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Electric-magnetic duality or S-duality, extending the symmetry of Maxwell&rsquo, s equations by including the symmetry between Noether electric charges and topological magnetic monopoles, is one of the most fundamental concepts of modern physics. In two-dimensional systems harboring Cooper pairs, S-duality manifests in the emergence of superinsulation, a state dual to superconductivity, which exhibits an infinite resistance at finite temperatures. The mechanism behind this infinite resistance is the linear charge confinement by a magnetic monopole plasma. This plasma constricts electric field lines connecting the charge&ndash, anti-charge pairs into electric strings, in analogy to quarks within hadrons. However, the origin of the monopole plasma remains an open question. Here, we consider a two-dimensional Josephson junction array (JJA) and reveal that the magnetic monopole plasma arises as quantum instantons, thus establishing the underlying mechanism of superinsulation as two-dimensional quantum tunneling events. We calculate the string tension and the dimension of an electric pion determining the minimal size of a system capable of hosting superinsulation. Our findings pave the way for study of fundamental S-duality in desktop experiments on JJA and superconducting films.

Despite more than three decades of tireless efforts, the nature of high-temperature superconductivity (HTS) remains a mystery. A recently proposed long-distance effective field theory, accounting for all the universal features of HTS and the equally mysterious pseudogap phase, related them to the coexistence of a charge condensate with a condensate of dyons, particles carrying both magnetic and electric charges. Central to this picture are magnetic monopoles emerging in the proximity of the topological quantum superconductor-insulator transition (SIT) that dominates the HTS phase diagram. However, the mechanism responsible for spatially localized electron pairing, characteristic of HTS, remains a puzzle. Here we show that real-space, localized electron pairing is mediated by magnetic monopoles and occurs at temperatures well above the superconducting transition temperature $T_{\mathrm c}$. Localized electron pairing promotes the formation of superconducting granules connected by Josephson links. Global superconductivity sets in when these granules form an infinite cluster at $T_{\mathrm c}$ which is estimated to fall in the range from hundred to thousand Kelvins. Our findings pave the way to tailoring materials with elevated superconducting transition temperatures.

We provide a microscopic-level derivation of earlier results showing that in the critical vicinity of the superconductor-to-insulator transition (SIT), disorder and localization become negligible and the structure of the emergent phases is determined by topological effects arising from the competition between two quantum orders, superconductivity and superinsulation. We find that around the critical point the ground state is a composite incompressible quantum fluid of Cooper pairs and vortices coexisting with an intertwined Wigner crystal comprising the excesses of both types of excitations with respect to integer filling.

Despite decades-long efforts, magnetic monopoles were never found as elementary particles. Monopoles and associated currents were directly measured in experiments and identified as topological quasiparticle excitations in emergent condensed matter systems. These monopoles and the related electric-magnetic symmetry were restricted to classical electrodynamics, with monopoles behaving as classical particles. Here we show that the electric-magnetic symmetry is most fundamental and extends to full quantum behavior. We demonstrate that at low temperatures magnetic monopoles can form a quantum Bose condensate dual to the charge Cooper pair condensate in superconductors. The monopole Bose condensate manifests as a superinsulating state with infinite resistance, dual to superconductivity. Monopole supercurrents result in the electric analog of the Meissner effect and lead to linear confinement of Cooper pairs by Polyakov electric strings in analogy to quarks in hadrons., Comment: 6 pages, 2 figures

A low-temperature intervening metallic regime arising in the two-dimensional superconductor-insulator transition challenges our understanding of electronic fluids. Here we develop a gauge theory revealing that this emergent anomalous metal is a bosonic topological insulator where bulk transport is suppressed by mutual statistics interactions between out-of-condensate Cooper pairs and vortices and the longitudinal conductivity is mediated by symmetry-protected gapless edge modes. We explore the magnetic-field-driven superconductor-insulator transition in a niobium titanium nitride device and find marked signatures of a bosonic topological insulator behavior of the intervening regime with the saturating resistance. The observed superconductor-anomalous metal and insulator-anomalous metal dual phase transitions exhibit quantum Berezinskii-Kosterlitz-Thouless criticality in accord with the gauge theory., 10 pages, 5 figures

