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Zohar Nussinov

Publications and source records attributed to Zohar Nussinov.

At least 109 records · Page 6Linked to original sources
arXiv2009

Multiresolution community detection for megascale networks by information-based replica correlations

We use a Potts model community detection algorithm to accurately and quantitatively evaluate the hierarchical or multiresolution structure of a graph. Our multiresolution algorithm calculates correlations among multiple copies ("replicas") of the same graph over a range of resolutions. Significant multiresolution structures are identified by strongly correlated replicas. The average normalized mutual information, the variation of information, and other measures in principle give a quantitative estimate of the "best" resolutions and indicate the relative strength of the structures in the graph. Because the method is based on information comparisons, it can in principle be used with any community detection model that can examine multiple resolutions. Our approach may be extended to other optimization problems. As a local measure, our Potts model avoids the "resolution limit" that affects other popular models. With this model, our community detection algorithm has an accuracy that ranks among the best of currently available methods. Using it, we can examine graphs over 40 million nodes and more than one billion edges. We further report that the multiresolution variant of our algorithm can solve systems of at least 200000 nodes and 10 million edges on a single processor with exceptionally high accuracy. For typical cases, we find a super-linear scaling, O(L^{1.3}) for community detection and O(L^{1.3} log N) for the multiresolution algorithm where L is the number of edges and N is the number of nodes in the system.

physics.soc-ph↗
arXiv2008

Bond Algebras and Exact Solvability of Hamiltonians: Spin S=1/2 Multilayer Systems and Other Curiosities

We introduce an algebraic methodology for designing exactly-solvable Lie model Hamiltonians. The idea consists in looking at the algebra generated by bond operators. We illustrate how this method can be applied to solve numerous problems of current interest in the context of topological quantum order. These include Kitaev's toric code and honeycomb models, a vector exchange model, and a Clifford gamma model on a triangular lattice.

cond-mat.mes-hall↗
arXiv2008

Non-uniform glassy electronic phases from competing local orders

We study non-uniform states and possible glassiness triggered by a competition between distinct local orders in disorder free systems. Both in Ginzburg-Landau theories and in simple field theories, such inhomogeneous states arise from negative gradient terms between the competing order parameters. We discuss applications of these ideas to a variety of strongly correlated systems.

cond-mat.str-el↗
arXiv2008

Orbital order driven quantum criticality

Charge, spin, and orbital degrees of freedom underlie the physics of transition metal compounds. Much work has revealed quantum critical points associated with spin and charge degrees of freedom in many of these systems. Here we illustrate that the simplest models that embody the orbital degrees of freedom - the two- and three-dimensional quantum orbital compass models - exhibit an exact quantum critical behavior on diluted square and cubic lattices (with a doping fraction of 1/4 and 1/2 respectively). This raises the possibility of quantum critical points triggered by the degradation of orbital order upon doping (or applying pressure to) such transition metal systems. We prove the existence of an orbital spin glass in several related systems in which the orbital couplings are made non-uniform. Moreover, a new orbital Larmor precession (i.e., a periodic change in the orbital state) is predicted when uniaxial pressure is applied.

cond-mat.str-el↗
arXiv2008

Exact results on the Kitaev model on a hexagonal lattice: spin states, string and brane correlators, and anyonic excitations

In this work, we illustrate how a Jordan-Wigner transformation combined with symmetry considerations enables a direct solution of Kitaev's model on the honeycomb lattice. We (i) express the p-wave type fermionic ground states of this system in terms of the original spins, (ii) adduce that symmetry alone dictates the existence of string and planar brane type correlators and their composites, (iii) compute the value of such non-local correlators by employing the Jordan-Wigner transformation, (iv) affirm that the spectrum is inconsequential to the existence of topological quantum order and that such information is encoded in the states themselves, and (v) express the anyonic character of the excitations in this system and the local symmetries that it harbors in terms of fermions.

cond-mat.stat-mech↗
arXiv2007

Autocorrelations and Thermal Fragility of Anyonic Loops in Topologically Quantum Ordered Systems

