Latest Papers in Condensed Matter Physics

Statistical Mechanics

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Subdiffusive front scaling in interacting integrable models (1810.08227v3)

Vir B. Bulchandani, Christoph Karrasch

2018-10-18

We show that any interacting integrable model possesses a class of initial states for which the leading corrections to ballistic transport are subdiffusive rather than diffusive. These initial states are natural to realize experimentally and include the domain wall initial condition that has been the object of much recent scrutiny. Upon performing numerical matrix product state simulations in the spin- XXZ chain, we find that such states can exhibit subdiffusive scaling of fronts of spin, energy and entanglement entropy across the entire range of anisotropies. This demonstrates that Tracy-Widom scaling is not incompatible with model interactions, as was previously believed.

On the scaling behaviour of the alternating spin chain (1903.05033v1)

Vladimir V. Bazhanov, Gleb A. Kotousov, Sergii M. Koval, Sergei L. Lukyanov

2019-03-12

In this note we report the results of our study of a 1D integrable spin chain whose critical behaviour is governed by a CFT possessing a continuous spectrum of scaling dimensions. It is argued that the computation of the density of Bethe states of the continuous theory can be reduced to the calculation of the connection coefficients for a certain class of differential equations whose monodromy properties are similar to those of the conventional confluent hypergeometric equation. The finite size corrections to the scaling are also discussed.

Desynchronization dynamics of the Kuramoto model on connectome graphs (1903.00385v2)

Géza Ódor, Jeffrey Kelling

2019-03-01

The time dependent behavior of the Kuramoto model, describing synchronization, has been studied numerically on small-world graphs. We determined the desynchronziation behavior, by solving this model via the 4th order Runge-Kutta algorithm on a large, weighted human connectome network and compared the results with those of a two-dimensional lattice, with additional random, long-range links. In the latter case a mean-field critical transition is expected and here we provide numerical results for the synchonization/desynchonization duration distributions. We find power-law tails, characterized by a critical exponent . In case of the connectome we assumed a homeostatic state, by the application of normalized incoming weights. Since this graph has a topological dimension a real synchronization phase transition is not possible in the thermodynamic limit, still we could locate a transition between partially synchronized and desynchronized states. At this crossover point we observe power-law--tailed desynchronization durations, with , away from experimental values for the brain. Additionally, we changed the signs of outgoing weights of 20% of randomly selected nodes, to mimic a model with inhibitory interactions. In this case the at the crossover point we found , which is in the range of human brain experiments.

Spectrum of anomalous dimensions in hypercubic theories (1903.04950v1)

Oleg Antipin, Jahmall Bersini

2019-03-12

We compute the spectrum of anomalous dimensions of non-derivative composite operators with an arbitrary number of fields in the vector model with cubic anisotropy at the one-loop order in the -expansion. The complete closed-form expression for the anomalous dimensions of the operators which do not undergo mixing effects is derived and the structure of the general solution to the mixing problem is outlined. As examples, the full explicit solution for operators with up to fields is presented and a sample of the OPE coefficients is calculated. The main features of the spectrum are described, including an interesting pattern pointing to the deeper structure.

Partial Isometries, Duality, and Determinantal Point Processes (1903.04945v1)

Makoto Katori, Tomoyuki Shirai

2019-03-12

A determinantal point process (DPP) is an ensemble of random nonnegative-integer-valued Radon measures on a space with measure , whose correlation functions are all given by determinants specified by an integral kernel called the correlation kernel. We consider a pair of Hilbert spaces, , which are assumed to be realized as -spaces, , , and introduce a bounded linear operator and its adjoint . We prove that if both of and are partial isometries and both of and are of locally trace class, then we have unique pair of DPPs, , , which satisfy useful duality relations. We assume that admits an integral kernel on , and give practical setting of which makes and satisfy the above conditions. In order to demonstrate that the class of DPPs obtained by our method is large enough to study universal structures in a variety of DPPs, we show many examples of DPPs in one-, two-, and higher-dimensional spaces , where several types of weak convergence from finite DPPs to infinite DPPs are given. One-parameter () series of infinite DPPs on and are discussed, which we call the Euclidean and the Heisenberg families of DPPs, respectively, following the terminologies of Zelditch.

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