We consider a formal discretisation of Euclidean quantum gravity defined by a statistical model of random $3$-regular graphs and making using of the Ollivier curvature, a coarse analogue of the Ricci curvature. Numerical analysis shows that the Hausdorff and spectral dimensions of the model approach $1$ in the joint classical-thermodynamic limit and we argue that the scaling limit of the model is the circle of radius $r$, $S^1_r$. Given mild kinematic constraints, these claims can be proven with full mathematical rigour: speaking precisely, it may be shown that for $3$-regular graphs of girth at least $4$, any sequence of action minimising configurations converges in the sense of Gromov-Hausdorff to $S^1_r$. We also present strong evidence for the existence of a second-order phase transition through an analysis of finite size effects. This -- essentially solvable -- toy model of emergent one-dimensional geometry is meant as a controllable paradigm for the nonperturbative definition of random flat surfaces., Comment: Minor revisions

The key to unraveling the nature of high-temperature superconductivity (HTS) lies in resolving the enigma of the pseudogap state. The pseudogap state in the underdoped region is a distinct thermodynamic phase characterized by nematicity, temperature-quadratic resistive behavior, and magnetoelectric effects. Till present, a general description of the observed universal features of the pseudogap phase and their connection with HTS was lacking. The proposed work constructs a unifying effective field theory capturing all universal characteristics of HTS materials and explaining the observed phase diagram. The pseudogap state is established to be a phase where a charged magnetic monopole condensate confines Cooper pairs to form an oblique version of a superinsulator. The HTS phase diagram is dominated by a tricritical point (TCP) at which the first order transition between a fundamental Cooper pair condensate and a charged magnetic monopole condensate merges with the continuous superconductor-normal metal and superconductor-pseudogap state phase transitions. The universality of the HTS phase diagram reflects a unique topological mechanism of competition between the magnetic monopole condensate, inherent to antiferromagnetic-order-induced Mott insulators and the Cooper pair condensate. The obtained results establish the topological nature of the HTS and provide a platform for devising materials with the enhanced superconducting transition temperature.

The nature of hadrons is one of the most fundamental mysteries of physics. It is generally agreed that they are made of “colored” quarks, which move nearly free at short scales but are confined inside hadrons by strong interactions at large distances. Because of confinement, quarks are never directly observable and, experimentally, their properties can be tested only indirectly, via high energy collisions. Here we show that superinsulating films realize a complete, one-color model system of hadron physics with Cooper pairs playing the role of quarks. We report measurements on highly controlled NbTiN films that provide a window into the interior of "Cooper pair mesons" and present the first direct evidence of asymptotic freedom, ‘t Hooft’s dual superconductivity confinement mechanism, and magnetic monopoles. Quarks in the interior of hadrons make up most of ordinary matter, yet their observation is not possible, and their properties can only be probed indirectly. Adopting an analogy between physics of superinsulators and high energy physics, the authors present direct observations of the interior of electric mesons made of Cooper pairs by standard transport measurements.

We present a Euclidean quantum gravity model in which random graphs dynamically self-assemble into discrete manifold structures. Concretely, we consider a statistical model driven by a discretisation of the Euclidean Einstein-Hilbert action; contrary to previous approaches based on simplicial complexes and Regge calculus our discretisation is based on the Ollivier curvature, a coarse analogue of the manifold Ricci curvature defined for generic graphs. The Ollivier curvature is generally difficult to evaluate due to its definition in terms of optimal transport theory, but we present a new exact expression for the Ollivier curvature in a wide class of relevant graphs purely in terms of the numbers of short cycles at an edge. This result should be of independent intrinsic interest to network theorists. Action minimising configurations prove to be cubic complexes up to defects; there are indications that such defects are dynamically suppressed in the macroscopic limit. Closer examination of a defect free model shows that certain classical configurations have a geometric interpretation and discretely approximate vacuum solutions to the Euclidean Einstein-Hilbert action. Working in a configuration space where the geometric configurations are stable vacua of the theory, we obtain direct numerical evidence for the existence of a continuous phase transition; this makes the model a UV completion of Euclidean Einstein gravity. Notably, this phase transition implies an area-law for the entropy of emerging geometric space. Certain vacua of the theory can be interpreted as baby universes; we find that these configurations appear as stable vacua in a mean field approximation of our model, but are excluded dynamically whenever the action is exact indicating the dynamical stability of geometric space. The model is intended as a setting for subsequent studies of emergent time mechanisms., Comment: 26 pages, 9 figures, 2 appendices

