The critical behavior of 2-d frustrated spin models with noncollinear order

We study the critical behavior of frustrated spin models with noncollinear order in two dimensions, including antiferromagnets on a triangular lattice and fully frustrated antiferromagnets. For this purpose we consider the corresponding $O(N) \times O(2)$ Landau-Ginzburg-Wilson (LGW) Hamiltonian and compute the field-theoretic expansion to four loops and determine its large-order behavior. We show the existence of a stable fixed point for the physically relevant cases of two- and three-component spin models. We also give a prediction for the critical exponent $\eta$ which is $\eta =0.24(6)$ and $\eta =0.29(5)$ for N=3 and 2 respectively.Comment: 11 pages, 8 figure

Ageing Properties of Critical Systems

In the past few years systems with slow dynamics have attracted considerable theoretical and experimental interest. Ageing phenomena are observed during this ever-lasting non-equilibrium evolution. A simple instance of such a behaviour is provided by the dynamics that takes place when a system is quenched from its high-temperature phase to the critical point. The aim of this review is to summarize the various numerical and analytical results that have been recently obtained for this case. Particular emphasis is put to the field-theoretical methods that can be used to provide analytical predictions for the relevant dynamical quantities. Fluctuation-dissipation relations are discussed and in particular the concept of fluctuation-dissipation ratio (FDR) is reviewed, emphasizing its connection with the definition of a possible effective temperature. The Renormalization-Group approach to critical dynamics is summarized and the scaling forms of the time-dependent non-equilibrium correlation and response functions of a generic observable are discussed. From them the universality of the associated FDR follows as an amplitude ratio. It is then possible to provide predictions for ageing quantities in a variety of different models. In particular the results for Model A, B, and C dynamics of the O(N) Ginzburg-Landau Hamiltonian, and Model A dynamics of the weakly dilute Ising magnet and of a \phi^3 theory, are reviewed and compared with the available numerical results and exact solutions. The effect of a planar surface on the ageing behaviour of Model A dynamics is also addressed within the mean-field approximation.Comment: rvised enlarged version, 72 Pages, Topical Review accepted for publication on JP

Unusual Corrections to Scaling in Entanglement Entropy

We present a general theory of the corrections to the asymptotic behaviour of the Renyi entropies which measure the entanglement of an interval A of length L with the rest of an infinite one-dimensional system, in the case when this is described by a conformal field theory of central charge c. These can be due to bulk irrelevant operators of scaling dimension x>2, in which case the leading corrections are of the expected form L^{-2(x-2)} for values of n close to 1. However for n>x/(x-2) corrections of the form L^{2-x-x/n} and L^{-2x/n} arise and dominate the conventional terms. We also point out that the last type of corrections can also occur with x less than 2. They arise from relevant operators induced by the conical space-time singularities necessary to describe the reduced density matrix. These agree with recent analytic and numerical results for quantum spin chains. We also compute the effect of marginally irrelevant bulk operators, which give a correction (log L)^{-2}, with a universal amplitude. We present analogous results for the case when the interval lies at the end of a semi-infinite system.Comment: 15 pages, no figure

Two-loop Critical Fluctuation-Dissipation Ratio for the Relaxational Dynamics of the O(N) Landau-Ginzburg Hamiltonian

The off-equilibrium purely dissipative dynamics (Model A) of the O(N) vector model is considered at criticality in an $\epsilon = 4- d > 0$ up to O($\epsilon^2$). The scaling behavior of two-time response and correlation functions at zero momentum, the associated universal scaling functions, and the nontrivial limit of the fluctuation-dissipation ratio are determined in the aging regime.Comment: 21 pages, 6 figures. Discussion enlarged and two figures added. Final version accepted for publication in Phys. Rev.

