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C. A. Trugenberger

Publications and source records attributed to C. A. Trugenberger.

At least 37 records · Page 2Linked to original sources
arXiv2018

Combinatorial Quantum Gravity: Emergence of Geometric Space from Random Graphs

We review and extend the recently proposed model of combinatorial quantum gravity. Contrary to previous discrete approaches, this model is defined on (regular) random graphs and is driven by a purely combinatorial version of Ricci curvature, the Ollivier curvature, defined on generic metric spaces equipped with a Markov chain. It dispenses thus of notions such as simplicial complexes and Regge calculus and is ideally suited to extend quantum gravity to combinatorial structures which have a priori nothing to do with geometry. Indeed, our results show that geometry and general relativity emerge from random structures in a second-order phase transition due to the condensation of cycles on random graphs, a critical point that defines quantum gravity non-perturbatively according to asymptotic safety. In combinatorial quantum gravity the entropy area law emerges naturally as a consequence of infinite-dimensional critical behaviour on networks rather than on lattices. We propose thus that the entropy area law is a signature of the random graph nature of space-(time) on the smallest scales.

hep-th↗
arXiv2018

Gauge Topological Nature of the Superconductor-Insulator Transition

It has long been believed that, at absolute zero, electrons can form only one quantum coherent state, a superconductor. Yet, several two dimensional superconducting systems were found to harbor the superinsulating state with infinite resistance, a mirror image of superconductivity, and a metallic state often referred to as Bose metal, characterized by finite longitudinal and vanishing Hall resistances. The nature of these novel and mysterious quantum coherent states is the subject of intense study.Here, we propose a topological gauge description of the superconductor-insulator transition (SIT) that enables us to identify the underlying mechanism of superinsulation as Polyakov's linear confinement of Cooper pairs via instantons. We find a criterion defining conditions for either a direct SIT or for the SIT via the intermediate Bose metal and demonstrate that this Bose metal phase is a Mott topological insulator in which the Cooper pair-vortex liquid is frozen by Aharonov-Bohm interactions.

cond-mat.supr-con↗
arXiv2017

Topological Network Entanglement as Order Parameter for the Emergence of Geometry

We show that, in discrete models of quantum gravity, emergent geometric space can be viewed as the entanglement pattern in a mixed quantum state of the "universe", characterized by a universal topological network entanglement. As a concrete example we analyze the recently proposed model in which geometry emerges due to the condensation of 4-cycles in random regular bipartite graphs, driven by the combinatorial Ollivier-Ricci curvature. Using this model we show that the emergence of geometric order decreases the entanglement entropy of random configurations. The lowest geometric entanglement entropy is realized in four dimensions.

hep-th↗
arXiv2014

Generalized Landauer Bound as Universal Thermodynamic Entropy in Continuous Phase Transitions

The classic Landauer bound can be lowered when erasure errors are permitted. Here we point out that continuous phase transitions characterized by an order parameter can also be viewed as information erasure by resetting a certain number of bits to a standard value. The information-theoretic expression for the generalized Landauer bound in terms of error probability implies thus a universal form for the thermodynamic entropy in the partially ordered phase. We explicitly show that the thermodynamic entropy as a function of interaction parameters and temperature is identical to the information-theoretic expression in terms of error probability alone in the specific example of the Hopfield neural network model of associative memory, a distributed information-processing system of many interacting stochastic bits. In this framework the Landauer bound sets a lower limit for the work associated with "remembering" rather than "forgetting"

cond-mat.dis-nn↗
arXiv2014

Spin-Charge Soldering from Tensor Higgs mechanism

Spin-charge separation, a crucial ingredient in 2D models of strongly correlated systems, in mostly considered in condensed matter applications. In this paper we present a relativistic field-theoretic model in which charged particles of spin 1/2 emerge by soldering spinless charges and magnetic vortices in a confinement quantum phase transition modelled as a tensor Higgs mechanism. The model involves two gauge fields, a vector one and a two-form gauge field interacting by the topological BF term. When this tensor gauge symmetry is spontaneously broken charges are soldered to the ends of magnetic vortices and thus confined by a linear potential. If the vector potential has a topological $θ$-term with value $θ= π$, the constituents of this "meson" acquire spin 1/2 in this transition.

hep-th↗
arXiv2011

The Fate of the Photon in Topological Matter: Superconductivity, Confinement and the Vortex Quantum Hall Effect

Topological matter is characterized by the presence of a topological BF term in its long-distance effective action. Topological defects due to the compactness of the U(1) gauge fields induce quantum phase transitions between topological insulators, topological superconductors and topological confinement. In conventional superconductivity, due to spontaneous symmetry breaking, the photon acquires a mass due to the Anderson-Higgs mechanism. In this paper we derive the corresponding effective actions for the electromagnetic field in topological superconductors and topological confinement phases. In topological superconductors magnetic flux is confined and the photon acquires a topological mass through the BF mechanism: no symmetry breaking is involved, the ground state has topological order and the transition is induced by quantum fluctuations. In topological confinement, instead, electric charge is linearly confined and the photon becomes a massive antisymmetric tensor via the Stückelberg mechanism. Oblique confinement phases arise when the string condensate carries both magnetic and electric flux (dyonic strings). Such phases are characterized by a vortex quantum Hall effect potentially relevant for the dissipationless transport of information stored on vortices.