We investigate the evolution of the electronic transport in disordered NbTiN films at the insulating side of the superconductor-insulator transition as function of the effective system size along the current direction. We demonstrate that both, the threshold voltage characterizing low-temperature superinsulating phase, and the Berezinskii-Kosterlitz-Thouless criticality of the conductance above the superinsulator critical temperature, vanish upon increasing disorder taking the system far from the disorder-driven superconductor-insulator transition. We find that decrease in the system’s effective size suppresses its insulating and superinsulating properties and that threshold voltage drops linearly with the diminishing system size. We demonstrate that this linear dependence can be used for experimental measurement of the linear tension of the electric string binding Cooper pairs and anti-Cooper pairs in a superinsulator.

We show that the nature of quantum phases around the superconductor-insulator transition (SIT) is controlled by charge-vortex topological interactions, and does not depend on the details of material parameters and disorder. We find three distinct phases, superconductor, superinsulator, and bosonic topological insulator. The superinsulator is a state of matter with infinite resistance in a finite temperature range, which is the S-dual of the superconductor and in which charge transport is prevented by electric strings binding charges of opposite sign. The electric strings ensuring linear confinement of charges are generated by instantons and are dual to superconducting Abrikosov vortices. Material parameters and disorder enter the London penetration depth of the superconductor, the string tension of the superinsulator and the quantum fluctuation parameter driving the transition between them. They are entirely encoded in four phenomenological parameters of a topological gauge theory of the SIT. Finally, we point out that, in the context of strong coupling gauge theories, the many-body localization phenomenon that is often referred to as an underlying mechanism for superinsulation is a mere transcription of the well-known phenomenon of confinement into solid-state physics language and is entirely driven by endogenous disorder embodied by instantons with no need of exogenous disorder.

It has been believed that the superinsulating state which is the low-temperature charge Berezinskii-Kosterlitz- Thouless (BKT) phase can exist only in two dimensions. We develop a general gauge description of the su- perinsulating state and the related deconfinement transition of Cooper pairs and predict the existence of the superinsulating state in three dimensions (3d). We find that 3d superinsulators exhibit Vogel-Fulcher-Tammann (VFT) critical behavior at the phase transition. This is the 3d string analogue of the Berezinski-Kosterlitz- Thouless (BKT) criticality for logarithmically and linearly interacting point particles in 2d. Our results show that singular exponential scaling behaviors of the BKT type are generic for phase transitions associated with the condensation of topological excitations., Comment: 5 pages, no figures

One of the most profound aspects of the standard model of particle physics, the mechanism of confinement binding quarks into hadrons, is not sufficiently understood. The only known semiclassical mechanism of confinement, mediated by chromo-electric strings in a condensate of magnetic monopoles still lacks experimental evidence. Here we show that the infinite resistance superinsulating state, which emerges on the insulating side of the superconductor-insulator transition in superconducting films offers a realization of confinement that allows for a direct experimental access. We find that superinsulators realize a single-color version of quantum chromodynamics and establish the mapping of quarks onto Cooper pairs. We reveal that the mechanism of superinsulation is the linear binding of Cooper pairs into neutral "mesons" by electric strings. Our findings offer a powerful laboratory for exploring and testing the fundamental implications of confinement, asymptotic freedom, and related quantum chromodynamics phenomena via desktop experiments on superconductors., Comment: Published version

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.

