| URL | Complex Replica zeros Ising Spin Glass zerotemeperature Ohuchi |
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| 摘要 | The quantum motion of N coupled kicked rotors is mapped to an interacting N-particle Anderson-Aubry-André tight-binding problem supporting many-body localised (MBL) phases. Interactions in configuration space are known to be insufficient for destroying Anderson localisation in a system in the MBL phase. The mapping we establish here predicts that a similar effect takes place in momentum space and determines the quantum dynamics of the coupled kicked rotors. Due to the boundedness of the Floquet quasi-energy spectrum there exists limitations on the interacting lattice models that can be mapped to quantum kicked rotors; in particular, no extensive observable can be mapped in the thermodynamic limit. |
| URL | Correlation functions 1d Fermi system Dzyaloshinskii Larkin |
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| 摘要 | The correlation functions (Green functions) are found for a one-dimensional system of Fermi particles with long-range interaction (Tomonaga model). It is shown that such a system does not behave like Fermi liquid since the Green function does not possess a pole and a "Fermi step" is absent from the momentum distribution of the particles. |
| URL | Dynamical Renormalization Group Approach Collective Swarms |
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| 摘要 | We study the critical behavior of a model with nondissipative couplings aimed at describing the collective behavior of natural swarms, using the dynamical renormalization group under a fixed-network approximation. At one loop, we find a crossover between an unstable fixed point, characterized by a dynamical critical exponent \(z=d/2\), and a stable fixed point with \(z=2\), a result we confirm through numerical simulations. The crossover is regulated by a length scale given by the ratio between the transport coefficient and the effective friction, so that in finite-size biological systems with low dissipation, dynamics is ruled by the unstable fixed point. In three dimensions this mechanism gives \(z=3/2\), a value significantly closer to the experimental window, \(1.0\leq z\leq1.3\), than the value \(z\simeq 2\) numerically found in fully dissipative models, either at or off equilibrium. This result indicates that nondissipative dynamical couplings are necessary to develop a theory of natural swarms fully consistent with experiments |
| URL | Dynamical scaling quenched disordered classical N-vector-model |
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| 摘要 | We revisit the effects of short-ranged random quenched disorder on the universal scaling properties of the classical N-vector model with cubic anisotropy. We set up the nonconserved relaxational dynamics of the model, and study the universal dynamic scaling near the second-order phase transition. We extract the critical exponents and the dynamic exponent in a one-loop dynamic renormalization group calculation with short-ranged isotropic disorder. We show that the dynamics near a critical point is generically slower when the quenched disorder is relevant than when it is not, independent of whether the pure model is isotropic or cubic anisotropic. We demonstrate the surprising thresholdless instability of the associated universality class due to perturbations from rotational invariance breaking quenched disorder-order parameter coupling, indicating breakdown of dynamic scaling. We speculate that this may imply a novel first-order transition in the model, induced by a symmetry breaking disorder. |
| URL | Flocking,herds,shools——a quantative theory of flocking |
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| 摘要 | We present a quantitative continuum theory of "flocking": the collective coherent motion of large numbers of self-propelled organisms. In agreement with everyday experience, our model predicts the existence of an "ordered phase" of flocks, in which all members of even an arbitrarily large flock move together with the same mean velocity \(\langle\vec{v}\rangle\neq0\). This coherent motion of the flock is an example of spontaneously broken symmetry: no preferred direction for the motion is picked out a priori in the model; rather, each flock is allowed to, and does, spontaneously pick out some completely arbitrary direction to move in. By analyzing our model we can make detailed, quantitative predictions for the long-distance, long-time behavior of this "broken symmetry state." The "Goldstone modes" associated with this "spontaneously broken rotational symmetry" are fluctuations in the direction of motion of a large part of the flock away from the mean direction of motion of the flock as a whole. These "Goldstone modes" mix with modes associated with conservation of bird number to produce propagating sound modes. These sound modes lead to enormous fluctuations of the density of the flock, far larger, at long wavelengths, than those in, e.g., an equilibrium gas. Our model is similar in many ways to the Navier-Stokes equations for a simple compressible fluid; in other ways, it resembles a relaxational time-dependent Ginsburg-Landau theory for an n=d component isotropic ferromagnet. In spatial dimensions d> 4, the long-distance behavior is correctly described by a linearized theory, and is equivalent to that of an unusual but nonetheless equilibrium model for spin systems. For d < 4, nonlinear fluctuation effects radically alter