice gauge theory

Nematic phases, breaking spontaneously rotational symmetry, provide for ubiquitously observed states of matter in both classical and quantum systems. These nematic states may be further classified by their $N$--fold rotational invariance described by cyclic groups $C_N$ in 2+1D. Starting from the space groups of underlying $2d$ crystals, we present a general classification scheme incorporating $C_N$ nematic phases that arise from dislocation-mediated melting and discuss the conventional tensor order parameters. By coupling the $O(2)$ matter fields to the $Z_N$ lattice gauge theory, an unified $O(2)/Z_N$ lattice gauge theory is constructed in order to describe all these nematic phases. This lattice gauge theory is shown to reproduce the $C_N$ nematic-isotropic liquid phase transitions and contains an additional deconfined phase. Finally, using our $O(2)/Z_N$ gauge theory framework, we discuss phase transitions between different $C_N$ nematics.

cond-mat.str-el↗

arXiv2014

Improving the performance of algorithms to find communities in networks

Many algorithms to detect communities in networks typically work without any information on the cluster structure to be found, as one has no a priori knowledge of it, in general. Not surprisingly, knowing some features of the unknown partition could help its identification, yielding an improvement of the performance of the method. Here we show that, if the number of clusters were known beforehand, standard methods, like modularity optimization, would considerably gain in accuracy, mitigating the severe resolution bias that undermines the reliability of the results of the original unconstrained version. The number of clusters can be inferred from the spectra of the recently introduced non-backtracking and flow matrices, even in benchmark graphs with realistic community structure. The limit of such two-step procedure is the overhead of the computation of the spectra.

physics.soc-ph↗

arXiv2014

Local multiresolution order in community detection

Community detection algorithms attempt to find the best clusters of nodes in an arbitrary complex network. Multi-scale ("multiresolution") community detection extends the problem to identify the best network scale(s) for these clusters. The latter task is generally accomplished by analyzing community stability simultaneously for all clusters in the network. In the current work, we extend this general approach to define local multiresolution methods, which enable the extraction of well-defined local communities even if the global community structure is vaguely defined in an average sense. Toward this end, we propose measures analogous to variation of information and normalized mutual information that are used to quantitatively identify the best resolution(s) at the community level based on correlations between clusters in independently-solved systems. We demonstrate our method on two constructed networks as well as a real network and draw inferences about local community strength. Our approach is independent of the applied community detection algorithm save for the inherent requirement that the method be able to identify communities across different network scales, with appropriate changes to account for how different resolutions are evaluated or defined in a particular community detection method. It should, in principle, easily adapt to alternative community comparison measures.

physics.soc-ph↗

arXiv2014

Symmetry and Topological Order

We prove sufficient conditions for Topological Quantum Order at both zero and finite temperatures. The crux of the proof hinges on the existence of low-dimensional Gauge-Like Symmetries (that notably extend and differ from standard local gauge symmetries) and their associated defects, thus providing a unifying framework based on a symmetry principle. These symmetries may be actual invariances of the system, or may emerge in the low-energy sector. Prominent examples of Topological Quantum Order display Gauge-Like Symmetries. New systems exhibiting such symmetries include Hamiltonians depicting orbital-dependent spin exchange and Jahn-Teller effects in transition metal orbital compounds, short-range frustrated Klein spin models, and p+ip superconducting arrays. We analyze the physical consequences of Gauge-Like Symmetries (including topological terms and charges), discuss associated braiding, and show the insufficiency of the energy spectrum, topological entanglement entropy, maximal string correlators, and fractionalization in establishing Topological Quantum Order. General symmetry considerations illustrate that not withstanding spectral gaps, thermal fluctuations may impose restrictions on certain suggested quantum computing schemes and lead to "thermal fragility". Our results allow us to go beyond standard topological field theories and engineer systems with Topological Quantum Order.

cond-mat.str-el↗

arXiv2014

Algorithm independent bounds on community detection problems and associated transitions in stochastic block model graphs

