Dynamic crossover in the global persistence at criticality

We investigate the global persistence properties of critical systems relaxing from an initial state with non-vanishing value of the order parameter (e.g., the magnetization in the Ising model). The persistence probability of the global order parameter displays two consecutive regimes in which it decays algebraically in time with two distinct universal exponents. The associated crossover is controlled by the initial value m_0 of the order parameter and the typical time at which it occurs diverges as m_0 vanishes. Monte-Carlo simulations of the two-dimensional Ising model with Glauber dynamics display clearly this crossover. The measured exponent of the ultimate algebraic decay is in rather good agreement with our theoretical predictions for the Ising universality class.Comment: 5 pages, 2 figure

Critical thermodynamics of two-dimensional N-vector cubic model in the five-loop approximation

The critical behavior of the two-dimensional N-vector cubic model is studied within the field-theoretical renormalization-group (RG) approach. The beta-functions and critical exponents are calculated in the five-loop approximation, RG series obtained are resummed using Pade-Borel-Leroy and conformal mapping techniques. It is found that for N = 2 the continuous line of fixed points is well reproduced by the resummed RG series and an account for the five-loop terms makes the lines of zeros of both beta-functions closer to each another. For N > 2 the five-loop contributions are shown to shift the cubic fixed point, given by the four-loop approximation, towards the Ising fixed point. This confirms the idea that the existence of the cubic fixed point in two dimensions under N > 2 is an artifact of the perturbative analysis. In the case N = 0 the results obtained are compatible with the conclusion that the impure critical behavior is controlled by the Ising fixed point.Comment: 18 pages, 4 figure

Observations Outside the Light-Cone: Algorithms for Non-Equilibrium and Thermal States

We apply algorithms based on Lieb-Robinson bounds to simulate time-dependent and thermal quantities in quantum systems. For time-dependent systems, we modify a previous mapping to quantum circuits to significantly reduce the computer resources required. This modification is based on a principle of "observing" the system outside the light-cone. We apply this method to study spin relaxation in systems started out of equilibrium with initial conditions that give rise to very rapid entanglement growth. We also show that it is possible to approximate time evolution under a local Hamiltonian by a quantum circuit whose light-cone naturally matches the Lieb-Robinson velocity. Asymptotically, these modified methods allow a doubling of the system size that one can obtain compared to direct simulation. We then consider a different problem of thermal properties of disordered spin chains and use quantum belief propagation to average over different configurations. We test this algorithm on one dimensional systems with mixed ferromagnetic and anti-ferromagnetic bonds, where we can compare to quantum Monte Carlo, and then we apply it to the study of disordered, frustrated spin systems.Comment: 19 pages, 12 figure

Correlations in an expanding gas of hard-core bosons

We consider a longitudinal expansion of a one-dimensional gas of hard-core bosons suddenly released from a trap. We show that the broken translational invariance in the initial state of the system is encoded in correlations between the bosonic occupation numbers in the momentum space. The correlations are protected by the integrability and exhibit no relaxation during the expansion

Entanglement properties of quantum spin chains

We investigate the entanglement properties of a finite size 1+1 dimensional Ising spin chain, and show how these properties scale and can be utilized to reconstruct the ground state wave function. Even at the critical point, few terms in a Schmidt decomposition contribute to the exact ground state, and to physical properties such as the entropy. Nevertheless the entanglement here is prominent due to the lower-lying states in the Schmidt decomposition.Comment: 5 pages, 6 figure

Zero dimensional area law in a gapless fermion system

The entanglement entropy of a gapless fermion subsystem coupled to a gapless bulk by a "weak link" is considered. It is demonstrated numerically that each independent weak link contributes an entropy proportional to lnL, where L is linear dimension of the subsystem.Comment: 6 pages, 11 figures; added 3d computatio

Frustrated magnets in three dimensions: a nonperturbative approach

Frustrated magnets exhibit unusual critical behaviors: they display scaling laws accompanied by nonuniversal critical exponents. This suggests that these systems generically undergo very weak first order phase transitions. Moreover, the different perturbative approaches used to investigate them are in conflict and fail to correctly reproduce their behavior. Using a nonperturbative approach we explain the mismatch between the different perturbative approaches and account for the nonuniversal scaling observed.Comment: 7 pages, 1 figure. IOP style files included. To appear in Journal of Physics: Condensed Matter. Proceedings of the conference HFM 2003, Grenoble, Franc

Field-theory results for three-dimensional transitions with complex symmetries

We discuss several examples of three-dimensional critical phenomena that can be described by Landau-Ginzburg-Wilson $\phi^4$ theories. We present an overview of field-theoretical results obtained from the analysis of high-order perturbative series in the frameworks of the $\epsilon$ and of the fixed-dimension d=3 expansions. In particular, we discuss the stability of the O(N)-symmetric fixed point in a generic N-component theory, the critical behaviors of randomly dilute Ising-like systems and frustrated spin systems with noncollinear order, the multicritical behavior arising from the competition of two distinct types of ordering with symmetry O($n_1$) and O($n_2$) respectively.Comment: 9 pages, Talk at the Conference TH2002, Paris, July 200

Entanglement entropy of two disjoint intervals in c=1 theories

We study the scaling of the Renyi entanglement entropy of two disjoint blocks of critical lattice models described by conformal field theories with central charge c=1. We provide the analytic conformal field theory result for the second order Renyi entropy for a free boson compactified on an orbifold describing the scaling limit of the Ashkin-Teller (AT) model on the self-dual line. We have checked this prediction in cluster Monte Carlo simulations of the classical two dimensional AT model. We have also performed extensive numerical simulations of the anisotropic Heisenberg quantum spin-chain with tree-tensor network techniques that allowed to obtain the reduced density matrices of disjoint blocks of the spin-chain and to check the correctness of the predictions for Renyi and entanglement entropies from conformal field theory. In order to match these predictions, we have extrapolated the numerical results by properly taking into account the corrections induced by the finite length of the blocks to the leading scaling behavior.Comment: 37 pages, 23 figure

Harmonic crossover exponents in O(n) models with the pseudo-epsilon expansion approach

We determine the crossover exponents associated with the traceless tensorial quadratic field, the third- and fourth-harmonic operators for O(n) vector models by re-analyzing the existing six-loop fixed dimension series with pseudo-epsilon expansion. Within this approach we obtain the most accurate theoretical estimates that are in optimum agreement with other theoretical and experimental results.Comment: 12 pages, 1 figure. Final version accepted for publicatio