the long distance behavior, making it different from that of any known equilibrium model. In particular, we find that in d=2, where we can calculate the scaling exponents exactly, flocks exhibit a true, long-range ordered, spontaneously broken symmetry state, in contrast to equilibrium systems, which cannot spontaneously break a continuous symmetry in d=2 ~ (the "Mermin-Wagner" theorem). We make detailed predictions for various correlation functions that could be measured either in simulations, or by quantitative imaging of real flocks. We also consider an anisotropic model, in which the birds move preferentially in an "easy" ~ (e.g., horizontal) plane, and make analogous, but quantitatively different, predictions for that model as well. For this anisotropic model, we obtain exact scaling exponents for all spatial dimensions, including the physically relevant case d=3 |
| URL | Functional integral bosonization an impurity luttinger liquid |
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| 摘要 | We use a functional integral formalism developed earlier for the pure Luttinger liquid(LL) to find an exact representation for the electron Green function of the LL in the presence of a single backscattering impurity in the low-temperature limit. This allows us to reproduce results(well known from the bosonization techniques) for the suppression of the electron local density of states (LDOS) at the position of the impurity and for the Friedel oscillations at finite temperature. In addition, we have extracted from the exact representation an analytic dependence of LDOS on the distance from the impurity and shown how it crosses over to that for the pure LL |
| URL | Graphene via large-N renormalization disorder foster |
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| 摘要 | We analyze the competing effects of moderate to strong Coulomb electron-electron interactions and weak quenched disorder in graphene. Using a one-loop renormalization group calculation controlled within the large-N approximation, we demonstrate that, at successively lower energy (temperature or chemical potential) scales, a type of non-Abelian vector potential disorder always asserts itself as the dominant elastic scattering mechanism for generic short-ranged microscopic defect distributions. Vector potential disorder is tied to both elastic lattice deformations (“ripples”) and topological lattice defects. We identify several well-defined scaling regimes, for which we provide scaling predictions for the electrical conductivity and thermopower, valid when the inelastic life time due to interactions exceeds the elastic lifetime due to disorder. Coulomb interaction effects should figure strongly into the physics of suspended graphene films, where \(r_s\) > 1; we expect vector potential disorder to play an important role in the description of transport in such films. |
| URL | Infinity number of order parameters spin glasses |
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| 摘要 | This Letter shows that in the mean-field approximation spin-glasses must be described by an infinite number of order parameters in the framework of the replica theory. |
| URL | Kunyang-many body instability coulomb interacting bilayer graphene |
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| 摘要 | Low-energy electronic structure of (unbiased and undoped) bilayer graphene consists of two Fermi points with quadratic dispersions if trigonal warping is ignored. We show that short-range (or screened Coulomb) interactions are marginally relevant and use renormalization group to study their effects on low-energy properties of the system. We find that the two quadratic Fermi points spontaneously split into four Dirac points. This results in a nematic state that spontaneously breaks the sixfold lattice rotation symmetry ( combined with layer permutation) down to a twofold one, with a finite transition temperature. Critical properties of the transition and effects of trigonal warping are also discussed |
| URL | PT-symmetric quantum-critical phenomena-Ueda |
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| 摘要 | Synthetic non-conservative systems with parity-time (PT) symmetric gain–loss structures can exhibit unusual spontaneous symmetry breaking that accompanies spectral singularity. Recent studies on PT symmetry in optics and weakly interacting open quantum systems have revealed intriguing physical properties, yet many-body correlations still play no role. Here by extending the idea of PT symmetry to strongly correlated many-body systems, we report that a combination of spectral singularity and quantum criticality yields an exotic universality class which has no counterpart in known critical phenomena. Moreover, we find unconventional low-dimensional quantum criticality, where superfluid correlation is anomalously enhanced owing to non-monotonic renormalization group flows in a PT-symmetry-broken quantum critical phase, in stark contrast to the Berezinskii–Kosterlitz–Thouless paradigm. Our findings can be experimentally tested in ultracold atoms and predict critical phenomena beyond the Hermitian paradigm of quantum many-body physics |
| URL | \(QED_3\) with quenched disorder quantum critical states with interactions disorders |