cond-mat.str-el↗
arXiv2010

SU(m) non-Abelian anyons in the Jain hierarchy of quantum Hall states

We show that different classes of topological order can be distinguished by the dynamical symmetry algebra of edge excitations. Fundamental topological order is realized when this algebra is the largest possible, the algebra of quantum area-preserving diffeomorphisms, called $W_{1+\infty}$. We argue that this order is realized in the Jain hierarchy of fractional quantum Hall states and show that it is more robust than the standard Abelian Chern-Simons order since it has a lower entanglement entropy due to the non-Abelian character of the quasi-particle anyon excitations. These behave as SU($m$) quarks, where $m$ is the number of components in the hierarchy. We propose the topological entanglement entropy as the experimental measure to detect the existence of these quantum Hall quarks. Non-Abelian anyons in the $ν= 2/5$ fractional quantum Hall states could be the primary candidates to realize qbits for topological quantum computation.

cond-mat.str-el↗
arXiv2008

Topological Order in Frustrated Josephson Junction Arrays

We show that electrically and magnetically frustrated Josephson junction arrays (JJAs) realize topological order with a non-trivial ground state degeneracy on manifolds with non-trivial topology. The low-energy theory has the same gauge dynamics of the unfrustrated JJAs but for different, "fractional" degrees of freedom, a principle reminescent of Jain's composite electrons in the fractional quantum Hall effect.

cond-mat.str-el↗
arXiv2007

Superconductors with Topological Order and their Realization in Josephson Junction Arrays

We will describe a new superconductivity mechanism, proposed by the authors in [1], which is based on a topologically ordered ground state rather than on the usual Landau mechanism of spontaneous symmetry breaking. Contrary to anyon superconductivity it works in any dimension and it preserves P-and T-invariance. In particular we will discuss the low-energy effective field theory, what would be the Landau-Ginzburg formulation for conventional superconductors.

hep-th↗
arXiv2005

Superconductors with Topological Order

We propose a mechanism of superconductivity in which the order of the ground state does not arise from the usual Landau mechanism of spontaneous symmetry breaking but is rather of topological origin. The low-energy effective theory is formulated in terms of emerging gauge fields rather than a local order parameter and the ground state is degenerate on topologically non-trivial manifolds. The simplest example of this mechanism of superconductivty is concretely realized as global superconductivty in Josephson junction arrays.

hep-th↗
arXiv2002

Confining Strings at High Temperature

We show that the high-temperature behaviour of the recently proposed confining strings reproduces exactly the correct large-N QCD result, for a large class of truncations of the long-range interaction between surface elements.

hep-th↗
arXiv2002

QCD-Like Behaviour of High-Temperature Confining Strings

We show that, contrary to previous string models, the high-temperature behaviour of the recently proposed confining strings reproduces exactly the correct large-N QCD result, a {\it necessary} condition for any string model of confinement.

hep-th↗
arXiv1999

Universality Class of Confining Strings

A recently proposed model of confining strings has a non-local world-sheet action induced by a space-time Kalb-Ramond tensor field. Here we show that, in the large-D approximation, an infinite set of ghost- and tachyon-free truncations of the derivative expansion of this action all lead to c=1 models. Their infrared limit describes smooth strings with world-sheets of Hausdorff dimension D_H=2 and long-range orientational order, as expected for QCD strings.

hep-th↗
arXiv1999

Floppy Membranes

Floppy membranes are tensionless surfaces without extrinsic stiffness, whose fluctuations are governed by fourth-order bending elasticity. This suppresses spiky superstructures and ensures that floppy membranes remain smooth over any distance, with Hausdorff dimension D=2, in contrast to surfaces with stiffness, which are rough on the scale of some finite persistence length.

cond-mat↗
arXiv1998

Strings with Negative Stiffness and Hyperfine Structure

We propose a new string model by adding a higher-order gradient term to the rigid string, so that the stiffness can be positive or negative without loosing stability. In the large-D approximation, the model has three phases, one of which with a new type of generalized "antiferromagnetic" orientational correlations. We find an infrared-stable fixed point describing world-sheets with vanishing tension and Hausdorff dimension D_H=2. Crumpling is prevented by the new term which suppresses configurations with rapidly changing extrinsic curvature.

hep-th↗
arXiv1998

Smoothening Transition of Rough Surfactant Surfaces

We propose a model for surfaces in mixtures of oil, water and surfactants with strong electric dipoles. The dipole interactions give rise to a non-local interaction with negative stiffness between surface elements. We show that, for large space dimension D, this model has a phase transition from rough to smooth surfaces. Contrary to models with a simple quadratic curvature energy of positive sign, which always have a finite persistence length typical of rough surfaces, the smooth surfaces in our model exhibit long-range correlations of a generalized antiferromagnetic type. These correlations might be related to the recently observed "egg carton" superstructure of membranes.

cond-mat.soft↗
arXiv1997

Surfaces with Long-Range Correlations from Non-Critical Strings

We show that the recently proposed confining string theory describes smooth surfaces with long-range correlations for the normal components of tangent vectors. These long-range correlations arise as a consequence of a "frustrated antiferromagnetic" interaction whose two main features are non-locality and a negative stiffness.

hep-th↗