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Register a new userNon-integrable fermionic chains near criticality
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We compute the Drude weight and the critical exponents as functions of the density in non-integrable generalizations of XXZ or Hubbard chains, in the critical zero temperature regime where Luttinger liquid description breaks down and Bethe ansatz cannot be used. Even in the regions where irrelevant terms dominate, no difference between integrable and non integrable models appear in exponents and conductivity. Our results are based on a fully rigorous two-regime multiscale analysis and a recently introduced partially solvable model.
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We derive the dominant contribution to the large-distance decay of correlation functions for a spin chain model that exhibits both Haldane and Neel phases in its ground state phase diagram. The analytic results are obtained by means of an approximate mapping between a spin-1 anisotropic Hamiltonian onto a fermionic model of noninteracting Bogolioubov quasiparticles related in turn to the XY spin-1/2 chain in a transverse field. This approach allows us to express the spin-1 string operators in terms of fermionic operators so that the dominant contribution to the string correlators at large distances can be computed using the technique of Toeplitz determinants. As expected, we find long-range string order both in the longitudinal and in the transverse channel in the Haldane phase, while in the Neel phase only the longitudinal order survives. In this way, the long-range string order can be explicitly related to the components of the magnetization of the XY model. Moreover, apart from the critical line, where the decay is algebraic, we find that in the gapped phases the decay is governed by an exponential tail multiplied by algebraic factors. As regards the usual two points correlation functions, we show that the longitudinal one behaves in a dual fashion with respect to the transverse string correlator, namely both the asymptotic values and the decay laws exchange when the transition line is crossed. For the transverse spin-spin correlator, we find a finite characteristic length which is an unexpected feature at the critical point. We also comment briefly the entanglement features of the original system versus those of the effective model. The goodness of the approximation and the analytical predictions are checked versus density-matrix renormalization group calculations.
Superdiffusive finite-temperature transport has been recently observed in a variety of integrable systems with nonabelian global symmetries. Superdiffusion is caused by giant Goldstone-like quasiparticles stabilized by integrability. Here, we argue that these giant quasiparticles remain long-lived, and give divergent contributions to the low-frequency conductivity $sigma(omega)$, even in systems that are not perfectly integrable. We find, perturbatively, that $ sigma(omega) sim omega^{-1/3}$ for translation-invariant static perturbations that conserve energy, and $sigma(omega) sim | log omega |$ for noisy perturbations. The (presumable) crossover to regular diffusion appears to lie beyond low-order perturbation theory. By contrast, integrability-breaking perturbations that break the nonabelian symmetry yield conventional diffusion. Numerical evidence supports the distinction between these two classes of perturbations.
We investigate integrable fermionic models within the scheme of the graded Quantum Inverse Scattering Method, and prove that any symmetry imposed on the solution of the Yang-Baxter Equation reflects on the constants of motion of the model; generalizations with respect to known results are discussed. This theorem is shown to be very effective when combined with the Polynomial $Rc$-matrix Technique (PRT): we apply both of them to the study of the extended Hubbard models, for which we find all the subcases enjoying several kinds of (super)symmetries. In particular, we derive a geometrical construction expressing any $gl(2,1)$-invariant model as a linear combination of EKS and U-supersymmetric models. Furtherly, we use the PRT to obtain 32 integrable $so(4)$-invariant models. By joint use of the Sutherlands Species technique and $eta$-pairs construction we propose a general method to derive their physical features, and we provide some explicit results.
Recent experiments have indicated that many biological systems self-organise near their critical point, which hints at a common design principle. While it has been suggested that information transmission is optimized near the critical point, it remains unclear how information transmission depends on the dynamics of the input signal, the distance over which the information needs to be transmitted, and the distance to the critical point. Here we employ stochastic simulations of a driven 2D Ising system and study the instantaneous mutual information and the information transmission rate between a driven input spin and an output spin. The instantaneous mutual information varies non-monotonically with the temperature, but increases monotonically with the correlation time of the input signal. In contrast, the information transmission rate exhibits a maximum as a function of the input correlation time. Moreover, there exists an optimal temperature that maximizes this maximum information transmission rate. It arises from a tradeoff between the necessity to respond fast to changes in the input so that more information per unit amount of time can be transmitted, and the need to respond to reliably. The optimal temperature lies above the critical point, but moves towards it as the distance between the input and output spin is increased.
We study self-organisation of collective motion as a thermodynamic phenomenon, in the context of the first law of thermodynamics. It is expected that the coherent ordered motion typically self-organises in the presence of changes in the (generalised) internal energy and of (generalised) work done on, or extracted from, the system. We aim to explicitly quantify changes in these two quantities in a system of simulated self-propelled particles, and contrast them with changes in the systems configuration entropy. In doing so, we adapt a thermodynamic formulation of the curvatures of the internal energy and the work, with respect to two parameters that control the particles alignment. This allows us to systematically investigate the behaviour of the system by varying the two control parameters to drive the system across a kinetic phase transition. Our results identify critical regimes and show that during the phase transition, where the configuration entropy of the system decreases, the rates of change of the work and of the internal energy also decrease, while their curvatures diverge. Importantly, the reduction of entropy achieved through expenditure of work is shown to peak at criticality. We relate this both to a thermodynamic efficiency and the significance of the increased order with respect to a computational path. Additionally, this study provides an information-geometric interpretation of the curvature of the internal energy as the difference between two curvatures: the curvature of the free entropy, captured by the Fisher information, and the curvature of the configuration entropy.
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