1,721,175 research outputs found
Entanglement entropy and quantum field theory: A non-technical introduction
No full textWe give a pedagogical and non-technical introduction to the quantum field theory approach to entanglement entropy. Particular attention is devoted to the one space dimensional case, with a linear dispersion relation, that, at a quantum critical point, can be effectively described by a two-dimensional conformal field theory
Entanglement entropy and quantum field theory
No full textWe develop a systematic method to extract the negativity in the ground state of a 1+1 dimensional relativistic quantum field theory, using a path integral formalism to construct the partial transpose ρAT 2 of the reduced density matrix of a subsystem A=A 1A 2, and introducing a replica approach to obtain its trace norm which gives the logarithmic negativity E=lnρAT 2. This is shown to reproduce standard results for a pure state. We then apply this method to conformal field theories, deriving the result E∼(c/4)ln[ 12/( 1+ 2)] for the case of two adjacent intervals of lengths 1, 2 in an infinite system, where c is the central charge. For two disjoint intervals it depends only on the harmonic ratio of the four end points and so is manifestly scale invariant. We check our findings against exact numerical results in the harmonic chain. © 2012 American Physical Society
Quantum quenches in extended systems
No full textWe study in general the time evolution of correlation functions in a extended quantum system after the quench of a parameter in the Hamiltonian. We show that correlation functions in d dimensions can be extracted using methods of boundary critical phenomena in d+1 dimensions. For d ≤ 1 this allows us to use the powerful tools of conformal field theory in the case of critical evolution. Several results are obtained in generic dimension in the Gaussian (mean field) approximation. These predictions are checked against the real time evolution of some solvable models that allow us also to understand which features are valid beyond the critical evolution. All our findings may be explained in terms of a picture generally valid, whereby quasiparticles, entangled over regions of the order of the correlation length in the initial state, then propagate with a finite speed through the system. Furthermore we show that the long time results can be interpreted in terms of a generalized Gibbs ensemble. We discuss some open questions and possible future developments. © IOP Publishing Ltd
Entanglement and correlation functions following a local quench: a conformal field theory approach
No full textWe show that the dynamics resulting from preparing a one-dimensional quantum system in the ground state of two decoupled parts, then joined together and left to evolve unitarily with a translational invariant Hamiltonian (a local quench), can be described by means of quantum field theory. In the case when the corresponding theory is conformal, we study the evolution of the entanglement entropy for different bipartitions of the line. We also consider the behavior of one-and two-point correlation functions. All our findings may be explained in terms of a picture, that we believe to be valid more generally, whereby quasiparticles emitted from the joining point at the initial time propagate semiclassically through the system. © IOP Publishing Ltd
Evolution of entanglement entropy in one-dimensional systems
No full textWe study the unitary time evolution of the entropy of entanglement of a one-dimensional system between the degrees of freedom in an interval of length l and its complement, starting from a pure state which is not an eigenstate of the Hamiltonian. We use path integral methods of quantum field theory as well as explicit computations for the transverse Ising spin chain. In both cases, there is a maximum speed v of propagation of signals. In general the entanglement entropy increases linearly with time t up to t = l/2v, after which it saturates at a value proportional to l, the coefficient depending on the initial state. This behaviour may be understood as a consequence of causality
Entanglement Hamiltonians in two-dimensional conformal field theory
Full text linkWe enumerate the cases in 2d conformal field theory where the logarithm of the reduced density matrix (the entanglement or modular hamiltonian) may be written as an integral over the energy-momentum tensor times a local weight. These include known examples and new ones corresponding to the time-dependent scenarios of a global and local quench. In these latter cases the entanglement hamiltonian depends on the momentum density as well as the energy density. In all cases the entanglement spectrum is that of the appropriate boundary CFT. We emphasize the role of boundary conditions at the entangling surface and the appearance of boundary entropies as universal O(1) terms in the entanglement entropy. ArXI
Universal amplitude ratios of two-dimensional percolation from field theory
No full textWe complete the determination of the universal amplitude ratios of two-dimensional percolation within the two-kink approximation of the form factor approach. For the cluster size ratio, which has for a long time been elusive both theoretically and numerically, we obtain the value 160.2, in good agreement with the lattice estimate 162.5 +/- 2 of Jensen and Ziff
The field theory of the q -> 4(+) Potts model
No full textThe q-state Potts model in two dimensions exhibits a first-order transition for q > 4. As q → 4+ the correlation length at this transition diverges. We argue that this limit defines a massive integrable quantum field theory whose lowest excitations are kinks connecting 4 + 1 degenerate ground states. We construct the S-matrix of this theory and the two-particle form factors, and hence estimate a number of universal amplitude ratios. These are in very good agreement with the results of extrapolated series in q(-1/2) as well as Monte Carlo results for q = 5. (C) 2000 Elsevier Science B.V
Entanglement entropy of two disjoint intervals in conformal field theory: II
Full text linkWe continue the study of the entanglement entropy of two disjoint intervals in conformal field theories that we started in Calabrese et al 2009 J. Stat. Mech. P11001. We compute Tr ρnA for any integer n for the Ising universality class and the final result is expressed as a sum of Riemann-Siegel theta functions. These predictions are checked against existing numerical data. We provide a systematic method that gives the full asymptotic expansion of the scaling function for small four-point ratio (i.e. short intervals). These formulas are compared with the direct expansion of the full results for a free compactified boson and Ising model. We finally provide the analytic continuation of the first term in this expansion in a completely analytic form. © 2011 IOP Publishing Ltd and SISSA
UNIVERSAL PROPERTIES OF SELF-AVOIDING WALKS FROM 2-DIMENSIONAL FIELD-THEORY
No full textWe use the recently conjectured exact S-matrix of the massive O(n) model to derive its form factors and ground state energy. This information is then used in the limit n → 0 to obtain quantitative results for various universal properties of self-avoiding chains and loops. In particular, we give the first theoretical prediction of the amplitude ratio C/D which relates the mean square end-to-end distance of chains to the mean square radius of gyration of closed loops. This agrees with the results from lattice enumeration studies to within their errors, and gives strong support for the various assumptions which enter into the field theoretic derivation. In addition, we obtain results for the scaling function of the structure factor of long loops, and for various amplitude ratios measuring the shape of self-avoiding chains. These quantities are all related to moments of correlation functions which are evaluated as a sum over m-particle intermediate states in the corresponding field theory. We show that in almost all cases, the restriction to m ≤ 2 gives results which are accurate to at least one part in 103. This remarkable fact is traced to a softening of the m > 2 branch cuts relative to their behaviour based on phase space arguments alone, a result which follows from the threshold behaviour of the two-body S-matrix, S(O) = -1. Since this is a general property of interacting 2D field theories, it suggests that similar approximation may well hold for other models. However, we also study the moments of the area of self-avoiding loops, and show that, in this case, the two-particle approximation is not valid. © 1993
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