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| 摘要 | quantum electrodynamics in 2+1dimensions(\(QED_3\)) is a strongly coupled conformal field theory(CFT) of a U(1) gauge field coupled to 2N two-component massless fermions.The \(N=2\) CFT has been proposed as a ground state of the spin\(-1/2\) kagome heisenberg antiferromagnet. We study \(QED_3\) in the presence of weak quenched disorder in its two spatial directions.When the disorder explicitly breaks the fermion flavor symmetry from \(SU(2N)\rightarrow U(1)\times SU(N)\) but preserves time-reversal symmetry, we find that the theory flows to a non-trivial fixed line at non-zero disorder with a continuously varying dynamical critical exponent z>1.We determine the zero-temperature flavor(spin) conductivity along the critical line.Our calculations are performed in the large-N limit,and the disorder is handled using the replica method. |
| URL | Replica symmetry breaking and nature spin glass phase-Parisi |
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| 摘要 | A probability distribution has been proposed recently by one of us as an order parameter for spin glasses. We show that this probability depends on the particular realization of the couplings even in the thermodynamic limit, and we study its distribution. We also show that the space of states has an ultrametric topology. |
| URL | renormalization group and critical phenomena.I.Renormalization Group and the Kadanoff scaling picture |
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| 摘要 | The Kadanoff theory of scaling near the critical point fox an Ising ferromagnet is cast in differential form. The resulting differential equations are an example of the differential equations of the renormalization group. It is shown that the Widom-Kadanoff scaling laws arise naturally from these differential equations if the coefficients in the equations are analytic at the critical point. A generalization of the Kadanoff scaling picture involving an "irrelevant" variable is considered;in this case the scaling laws result from the renormalization-group equations only if the solution of the equations goes asymptotically to a fixed point. |
| URL | the renormalization group flow in field theories with quenched disorder |
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| 摘要 | In this paper we analyze the renormalization group(RG)flow of field theories with quenched disorder, in which the couplings vary randomly in space. We analyze both classical(Euclidean) disorder and quantum disorder, emphasizing general properties rather than specific cases. The RG flow of the disorder-averaged theories takes place in the space of their coupling constants and also in the space of distributions for the disordered couplings, and the two mix together. We write down a generalization of the Callan-Symanzik equation for the flow of disorder-averaged correlation functions. We find that local operators can mix with the response of the theory to local changes in the disorder distribution, and that the generalized Callan-Symanzik equation mixes the disorder averages of several different correlation functions. For classical disorder we show that this can lead to new types of anomalous dimensions and to logarithmic behavior at fixed points. For quantum disorder we find that the RG flow always generates a rescaling of time relative to space, which at a fixed point generically leads to Lifshitz scaling. The dynamical scaling exponent z behaves as an anomalous dimension(as in other nonrelativistic RG flows), and we compute it at leading order in perturbation theory in the disorder for a general theory. Our results agree with a previous perturbative computation by Boyanovsky and Cardy, and with a holographic disorder computation of Hartnoll and Santos. We also find in quantum disorder that local operators mix with non-local(in time)operators under the RG, and that there are critical exponents associated with the disorder distribution that have not previously been discussed. In large N theories the disorder averages may be computed exactly, and we verify that they are consistent with the generalized Callan-Symanzik equations |
| URL | Renormalization,vortices,and symmetry-breaking perturbations in the two-dimensional planar model |
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| 摘要 | The classical planar Heisenberg model is studied at low temperatures by means of renormalization theory and a series of exact transformations. A numerical study of the Migdal recursion relation suggests that models with short-range isotropic interactions rapidly become equivalent to a simplified model system proposed by Villain. A series of exact transformations then allows us to treat the Villain model analytically at low temperatures. To lowest order in a parameter which becomes exponentially small with decreasing temperature, we reproduce results obtained previously by Kosterlitz. We also examine the effect of symmetry-breaking crystalline fields on the isotropic planar model. A numerical study of the Migdal recursion scheme suggests that these fields(which must occur in real quasi-two-dimensional crystals)are strongly relevant variables,leading to critical behavior distinct from that found for the planar model.However, a more exact low-temperature treatment of the Villain model shows that hexagonal crystalline fields eventually become irrelevant at temperatures below the\(T_c\) of the isotropic model. Isotropic planar critical behavior should be experimentally accessible in this case.Nonuniversal behavior may result if cubic crystalline fields dominate the symmetry breaking. Interesting duality transformations, which aid in the analysis of symmetry-breaking fields are also discussed. |
