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Z. Nussinov

Publications and source records attributed to Z. Nussinov.

At least 55 records · Page 3Linked to original sources
arXiv2005

Topological kinematic constraints: quantum dislocations and the glide principle

Topological defects play an important role in physics of elastic media and liquid crystals. Their kinematics is determined by constraints of topological origin. An example is the glide motion of dislocations which has been extensively studied by metallurgists. In a recent theoretical study dealing with quantum dualities associated with the quantum melting of solids it was argued that these kinematic constraints play a central role in defining the quantum field theories of relevance to the description of quantum liquid crystalline states of the nematic type. This forms the motivation to analyze more thoroughly the climb constraints underlying the glide motions. In the setting of continuum field theory the climb constraint is equivalent to the condition that the density of constituent particles is vanishing and we derive a mathematical definition of this constraint which has a universal status. This makes possible to study the kinematics of dislocations in arbitrary space-time dimensions and as an example we analyze the restricted climb associated with edge dislocations in 3+1D. Very generally, it can be shown that the climb constraint is equivalent to the condition that dislocations do not communicate with compressional stresses at long distances. However, the formalism makes possible to address the full non-linear theory of relevance to short distance behaviors where violations of the constraint become possible.

cond-mat.str-el↗
arXiv2004

A Novel Dielectric Anomaly in Cuprates and Nickelates: Signature of an Electronic Glassy State

The low-frequency dielectric response of hole-doped insulators La_{2}Cu_{1-x}Li_{x}O_{4} and La_{2-x}Sr_{x}NiO_{4} shows a large dielectric constant ε^{'} at high temperature and a step-like drop by a factor of 100 at a material-dependent low temperature T_{f}. T_{f} increases with frequency and the dielectric response shows universal scaling in a Cole-Cole plot, suggesting that a charge glass state is realized both in the cuprates and in the nickelates.

cond-mat.str-el↗
arXiv2004

Spin and Current Variations in Josephson Junctions

We study the dynamics of a single spin embedded in the tunneling barrier between two superconductors. As a consequence of pair correlations in the superconducting state, the spin displays rich and unusual dynamics. To properly describe the time evolution of the spin we derive the effective Keldysh action for the spin. The superconducting correlations lead to an effective spin action, which is non-local in time, leading to unconventional precession. We further illustrate how the current is modulated by this novel spin dynamics.

cond-mat.mes-hall↗
arXiv2003

Geometry and the Hidden Order of Luttinger Liquids: the Universality of Squeezed Space

We present the case that Luttinger liquids are characterized by a form of hidden order which is similar, but distinct in some crucial regards, to the hidden order characterizing spin-1 Heisenberg chains. We construct a string correlator for the Luttinger liquid which is similar to the string correlator constructed by den Nijs and Rommelse for the spin chain. From a geometric prespective on the so-called `squeezed space' construction, we demonstrate that the physics at long wavelength can be reformulated in terms of a $Z_2$ gauge theory. Peculiarly, the normal spin chain lives at infinite gauge coupling where it is characterized by deconfinement. We identify the microscopic conditions required for confinement thereby identifying a novel phase of the spin-chain. We demonstrate that the Luttinger liquid can be approached in the same general framework. The difference from the spin chain is that the gauge sector is critical in the sense that the Luttinger liquid is at the phase boundary where the $Z_2$ local symmetry emerges. We evaluate the string correlator analytically and show that the squeezed space structure is present both for the strongly coupled Hubbard model and the non-interacting fermion gas. These structures are hard-wired in the mathematical structure of bosonization and this becomes obvious by considering string correlators. Numerical results are presented for the string correlator using a non-abelian version of the density matrix renormalization group algorithm, confirming in detail the expectations following from the theory. We conclude with some observations regarding the generalization of bosonization to higher dimensions.

cond-mat.str-el↗
arXiv2003

Duality in 2+1D Quantum Elasticity: superconductivity and Quantum Nematic Order

The generalization of the Nelson-Halperin-Young theory of 2D melting to the dynamical 2+1D quantum case is presented. The bosonic quantum crystal dualizes in superfluids or superconductors exhibiting nematic liquid crystalline orders, corresponding with bose condensates of dislocations exhibiting a dual shear Meissner-Higgs mechanism. The topologically ordered nematic phase suggested by Lammert, Toner and Rokshar finds a simple interpretation in this framework. The ordered nematic is a true quantum phase: the dynamical glide principle interferes with the effect that the phonon spectrum of the crystal re-emerges in the direction orthogonal to the director. Novel insights follow from the duality on the fundamental nature of superfluidity and superconductivity. The superfluid can be viewed as an elastic medium having lost its rigidity against shear stresses. Upon dualizing the electrically charged crystal the electromagnetic Meissner phase is recovered, showing peculiar screening current oscillations when the shear penetration depth becomes larger than the London penetration depth.

cond-mat.supr-con↗
arXiv2003

Powerlaw optical conductivity with a constant phase angle in high Tc superconductors