We present a new Higgsless model of superconductivity, inspired from anyon superconductivity but P- and T-invariant and generalizable to any dimension. While the original anyon superconductivity mechanism was based on incompressible quantum Hall fluids as average field states, our mechanism involves topological insulators as average field states. In D space dimensions it involves a (D-1)-form fictitious pseudovector gauge field which originates from the condensation of topological defects in compact low-energy effective BF theories. There is no massive Higgs scalar as there is no local order parameter. When electromagnetism is switched on, the photon acquires mass by the topological BF mechanism. Although the charge of the gapless mode (2) and the topological order (4) are the same as those of the standard Higgs model, the two models of superconductivity are clearly different since the origins of the gap, reflected in the high-energy sectors are totally different. In 2D this type of superconductivity is explicitly realized as global superconductivity in Josephson junction arrays. In 3D this model predicts a possible phase transition from topological insulators to Higgsless superconductors., Prepared for the proceedings of the XII Quark Confinement and the Hadron Spectrum, 29 August to 3 September 2016, Thessaloniki, Greece. arXiv admin note: substantial text overlap with arXiv:1408.5066

I propose a random network model governed by a Gaussian weight corresponding to Ising link antiferromagnetism as a model for emergent quantum space-time. In this model, discrete space is fundamental, not a regularization, its spectral dimension $d_s$ is not a model input but is, rather, completely determined by the antiferromagnetic coupling constant. Perturbative terms suppressing triangles and favouring squares lead to locally Euclidean ground states that are Ricci flat "large worlds" with power-law extension. I then consider the quenched graphs of lowest energy for $d_s=2$ and $d_s=3$ and I show how quenching leads to the spontaneous emergence of embedding spaces of Hausdorff dimension $d_H=4$ and $d_H=5$, respectively. One of the additional, spontaneous dimensions can be interpreted as time, causality being an emergent property that arises in the large $N$ limit (with $N$ the number of vertices). For $d_s=2$, the quenched graphs constitute a discrete version of a 5D-space-filling surface with a number of fundamental degrees of freedom scaling like $N^{2/5}$, a graph version of the holographic principle. These holographic degrees of freedom can be identified with the squares of the quenched graphs, which, being these triangle-free, are the fundamental area (or loop) quanta., To appear in Physical Review E

By establishing a relation between information erasure and continuous phase transitions we generalise the Landauer bound to analog computing systems. The entropy production per degree of freedom during erasure of an analog variable (reset to standard value) is given by the logarithm of the configurational volume measured in units of its minimal quantum. As a consequence every computation has to be carried on with a finite number of bits and infinite precision is forbidden by the fundamental laws of physics, since it would require an infinite amount of energy., 5 pages, no figures, to appear in Phys. Rev. E

Recently I proposed a simple dynamical network model for discrete space-time which self-organizes as a graph with Hausdorff dimension d_H=4. The model has a geometric quantum phase transition with disorder parameter (d_H-d_s) where d_s is the spectral dimension of the dynamical graph. Self-organization in this network model is based on a competition between a ferromagnetic Ising model for vertices and an antiferromagnetic Ising model for edges. In this paper I solve a toy version of this model defined on a bipartite graph in the mean field approximation. I show that the geometric phase transition corresponds exactly to the antiferromagnetic transition for edges, the dimensional disorder parameter of the former being mapped to the staggered magnetization order parameter of the latter. The model has a critical point with long-range correlations between edges, where a continuum random geometry can be defined, exactly as in Kazakov's famed 2D random lattice Ising model but now in any number of dimensions., Comment: To appear in Physical Review E

We review our models of quantum associative memories that represent the "quantization" of fully coupled neural networks like the Hopfield model. The idea is to replace the classical irreversible attractor dynamics driven by an Ising model with pattern-dependent weights by the reversible rotation of an input quantum state onto an output quantum state consisting of a linear superposition with probability amplitudes peaked on the stored pattern closest to the input in Hamming distance, resulting in a high probability of measuring a memory pattern very similar to the input. The unitary operator implementing this transformation can be formulated as a sequence of one-qubit and two-qubit elementary quantum gates and is thus the exponential of an ordered quantum Ising model with sequential operations and with pattern-dependent interactions, exactly as in the classical case. Probabilistic quantum memories, that make use of postselection of the measurement result of control qubits, overcome the famed linear storage limitation of their classical counterparts because they permit to completely {\it eliminate crosstalk and spurious memories}. The number of control qubits plays the role of an inverse fictitious temperature, the accuracy of pattern retrieval can be tuned by lowering the fictitious temperature under a critical value for quantum content association while the complexity of the retrieval algorithm remains polynomial for any number of patterns polynomial in the number of qubits. These models solve thus the capacity shortage problem of classical associative memories, providing a {\it polynomial improvement} in capacity. The price to pay is the probabilistic nature of information retrieval., Review article, 43 pages, 2 figures, to appear in "Quantum Computational Intelligence: Research and Applications", published by Elsevier