| URL | Spin-I ladder:a bosonization study |
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| 摘要 | We construct a field-theoretic description of two coupled spin-1 Heisenberg chains, starting with the known representation of a single spin-1 chain in terms of Majorana fermions(or ising models).After reexamining the bosonization rules for two Ising models, taking particular care of order and disorder operators, we obtain a bosonic description of the spin-1 ladder. From renormalization-group and mean-field arguments, we conclude that, for a small interchain coupling, the spin-1 ladder is approximately described by three decoupled, two frequency sine-Gordon models. We then predict that, starting with decoupled chains, the spin gap decreases linearly with interchain coupling, in both the ferromagnetic and antiferromagnetic directions. Finally, we discuss the possibility of an incommensurate phase in the spin-1 zigzag chain. |
| URL | Renormalization group approach to two-dimensional coulomb interacting dirac fermions with random gauge potential |
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| 摘要 | We argue that massless Dirac particles in two spatial dimensions with 1/r Coulomb repulsion and quenched random gauge field are described by a manifold of fixed points which can be accessed perturbatively in disorder and interaction strength, thereby confirming and extending the results of Herbut, Juricic, and Vafek [arXiv:0707.4171(unpublished)]At small interaction and small randomness, there is an infrared stable fixed curve which merges with the strongly interacting infrared unstable line at a critical endpoint, along which the dynamical critical exponent z=1. |
| URL | Witten-Nonabelian bosonization in 2D |
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| 摘要 | A non-abelian generalization of the usual formulas for bosonization of fermions in 1 + 1 dimensions is presented. Any fermi theory in 1 +1 dimensions is equivalent to a local bose theory which manifestly possesses all the symmetries of the fermi theory |
| URL | Dissipative Luttinger Liquids |
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| 摘要 | We investigate a one dimensional quantum fluid coupled to a dissipative bath. The quantum fluid is captured by the canonical Luttinger liquid; the bath is given by the model of Caldeira and Leggett, i.e. a tower of oscillators coupled linearly to the fluid density, ρ. The bath can be integrated out exactly, producing an effective interaction for the fluid that is nonlocal in time; we argue that the form corresponding to Ohmic dissipation is generic. Compared to previous works, we compute correlation functions for this minimal model without approximation, including at finite temperature T > 0. From these and a Kubo calculation, we conclude that arbitrary dissipation destroys the perfect conductivity of the Luttinger liquid via Zeno localization, even in the absence of a spatial potential; from RG analysis of harmonic terms, we also find that the open Luttinger liquid is significantly more prone to localization by such potentials, in contrast to the usual intuition that baths make systems less localized. |
| URL | Introduction GL phase transitions nonequilibrium patterns |
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| 摘要 | This paper presents an introduction to phase transitions and critical phenomena on the one hand, and nonequilibrium patterns on the other, using the Ginzburg-Landau theory as a unified language. In the first part, mean-field theory is presented, for both statics and dynamics, and its validity tested self-consistently. As is well known, the mean-field approximation breaks down below four spatial dimensions, where it can be replaced by a scaling phenomenology. The Ginzburg-Landau formalism can then be used to justify the phenomenological theory using the renormalization group, which elucidates the physical and mathematical mechanism for universality. In the second part of the paper it is shown how near pattern forming linear instabilities of dynamical systems, a formally similar Ginzburg-Landau theory can be derived for nonequilibrium macroscopic phenomena. The real and complex Ginzburg-Landau equations thus obtained yield nontrivial solutions of the original dynamical system, valid near the linear instability. Examples of such solutions are plane waves, defects such as dislocations or spirals, and states of temporal or spatiotemporal (extensive) chaos. |
| URL | Kondo effect with Wilson fermions-PRD |
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| 摘要 | We investigate the Kondo effect with Wilson fermions. This is based on a mean-field approach for the chiral Gross-Neveu model including four-point interactions between a light Wilson fermion and a heavy fermion. For massless Wilson fermions, we demonstrate the appearance of the Kondo effect. We point out that there is a coexistence phase with both the light-fermion scalar condensate and Kondo condensate, and the critical chemical potentials of the scalar condensate are shifted by the Kondo effect. For negative-mass Wilson fermions, we find that the Kondo effect is favored near the parameter region realizing the Aoki phase. Our findings will be useful for understanding the roles of heavy impurities in Dirac semimetals, topological insulators, and lattice simulations. |
| URL | Landauer conductance of Luttinger liquids with leads |