Correlation functions of one-dimensional anyonic fluids

A universal description of correlation functions of one-dimensional anyonic gapless systems in the low-momentum regime is presented. We point out a number of interesting features, including universal oscillating terms with frequency proportional to the statistical parameter and beating effects close to the fermion points. The results are applied to the one-dimensional anyonic Lieb-Liniger model and checked against the exact results in the impenetrable limit.Comment: 4 pages, 1 figur

Entanglement entropy and conformal field theory

We review the conformal field theory approach to entanglement entropy. We show how to apply these methods to the calculation of the entanglement entropy of a single interval, and the generalization to different situations such as finite size, systems with boundaries, and the case of several disjoint intervals. We discuss the behaviour away from the critical point and the spectrum of the reduced density matrix. Quantum quenches, as paradigms of non-equilibrium situations, are also considered.Comment: 39 Pages, 10 figures. Review article for the special issue "Entanglement entropy in extended systems" in J. Phys. A. V2 Refs added, typos correcte

Entanglement Entropy and Quantum Field Theory

We carry out a systematic study of entanglement entropy in relativistic quantum field theory. This is defined as the von Neumann entropy S_A=-Tr rho_A log rho_A corresponding to the reduced density matrix rho_A of a subsystem A. For the case of a 1+1-dimensional critical system, whose continuum limit is a conformal field theory with central charge c, we re-derive the result S_A\sim(c/3) log(l) of Holzhey et al. when A is a finite interval of length l in an infinite system, and extend it to many other cases: finite systems,finite temperatures, and when A consists of an arbitrary number of disjoint intervals. For such a system away from its critical point, when the correlation length \xi is large but finite, we show that S_A\sim{\cal A}(c/6)\log\xi, where \cal A is the number of boundary points of A. These results are verified for a free massive field theory, which is also used to confirm a scaling ansatz for the case of finite-size off-critical systems, and for integrable lattice models, such as the Ising and XXZ models, which are solvable by corner transfer matrix methods. Finally the free-field results are extended to higher dimensions, and used to motivate a scaling form for the singular part of the entanglement entropy near a quantum phase transition.Comment: 33 pages, 2 figures. Our results for more than one interval are in general incorrect. A note had been added discussing thi

Aging and fluctuation-dissipation ratio for the diluted Ising Model

We consider the out-of-equilibrium, purely relaxational dynamics of a weakly diluted Ising model in the aging regime at criticality. We derive at first order in a $\sqrt{\epsilon}$ expansion the two-time response and correlation functions for vanishing momenta. The long-time limit of the critical fluctuation-dissipation ratio is computed at the same order in perturbation theory.Comment: 4 pages, 2 figure

The KPZ equation with flat initial condition and the directed polymer with one free end

We study the directed polymer (DP) of length $t$ in a random potential in dimension 1+1 in the continuum limit, with one end fixed and one end free. This maps onto the Kardar-Parisi-Zhang growth equation in time $t$, with flat initial conditions. We use the Bethe Ansatz solution for the replicated problem which is an attractive bosonic model. The problem is more difficult than the previous solution of the fixed endpoint problem as it requires regularization of the spatial integrals over the Bethe eigenfunctions. We use either a large fixed system length or a small finite slope KPZ initial conditions (wedge). The latter allows to take properly into account non-trivial contributions, which appear as deformed strings in the former. By considering a half-space model in a proper limit we obtain an expression for the generating function of all positive integer moments $\bar{Z^n}$ of the directed polymer partition function. We obtain the generating function of the moments of the DP partition sum as a Fredholm Pfaffian. At large time, this Fredholm Pfaffian, valid for all time $t$, exhibits convergence of the free energy (i.e. KPZ height) distribution to the GOE Tracy Widom distributionComment: 62 page

Multicritical behavior in frustrated spin systems with noncollinear order

We investigate the phase diagram and, in particular, the nature of the the multicritical point in three-dimensional frustrated $N$-component spin models with noncollinear order in the presence of an external field, for instance easy-axis stacked triangular antiferromagnets in the presence of a magnetic field along the easy axis. For this purpose we study the renormalization-group flow in a Landau-Ginzburg-Wilson \phi^4 theory with symmetry O(2)x[Z_2 +O(N-1)] that is expected to describe the multicritical behavior. We compute its MS \beta functions to five loops. For N\ge 4, their analysis does not support the hypothesis of an effective enlargement of the symmetry at the multicritical point, from O(2) x [Z_2+O(N-1)] to O(2)xO(N). For the physically interesting case N=3, the analysis does not allow us to exclude the corresponding symmetry enlargement controlled by the O(2)xO(3) fixed point. Moreover, it does not provide evidence for any other stable fixed point. Thus, on the basis of our field-theoretical results, the transition at the multicritical point is expected to be either continuous and controlled by the O(2)xO(3) fixed point or to be of first order.Comment: 28 pages, 3 fig