In certain materials with strong electron correlations a quantum phase transition (QPT) at zero temperature can occur, in the proximity of which a quantum critical state of matter has been anticipated. This possibility has recently attracted much attention because the response of such a state of matter is expected to follow universal patterns defined by the quantum mechanical nature of the fluctuations. Forementioned universality manifests itself through power-law behaviours of the response functions. Candidates are found both in heavy fermion systems and in the cuprate high Tc superconductors. Although there are indications for quantum criticality in the cuprate superconductors, the reality and the physical nature of such a QPT are still under debate. Here we identify a universal behaviour of the phase angle of the frequency dependent conductivity that is characteristic of the quantum critical region. We demonstrate that the experimentally measured phase angle agrees precisely with the exponent of the optical conductivity. This points towards a QPT in the cuprates close to optimal doping, although of an unconventional kind.

cond-mat.str-el↗
arXiv2003

Atomic scale elastic textures coupled to electrons in superconductors

We present an atomic scale theory of lattice distortions using strain related variables and their constraint equations. Our approach connects constrained atomic length scale variations to continuum elasticity and describes elasticity at all length scales. We apply the general approach to a two-dimensional square lattice with a monatomic basis, and find the atomic scale elastic textures around a structural domain wall and a single defect, as exemplary textures. We clarify the microscopic origin of gradient terms, some of which are included phenomenologically in Landau-Ginzburg theory. The obtained elastic textures are used to investigate the effects of elasticity-driven lattice deformation on the nanoscale electronic structure in superconductor by solving the Bogliubov-de Gennes equations with the electronic degrees of freedom coupled to the lattice ones. It is shown that the order parameter is depressed in the regions where the lattice deformation takes place. The calculated local density of states suggests the electronic structure is strongly modulated as a response to the lattice deformation-- the elasticity propagates the electronic response over long distances. In particular, it is possible for the trapping of low-lying quasiparticle states around the defects. These predictions could be directly tested by STM experiments in superconducting materials.

cond-mat.supr-con↗
arXiv2003

Elasticity-Driven Nanoscale Electronic Structure in Superconductors

The effects of long-range anisotropic elastic deformations on electronic structure in superconductors are analyzed within the framework of the Bogoliubov-de Gennes equations. Cases of twin boundaries and isolated defects are considered as illustrations. We find that the superconducting order parameter is depressed in the regions where pronounced lattice deformation occurs. The calculated local density of states suggests that the electronic structure is strongly modulated in response to lattice deformations, and propagates to longer distances. In particular, this allows the trapping of low-lying quasiparticle states around defects. Some of our predictions can be directly tested by STM experiments.

cond-mat.supr-con↗
arXiv2003

Vibration Mode Induced Shapiro Steps and Backaction in Josephson Junctions

A model of a superconducting tunnel junction coupled to a mechanical oscillator is studied at zero temperature in the case of linear coupling between the oscillator and tunneling electrons. It is found that the Josephson current flowing between two superconductors is modulated by the motion of the oscillator. Coupling to harmonic oscillator produces additional Shapiro steps in $I-V$ characteristic of Josephson junction whose position is tuned by the frequency of the vibration mode. We also find a new velocity dependent term originating from the backaction of the ac Josephson current. This term is periodic in time and vanishes at zero bias voltage.

cond-mat.mes-hall↗
arXiv2002

Geometry and topological order in the non-relativistic Luttinger liquid

We demonstrate that the notion of spin-charge separation as follows from the Tomonaga-Luttinger theory of relativistic fermions does not suffice to completely specify the Luttinger liquid state associated with the fermions of condensed matter physics. The latter carries in addition a form of topological order which can be made visible using non-local correlation functions familiar from lattice gauge theory.

cond-mat.str-el↗
arXiv2002

Stripe fractionalization I: the generation of Ising local symmetry

This is part one in a series of two papers dedicated to the notion that the destruction of the topological order associated with stripe phases is about the simplest theory controlled by local symmetry: Ising gauge theory. This first part is intended to be a tutorial- we will exploit the simple physics of the stripes to vividly display the mathematical beauty of the gauge theory. Stripes, as they occur in the cuprates, are clearly `topological' in the sense that the lines of charges are at the same time domain walls in the antiferromagnet. Imagine that the stripes quantum melt so that all what seems to be around is a singlet superconductor. What if this domain wall-ness is still around in a delocalized form? This turns out to be exactly the kind of `matter' which is described by the Ising gauge theory. The highlight of the theory is the confinement phenomenon, meaning that when the domain wall-ness gives up it will do so in a meat-and-potato phase transition. We suggest that this transition might be the one responsible for the quantum criticality in the cuprates. In part two, we will become more practical, arguing that another phase is possible according to the theory. It might be that this quantum spin-nematic has already been observed in strongly underdoped LSCO.