Are systems that display Topological Quantum Order (TQO), and have a gap to excitations, hardware fault-tolerant at finite temperatures? We show that in surface code models that display low d-dimensional Gauge-Like Symmetries, such as Kitaev's and its generalizations, the expectation value of topological symmetry operators vanishes at any non-zero temperature, a phenomenon that we coined thermal fragility. The autocorrelation time for the non-local topological quantities in these systems may remain finite even in the thermodynamic limit. We provide explicit expressions for the autocorrelation functions in Kitaev's model. If temperatures far below the gap may be achieved then these autocorrelation times, albeit finite, can be made large. The physical engine behind the loss of correlations at large spatial and/or temporal distance is the proliferation of topological defects at any finite temperature as a result of a dimensional reduction. This raises an important question: How may we best quantify the degree of protection of quantum information in a topologically ordered system at finite temperature?

cond-mat.str-el↗
arXiv2007

A symmetry principle for Topological Quantum Order

We present a unifying framework to study physical systems which exhibit topological quantum order (TQO). The guiding principle behind our approach is that of symmetries and entanglement. We introduce the concept of low-dimensional Gauge-Like Symmetries (GLSs), and the physical conservation laws (including topological terms and fractionalization) which emerge from them. We prove then sufficient conditions for TQO at both zero and finite temperatures. The topological defects which are associated with the restoration of GLSs lead to TQO. Selection rules associated with the GLSs enable us to systematically construct states with TQO; these selection rules do not rely on the existence of a finite gap between the ground states to all other excited states. All currently known examples of TQO display GLSs. We analyze spectral structures and show that Kitaev's toric code model and Wen's plaquette model are equivalent and reduce, by a duality mapping, to an Ising chain. Despite the spectral gap in these systems, the toric operator expectation values may vanish once thermal fluctuations are present. This mapping illustrates that the quantum states themselves in a particular (operator language) representation encode TQO and that the duality mappings, being non-local in the original representation, disentangle the order. We present a general algorithm for the construction of long-range string orders in general systems with entangled ground states.

cond-mat.str-el↗
arXiv2006

Klein spin model ground states on general lattices

We prove that in short range Klein spin models on general lattices, all ground states are of the dimer type- each fundamental plaquette must host at least one singlet. These ground states are known to rigorously exhibit high dimensional fractionalization. When combined with a recent theorem, this establishes that Klein spin models exhibit topological order on the pyrochlore and checkerboard lattices.

cond-mat.str-el↗
arXiv2006

Intermediate Symmetries In Electronic Systems: Dimensional Reduction, Order Out Of Disorder, Dualities, And Fractionalization

We discuss symmetries intermediate between global and local and formalize the notion of dimensional reduction adduced from such symmetries. We apply this generalization to several systems including liquid crystalline phases of Quantum Hall systems, transition metal orbital systems, frustrated spin systems, (p+ip) superconducting arrays, and sliding Luttinger liquids. By considering space-time reflection symmetries, we illustrate that several of these systems are dual to each other. In some systems exhibiting these symmetries, low temperature local orders emerge by an "order out of disorder" effect while in other systems, the dimensional reduction precludes standard orders yet allows for multiparticle orders (including those of a topological nature).

cond-mat.str-el↗
arXiv2006

Voltage dependence of Landau-Lifshitz-Gilbert damping of a spin in a current driven tunnel junction

We present a theory of Landau-Lifshitz-Gilbert damping $α$ for a localized spin ${\vec S}$ in the junction coupled to the conduction electrons in both leads under an applied volatege $V$. We find the voltage dependence of the damping term reflecting the energy dependence of the density of states. We find the effect is linear in the voltage and cotrolled by particle-hole asymmetry of the leads.

cond-mat.mes-hall↗
arXiv2005

The BCS - BEC Crossover In Arbitrary Dimensions

Cold atom traps and certain neutron star layers may contain fermions with separation much larger than the range of pair-wise potentials yet much shorter than the scattering length. Such systems can display {\em universal} characteristics independent of the details of the short range interactions. In particular, the energy per particle is a fraction $ξ$ of the Fermi energy of the free Fermion system. Our main result is that for space dimensions D smaller than two and larger than four a specific extension of this problem readily yields $ξ=1$ for all $D \le 2$ whereas $ξ$ is rigorously non-positive (and potentially vanishing) for all $ D \ge 4$. We discuss the D=3 case. A particular unjustified recipe suggests $ξ=1/2$ in D=3.