I propose a quantum gravity model in which the fundamental degrees of freedom are information bits for both discrete space-time points and links connecting them. The Hamiltonian is a very simple network model consisting of a ferromagnetic Ising model for space-time vertices and an antiferromagnetic Ising model for the links. As a result of the frustration between these two terms, the ground state self-organizes as a new type of low-clustering graph with finite Hausdorff dimension 4. The spectral dimension is lower than the Hausdorff dimension: it coincides with the Hausdorff dimension 4 at a first quantum phase transition corresponding to an IR fixed point while at a second quantum phase transition describing small scales space-time dissolves into disordered information bits. The large-scale dimension 4 of the universe is related to the upper critical dimension 4 of the Ising model. At finite temperatures the universe graph emerges without big bang and without singularities from a ferromagnetic phase transition in which space-time itself forms out of a hot soup of information bits. When the temperature is lowered the universe graph unfolds and expands by lowering its connectivity, a mechanism I have called topological expansion. The model admits topological black hole excitations corresponding to graphs containing holes with no space-time inside and with "Schwarzschild-like" horizons with a lower spectral dimension., Revised version, to appear in Physical Review D

I review and expand the model of quantum associative memory that I have recently proposed. In this model binary patterns of n bits are stored in the quantum superposition of the appropriate subset of the computational basis of n qbits. Information can be retrieved by performing an input-dependent rotation of the memory quantum state within this subset and measuring the resulting state. The amplitudes of this rotated memory state are peaked on those stored patterns which are closest in Hamming distance to the input, resulting in a high probability of measuring a memory pattern very similar to it. The accuracy of pattern recall can be tuned by adjusting a parameter playing the role of an effective temperature. This model solves the well-known capacity shortage problem of classical associative memories, providing a large improvement in capacity. PACS: 03.67.-a

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 $\theta $-term with value $\theta = \pi$, the constituents of this "meson" acquire spin 1/2 in this transition., Comment: 5 pages, no figures. arXiv admin note: substantial text overlap with arXiv:1112.3281

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", 5 pages, no figures

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., Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of paper also at http://www.physik.fu-berlin.de/~kleinert/kleiner_re276

We present a new Higgsless model of superconductivity, inspired from anyon superconductivity but P- and T-invariant and generalizable to any dimension. While the original anyon superconductivity mechanism was based on incompressible quantum Hall fluids as average field states, our mechanism involves topological insulators as average field states. In D space dimensions it involves a (D-1)-form fictitious pseudovector gauge field which originates from the condensation of topological defects in compact low-energy effective BF theories. In the average field approximation, the corresponding uniform emergent charge creates a gap for the (D-2)-dimensional branes via the Magnus force, the dual of the Lorentz force. One particular combination of intrinsic and emergent charge fluctuations that leaves the total charge distribution invariant constitutes an isolated gapless mode leading to superfluidity. The remaining massive modes organise themselves into a D-dimensional charged, massive vector. There is no massive Higgs scalar as there is no local order parameter. When electromagnetism is switched on, the photon acquires mass by the topological BF mechanism. Although the charge of the gapless mode (2) and the topological order (4) are the same as those of the standard Higgs model, the two models of superconductivity are clearly different since the origins of the gap, reflected in the high-energy sectors are totally different. In 2D this type of superconductivity is explicitly realized as global superconductivity in Josephson junction arrays. In 3D this model predicts a possible phase transition from topological insulators to Higgsless superconductors., Comment: 12 pages, no figures