cond-mat.supr-con↗
arXiv2002

Stripe fractionalization II: the quantum spin nematic and the Abrikosov lattice

In part (I) of this two paper series on stripe fractionalization, we argued that in principle the `domain wall-ness' of the stripe phase could persist in the spin and charge disordered superconductors, and we demonstrated how this physics is in one-to-one correspondence with Ising gauge theory. Here we focus on yet another type of order suggested by the gauge theory: the quantum spin nematic. Although it is not easy to measure this order directly, we argue that the superconducting vortices act as perturbations destroying the gauge symmetry locally. This turns out to give rise to a simple example of a gauge-theoretical phenomenon known as topological interaction. As a consequence, at any finite vortex density a globally ordered antiferromagnet emerges. This offers a potential explanation for recent observations in the underdoped 214 system.

cond-mat.supr-con↗
arXiv2001

An Exact Solution to a Three Dimensional Ising Model and Dimensional Reductions

A high temperature expansion is employed to map some complex anisotropic nonhermitian three and four dimensional Ising models with algebraic long range interactions into a solvable two dimensional variant. We also address the dimensional reductions for anisotropic two dimensional XY and other models. For the latter and related systems it is possible to have an effective reduction in the dimension without the need of compactifying some dimensions. Some solutions are presented. This framework further allows for some very simple general observations. It will be seen that the absence of a ``phase interference'' effect plays an important role in high dimensional problems. A very forbidding purely algebraic recursive series solution to the three dimensional nearest neighbor Ising model will be given. In the aftermath, the full-blown three dimensional nearest neighbor Ising model is exactly mapped onto a single spin 1/2 particle with nontrivial dynamics. All this allows for a formal high dimensional Bosonization.

hep-th↗
arXiv2001

Emergent Z_2 gauge symmetry and spin-charge separation in one dimensional physics

We demonstrate that in the scaling limit the phenomenon of spin-charge separation as encountered in Luttinger liquids defined on the lattice can be associated with the emergence of local Ising symmetry. This Z_2 gauge field is of geometrical nature (sublattice parity) and the Luttinger liquid corresponds with the critical point where the symmetry is on the verge of becoming local. We argue that in a true one dimensional superconductor the local symmetry will be fully realized as long as the geometrical structure associated with spin-charge separation is maintained.

cond-mat.str-el↗
arXiv2001

O(n) Spin Systems- Some General Properties: A Generalized Mermin-Wagner-Coleman Theorem, Ground States, Peierls Bounds, and Dynamics

Here we examine O(n) systems with arbitrary two spin interactions (of unspecified range) within a general framework. We shall focus on translationally invariant interactions. In the this case, we determine the ground states of the $O(n \ge 2)$ systems. We further illustrate how one may establish Peierls bounds for many Ising systems with long range interactions. We study the effect of thermal fluctuations on the ground states and derive the corresponding fluctuation integrals. The study of the thermal fluctuation spectra will lead us to discover a very interesting odd-even $n$ (coupling-decoupling) effect. We will prove a generalized Mermin-Wagner-Coleman theorem for all two dimensional systems (of arbitrary range) with analytic kernels in $k$ space. We will show that many three dimensional systems have smectic like thermodynamics. We will examine the topology of the ground state manifolds for both translationally invariant and spin glass systems. We conclude with a discussion of O(n) spin dynamics in the general case.

hep-th↗
arXiv2001

O(n) Spin Systems- Some General Properties: A Generalized Mermin-Wagner-Coleman Theorem, Ground States, Peierls Bounds, and Dynamics

Here we examine O(n) systems with arbitrary two spin interactions (of unspecified range) within a general framework. We shall focus on translationally invariant interactions. In the this case, we determine the ground states of the $O(n \ge 2)$ systems. We further illustrate how one may establish Peierls bounds for many Ising systems with long range interactions. We study the effect of thermal fluctuations on the ground states and derive the corresponding fluctuation integrals. The study of the thermal fluctuation spectra will lead us to discover a very interesting odd-even $n$ (coupling-decoupling) effect. We will prove a generalized Mermin-Wagner-Coleman (integral divergence) theorem for all translationally invariant interactions in two dimensions with an analytic kernel in momentum space. We will show that many three dimensional systems have smectic like thermodynamics. We will examine the topology of the ground state manifolds for both translationally invariant and spin glass systems. We conclude with a discussion of O(n) spin dynamics in the general case.

hep-ph↗
arXiv2001

Singular Fermi Liquids

An introductory survey of the theoretical ideas and calculations and the experimental results which depart from Landau Fermi-liquids is presented. Common themes and possible routes to the singularities leading to the breakdown of Landau Fermi liquids are categorized following an elementary discussion of the theory. Soluble examples of Singular Fermi liquids (often called Non-Fermi liquids) include models of impurities in metals with special symmetries and one-dimensional interacting fermions. A review of these is followed by a discussion of Singular Fermi liquids in a wide variety of experimental situations and theoretical models. These include the effects of low-energy collective fluctuations, gauge fields due either to symmetries in the hamiltonian or possible dynamically generated symmetries, fluctuations around quantum critical points, the normal state of high temperature superconductors and the two-dimensional metallic state. For the last three systems, the principal experimental results are summarized and the outstanding theoretical issues highlighted.

cond-mat.str-el↗