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| 摘要 | We show that the dc conductance of a quantum wire containing a Luttinger liquid and attached to noninteracting leads is given by e ih per spin orientation, regardless of the interactions in the wire. This explains the recent observations of the absence of conductance renormalization in long high-mobility GaAs wires by Tarucha, Honda, and Saku [Solid State Commun. 94, 413 (1995)]. |
| URL | The Luther-Emery liquid: Spin gap and anomalous flux period |
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| 摘要 | We study the dependence of the ground state energy on an applied Aharonov-Bohm flux F for the Luttinger model with large momentum scattering. Employing the method of finite size bosonization, we show that for systems with a spin gap but with gapless charge degrees of freedom, the ground state energy has an exact period of hc/2e, i.e., half a flux quantum, in the limit of large system size L. Finite size corrections are found to vanish exponentially in L. This behavior is contrasted to that of the spin gapless case, for both even and odd particle number. Generalizations to finite temperature are also discussed. |
| URL | Nonequilibrium dynamics of random field Ising spin chains: Exact results via real space renormalization group |
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| 摘要 | The nonequilibrium dynamics of classical random Ising spin chains with nonconserved magnetization are studied using an asymptotically exact real space renormalization group(RSRG).We focus on random field ising model(RFIM) spin chains with and without a uniform applied field, as well as on Ising spin glass chains in an applied field. For the RFIM we consider a universal regime where the random field and the temperature are both much smaller than the exchange coupling. In this regime, the Imry-Ma length that sets the scale of the equilibrium correlations is large and the coarsening of domains from random initial conditions(e.g.,a quench from high temperature) occurs over a wide range of length scales. The two types of domain walls that occur diffuse in opposite random potentials, of the form studied by Sinai, and domain walls annihilate when they meet. Using the RSRG we compute many universal asymptotic properties of both the nonequilibrium dynamics and the equilibrium limit. We find that the configurations of the domain walls converge rapidly toward a set of system-specific time-dependent positions that are independent of the initial conditions. Thus the behavior of this nonequilibrium system is pseudodeterministic at long times because of the broad distributions of barriers that occur on the long length scales involved. Specifically, we obtain the time dependence of the energy, the magnetization, and the distribution of domain sizes(found to be statistically independent). The equilibrium limits agree with known exact results. We obtain the exact scaling form of the two-point equal time correlation function\(\langle\bar{S_0(t)S_x(t)}\rangle\) and the two-time autocorrelations \(\langle\bar{S_0(t')S_0(t)}\rangle\). We also compute the persistence properties of a single spin, of local magnetization, and of domains. The analogous quantities for the 6 J Ising spin glass in an applied field are obtained from the RFIM via a gauge transformation. In addition to these we compute the two-point two-time correlation function\(\bar{\langle S_0(t)S_x(t)\rangle\langle S_0(t')S_x(t')\rangle}\)which can in principle be measured by experiments on spin-glass-like systems. The thermal fluctuations are studied and found to be dominated by rare events; in particular all moments of truncated equal time correlations are computed. Physical properties which are typically measured in aging experiments are also studied, focusing on the response to a small magnetic field which is applied after waiting for the system to equilibrate for a time\(t_w\).The nonequilibrium fluctuation-dissipation ratio \(X(t,t_w)\) is computed.We find that for\(t-t_w\sim t_w^{\alpha}\) with \(\alpha<1\), the ratio equal to its equilibrium value \(X=1\), although time translational invariance does not hold in this regime. For \(t-t_w\sim t_w\)the ratio exhibits an aging regime with a nontrivial \(X=X(t/t_w)\neq1\), but the behavior is markedly different from mean field theory. Finally the distribution of the total magnetization and of the number of domains is computed for large finite size systems. General issues about convergence toward equilibrium and the possibilities of weakly history-dependent t evolution in other random systems are discussed. |
| URL | Renormalization group and stability in the exciton Bose liquid |
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| 摘要 | The exciton Bose liquid (EBL) is a hypothesized phase of bosons in 2+1D which possesses a dispersion that is gapless along the coordinate axes in momentum space. The low energy theory of the EBL involves modes on all length scales, extending all the way down to the lattice spacing. In this paper, we discuss a renormalization group scheme that can be used to address the stability of this and related phases of matter. We find that, in the absence of an extensively large symmetry group, realizing the simplest formulation of the EBL always requires fine-tuning. However, we also argue that the addition of certain marginal interactions can be used to realize a stable phase, without the need for fine-tuning. A simple generalization to 3+1D is also discussed. |
| URL | Solution of 'Solvable model of a spin glass' |