We derive rigorous bounds for well-defined community structure in complex networks for a stochastic block model (SBM) benchmark. In particular, we analyze the effect of inter-community "noise" (inter-community edges) on any "community detection" algorithm's ability to correctly group nodes assigned to a planted partition, a problem which has been proven to be NP complete in a standard rendition. Our result does not rely on the use of any one particular algorithm nor on the analysis of the limitations of inference. Rather, we turn the problem on its head and work backwards to examine when, in the first place, well defined structure may exist in SBMs.The method that we introduce here could potentially be applied to other computational problems. The objective of community detection algorithms is to partition a given network into optimally disjoint subgraphs (or communities). Similar to k-SAT and other combinatorial optimization problems, "community detection" exhibits different phases. Networks that lie in the "unsolvable phase" lack well-defined structure and thus have no partition that is meaningful. Solvable systems splinter into two disparate phases: those in the "hard" phase and those in the "easy" phase. As befits its name, within the easy phase, a partition is easy to achieve by known algorithms. When a network lies in the hard phase, it still has an underlying structure yet finding a meaningful partition which can be checked in polynomial time requires an exhaustive computational effort that rapidly increases with the size of the graph. When taken together, (i) the rigorous results that we report here on when graphs have an underlying structure and (ii) recent results concerning the limits of rather general algorithms, suggest bounds on the hard phase.

cond-mat.stat-mech↗

arXiv2014

Topological Charge Order and Binding in a Frustrated XY Model and Related systems

We prove the existence of a finite temperature Z_{2} phase transition for the topological charge ordering within the Fully Frustrated XY Model. Our method enables a proof of the topological charge confinement within the conventional XY models from a rather general vista. One of the complications that we face is the non-exact equivalence of the continuous (angular) XY model and its discrete topological charge dual. In reality, the energy spectra of the various topological sectors are highly nested much unlike that suggested by the discrete dual models. We surmount these difficulties by exploiting the Reflection Positivity symmetry that this periodic flux phase model possesses. The techniques introduced here may prove binding of topological charges in numerous models and might be applied to examine transitions associated with various topological defects, e.g., the confinement of disclinations in the isotropic to nematic transition.

cond-mat.stat-mech↗

arXiv2013

Repulsive Interactions in Quantum Hall Systems as a Pairing Problem

A subtle relation between Quantum Hall physics and the phenomenon of pairing is unveiled. By use of second quantization, we establish a connection between (i) a broad class of rotationally symmetric two-body interactions within the lowest Landau level and (ii) integrable hyperbolic Richardson-Gaudin type Hamiltonians that arise in (p_{x}+ip_{y}) superconductivity. Specifically, we show that general Haldane pseudopotentials (and their sums) can be expressed as a sum of repulsive non-commuting (p_{x}+ip_{y})-type pairing Hamiltonians. For the Laughlin sequence, it is observed that this problem is frustration free and zero energy ground states lie in the common null space of all of these non-commuting Hamiltonians. This property allows for the use of a new truncated basis of pairing configurations in which to express Laughlin states at general filling factors. We prove separability of arbitrary Haldane pseudopotentials, providing explicit expressions for their second quantized forms, and further show by explicit construction how to exploit the topological equivalence between different geometries (disk, cylinder, and sphere) sharing the same topological genus number, in the second quantized formalism, through similarity transformations. As an application of the second quantized approach, we establish a "squeezing principle" that applies to the zero modes of a general class of Hamiltonians, which includes but is not limited to Haldane pseudopotentials. We also show how one may establish (bounds on) "incompressible filling factors" for those Hamiltonians. By invoking properties of symmetric polynomials, we provide explicit second quantized quasi-hole generators; the generators that we find directly relate to bosonic chiral edge modes and further make aspects of dimensional reduction in the Quantum Hall systems precise.

cond-mat.str-el↗

arXiv2013

Automatic Segmentation of Fluorescence Lifetime Microscopy Images of Cells Using Multi-Resolution Community Detection

We have developed an automatic method for segmenting fluorescence lifetime (FLT) imaging microscopy (FLIM) images of cells inspired by a multi-resolution community detection (MCD) based network segmentation method. The image processing problem is framed as identifying segments with respective average FLTs against a background in FLIM images. The proposed method segments a FLIM image for a given resolution of the network composed using image pixels as the nodes and similarity between the pixels as the edges. In the resulting segmentation, low network resolution leads to larger segments and high network resolution leads to smaller segments. Further, the mean-square error (MSE) in estimating the FLT segments in a FLIM image using the proposed method was found to be consistently decreasing with increasing resolution of the corresponding network. The proposed MCD method outperformed a popular spectral clustering based method in performing FLIM image segmentation. The spectral segmentation method introduced noisy segments in its output at high resolution. It was unable to offer a consistent decrease in MSE with increasing resolution.

physics.med-ph↗

arXiv2013

Heat equation approach to geometric changes of the torus Laughlin-state

We study the second quantized -or guiding center- description of the torus Laughlin state. Our main focus is the change of the guiding center degrees of freedom with the torus geometry, which we show to be generated by a two-body operator. We demonstrate that this operator can be used to evolve the full torus Laughlin state at given modular parameter τ from its simple (Slater-determinant) thin torus limit, thus giving rise to a new presentation of the torus Laughlin state in terms of its "root partition" and an exponential of a two-body operator. This operator therefore generates in particular the adiabatic evolution between Laughlin states on regular tori and the quasi-one-dimensional thin torus limit. We make contact with the recently introduced notion of a "Hall viscosity" for fractional quantum Hall states, to which our two-body operator is naturally related, and which serves as a demonstration of our method to generate the Laughlin state on the torus.