cond-mat.str-el↗
arXiv2005

Spin and Spin-Wave Dynamics in Josephson Junctions

We extend the Keldysh formulation to quantum spin systems and derive exact equations of motion. This allows us to explore the dynamics of single spins and of ferromagnets when these are inserted between superconducting leads. Several new effects are reported. Chief amongst these are nutations of single S=1/2 spins in Josephson junctions. These nutations are triggered by the superconducting pairing correlations in the leads. Similarly, we find that on rather universal grounds, magnets display unconventional spin wave dynamics when placed in Josephson junctions. These lead to modifications in the tunneling current.

cond-mat.supr-con↗
arXiv2005

A Derivation of the Fradkin-Shenker Result From Duality: Links to Spin Systems in External Magnetic Fields and Percolation Crossovers

In this article, we illustrate how the qualitative phase diagram of a gauge theory coupled to matter can be directly proved and how rigorous numerical bounds may be established. Our work reaffirms the seminal result of Fradkin and Shenker from another vista. Our main ingredient is the combined use of the self-duality of the three dimensional Z2/Z2 theory and an extended Lee-Yang theorem. We comment on extensions of these ideas and firmly establish the existence of a sharp crossover line in the two dimensional Z2/Z2 theory.

cond-mat.stat-mech↗
arXiv2005

Thermally Increasing Correlation/Modulation Lengths and Other Selection Rules in Systems with Long Range Interactions

In this article, addressing large $n$ systems, we report that in numerous systems hosting long and short range interactions, multiple correlation lengths may appear. The largest correlation lengths often monotonically increase with temperature and diverge in the high temperature limit. Notwithstanding, the magnitude of the correlations themselves decreases with increasing temperature. We examine correlation function in the presence of competing interactions of long and short ranges. The behavior of the correlation and modulation lengths as a function of temperature provides us with selection rules on the possible underlying microscopic interactions. As a concrete example of these notions, we consider the correlations in a system of screened Coulomb interactions coexisting with attractive short range interactions.

cond-mat.soft↗
arXiv2005

Generalized Elitzur's Theorem and Dimensional Reduction

We extend Elitzur's theorem to systems with symmetries intermediate between global and local. In general, our theorem formalizes the idea of {\it dimensional reduction}. We apply the results of this generalization to many systems that are of current interest. These include liquid crystalline phases of Quantum Hall systems, orbital systems, geometrically frustrated spin lattices, Bose metals, and models of superconducting arrays.

cond-mat.stat-mech↗
arXiv2005

Non-Relativistic Bose-Einstein Condensates, Kaon droplets, and Q- Balls

We note the similarity between BEC (Bose-Einstein Condensates) formed of atoms between which we have long-range attraction (and shorter-range repulsions) and the field theoretic "Q balls". This allows us in particular to address the stability of various putative particle physics Q balls made of non-relativistic bosons using variational methods of many-body physics.

cond-mat.other↗
arXiv2005

Discrete Sliding Symmetries, Dualities, and Self-dualities of Quantum Orbital Compass Models and (p+ip) Superconducting Arrays

We study the spin- 1/2 two and three dimensional Orbital Compass Models relevant to the problem of orbital ordering in transition metal oxides. We show that these systems display self-dualities and novel (gauge-like) discrete sliding symmetries. An important and surprising consequence is that these models are dual to (seemingly unrelated) recently studied models of p+ip superconducting arrays. The duality transformations are constructed by means of a path-integral representation in discretized imaginary time and considering its Z_{2} spatial reflection symmetries and space-time discrete rotations, we obtain, in a transparent unified geometrical way, several dualities. We also introduce an alternative construction of the duality transformations using operator identities. We discuss the consequences of these dualities for the order parameters and phase transitions of the orbital compass model and its generalizations, and apply these ideas to a number of related systems.

cond-mat.str-el↗