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| 摘要 | The Sherrington-Kirkpatrick model of a spin glass is solved by a mean field technique which is probably exact in the limit of infinite range interactions. At and above\(T_c\) the solution is identical to that obtained by Sherrington and Kirkpatrick (1975) using the\(n\rightarrow0\)replica method, but below\(T_c\) the new result exhibits several differences and remains physical down to\(T=0\) |
| URL | Spin glasses: Experimental facts, theoretical concepts,and open questions |
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| 摘要 | This review summarizes recent developments in the theory of spin glasses, as well as pertinent experimental data. The most characteristic properties of spin glass systems are described, and related phenomena in other glassy systems (dielectric and orientational glasses) are mentioned. The Edwards-Anderson model of spin glasses and its treatment within the replica method and mean-field theory are outlined, and concepts such as "frustration, " "broken replica symmetry, " "broken ergodicity, " etc., are discussed. The dynamic approach to describing the spin glass transition is emphasized. Monte Carlo simulations of spin glasses and the insight gained by them are described. Other topics discussed include site-disorder models, phenomenological theories for the frozen phase and its excitations, phase diagrams in which spin glass order and ferromagnetism or antiferromagnetism compete, the Neel model of superparamagnetism and related approaches, and possible connections between spin glasses and other topics in the theory of disordered condensed matter systems. |
| URL | Thermopower of an infinite Luttinger liquid |
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| 摘要 | The thermopower of a Luttinger liquid(LL), originating from the energy dispersion of electrons at the Fermi level and/or from the backscattering of electrons by impurities, is analytically evaluated. It is shown that in both cases the thermopower is described by a corresponding Fermi-liquid formula renormalized by an interaction-dependent factor. For an infinite LL the renormalization coefficients decrease with an increase of the electron-electron interaction. In a realistic situation, when a LL wire is connected to leads of noninteracting electrons, the dispersion-induced thermopower in the limit of strong repulsive interaction is strongly suppressed, \(S_W^{(d)}\sim g^2S_0^{(d)}<< S_0^{(d)}\)(here \(S_0^{(d)}\)is the corresponding Fermi-liquid value for the thermopower and \(g<<1\) is the LL correlation parameter), , while the impurity-induced thermopower \(S_W^{(i)}\sim S_0^{(i)}/g\) is enhanced by the interelectron interaction |
| URL | Thouless-Anderson-Palmer equations for neural networks |
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| 摘要 | Previous derivation of the Thouless-Anderson-Palmer(TAP) equations for the Hopfield model by the cavity method yielded results that were inconsistent with those of the perturbation theory as well as the results derived by the replica theory of the model. Here we present a derivation of the TAP equation for the Hopfield model by the cavity method and show that it agrees with the form derived by perturbation theory. We also use the cavity method to derive TAP equations for the pseudoinverse neural network model. These equations are consistent with the results of the replica theory of these models. |
| URL | Tunneling into a Finite Luttinger Liquid Coupled to Noisy Capacitive Leads |
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| 摘要 | Tunneling spectroscopy of one-dimensional interacting wires can be profoundly sensitive to the boundary conditions of the wire. Here, we analyze the tunneling spectroscopy of a wire coupled to capacitive metallic leads. Strikingly, with increasing many-body interactions in the wire, the impact of the boundary noise becomes more prominent. This interplay allows for a smooth crossover from standard 1D tunneling signatures into a regime where the tunneling is dominated by the fluctuations at the leads. This regime is characterized by an elevated zero-bias tunneling alongside a universal power-law decay at high energies. Furthermore, local tunneling measurements in this regime show a unique spatial dependence that marks the formation of plasmonic standing waves in the wire. Our result offers a tunable method by which to control the boundary effects and measure the interaction strength(Luttinger parameter)within the wire. |
| URL | \(Z_4\)parafermions in Weakly Interacting Superconducting Constrictions at the Helical Edge of Quantum Spin Hall Insulators |
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| 摘要 | Parafermions are generalizations of Majorana fermions that may appear in interacting topological systems. They are known to be powerful building blocks of topological quantum computers. Existing proposals for realizations of parafermions typically rely on strong electronic correlations which are hard to achieve in the laboratory. We identify a novel physical system in which parafermions generically develop. It is based on a quantum constriction formed by the helical edge states of a quantum spin Hall insulator in the vicinity of an ordinary s-wave superconductor. Interestingly, our analysis suggests that \(Z_4\)4 parafermions are emerging bound states in this setup in the weakly interacting regime. Furthermore, we identify a situation in which Majorana fermions and parafermions can coexist. |