cond-mat.str-el↗

arXiv2013

A dynamical relation between dual finite temperature classical and zero temperature quantum systems: quantum critical jamming and quantum dynamical heterogeneities

Many electronic systems exhibit striking features in their dynamical response over a prominent range of experimental parameters. While there are empirical suggestions of particular increasing length scales that accompany such transitions, this identification is not universal. To better understand such behavior in quantum systems, we extend a known mapping (earlier studied in stochastic, or supersymmetric, quantum mechanics) between finite temperature classical Fokker-Planck systems and related quantum systems at zero temperature to include general non-equilibrium dynamics. Unlike Feynman mappings or stochastic quantization methods (or holographic type dualities), the classical systems that we consider and their quantum duals reside in the same number of space-time dimensions. The upshot of our exact result is that a Wick rotation relates (i) dynamics in general finite temperature classical dissipative systems to (ii) zero temperature dynamics in the corresponding dual many-body quantum systems. Using this correspondence, we illustrate that, even in the absence of imposed disorder, many continuum quantum fluid systems (and possible lattice counterparts) may exhibit a zero-point "quantum dynamical heterogeneity" wherein the dynamics, at a given instant, is spatially non-uniform. While the static length scales accompanying this phenomenon do not exhibit a clear divergence in standard correlation functions, the length scale of the dynamical heterogeneities can increase dramatically. We study "quantum jamming" and illustrate how a hard core bosonic system may undergo a zero temperature quantum critical metal-to-insulator-type transition with an extremely large effective dynamical exponent z>4 consistent with length scales that increase far more slowly than the relaxation time as a putative critical transition is approached. We suggest ways to analyze experimental data.

cond-mat.stat-mech↗

arXiv2013

Compass and Kitaev models -- Theory and Physical Motivations

Compass models are theories of matter in which the couplings between the internal spin (or other relevant field) components are inherently spatially (typically, direction) dependent. Compass-type interactions appear in diverse physical systems including Mott insulators with orbital degrees of freedom (where interactions sensitively depend on the spatial orientation of the orbitals involved), the low energy effective theories of frustrated quantum magnets, systems with strong spin-orbit couplings (such as the iridates), vacancy centers, and cold atomic gases. Kitaev's models, in particular the compass variant on the honeycomb lattice, realize basic notions of topological quantum computing. The fundamental inter-dependence between internal (spin, orbital, or other) and external (i.e., spatial) degrees of freedom which underlies compass models generally leads to very rich behaviors including the frustration of (semi-)classical ordered states on non-frustrated lattices and to enhanced quantum effects prompting, in certain cases, the appearance of zero temperature quantum spin liquids. As a consequence of these frustrations, new types of symmetries and their associated degeneracies may appear. These intermediate symmetries lie midway between the extremes of global symmetries and local gauge symmetries and lead to effective dimensional reductions. We review compass models in a unified manner, paying close attention to exact consequences of these symmetries, and to thermal and quantum fluctuations that stabilize orders via order out of disorder effects. We review non-trivial statistics and the appearance of topological quantum orders in compass systems in which, by virtue of their intermediate symmetry standard orders do not arise. This is complemented by a survey of numerical results. Where appropriate theoretical and experimental results are compared.

cond-mat.str-el↗

arXiv2013

Connectivity of the Icosahedral Network and a Dramatically Growing Static Length Scale in Cu-Zr Binary Metallic Glasses

We report on and characterize, via molecular dynamics (MD) studies, the evolution of the structure of Cu50Zr50 and Cu64Zr36 metallic glasses (MGs) as temperature is varied. Interestingly, a percolating icosahedral network appears in the Cu64Zr36 system as it is supercooled. This leads us to introduce a static length scale, which grows dramatically as this three dimensional system approaches the glass transition. Amidst interpenetrating connections, non-interpenetrating connections between icosahedra are shown to become prevalent upon supercooling and to greatly enhance the connectivity of the MG's icosahedral network. Additionally, we characterize the chemical compositions of the icosahedral networks and their components. These findings demonstrate the importance of non-interpenetrating connections for facilitating extensive structural networks in Cu-Zr MGs, which in turn drive dynamical slowing in these materials.

cond-mat.mtrl-sci↗