An Example of Poincare Symmetry with a Central Charge

We discuss a simple system which has a central charge in its Poincare algebra. We show that this system is exactly solvable after quantization and that the algebra holds without anomalies.Comment: 11 pages, Revte

Two-spin entanglement distribution near factorized states

We study the two-spin entanglement distribution along the infinite $S=1/2$ chain described by the XY model in a transverse field; closed analytical expressions are derived for the one-tangle and the concurrences $C_r$, $r$ being the distance between the two possibly entangled spins, for values of the Hamiltonian parameters close to those corresponding to factorized ground states. The total amount of entanglement, the fraction of such entanglement which is stored in pairwise entanglement, and the way such fraction distributes along the chain is discussed, with attention focused on the dependence on the anisotropy of the exchange interaction. Near factorization a characteristic length-scale naturally emerges in the system, which is specifically related with entanglement properties and diverges at the critical point of the fully isotropic model. In general, we find that anisotropy rule a complex behavior of the entanglement properties, which results in the fact that more isotropic models, despite being characterized by a larger amount of total entanglement, present a smaller fraction of pairwise entanglement: the latter, in turn, is more evenly distributed along the chain, to the extent that, in the fully isotropic model at the critical field, the concurrences do not depend on $r$.Comment: 14 pages, 6 figures. Final versio

Dynamics of an inhomogeneous quantum phase transition

We argue that in a second order quantum phase transition driven by an inhomogeneous quench density of quasiparticle excitations is suppressed when velocity at which a critical point propagates across a system falls below a threshold velocity equal to the Kibble-Zurek correlation length times the energy gap at freeze-out divided by $\hbar$. This general prediction is supported by an analytic solution in the quantum Ising chain. Our results suggest, in particular, that adiabatic quantum computers can be made more adiabatic when operated in an "inhomogeneous" way.Comment: 7 pages; version to appear in a special issue of New J. Phy

How to fix a broken symmetry: Quantum dynamics of symmetry restoration in a ferromagnetic Bose-Einstein condensate

We discuss the dynamics of a quantum phase transition in a spin-1 Bose-Einstein condensate when it is driven from the magnetized broken-symmetry phase to the unmagnetized ``symmetric'' polar phase. We determine where the condensate goes out of equilibrium as it approaches the critical point, and compute the condensate magnetization at the critical point. This is done within a quantum Kibble-Zurek scheme traditionally employed in the context of symmetry-breaking quantum phase transitions. Then we study the influence of the nonequilibrium dynamics near a critical point on the condensate magnetization. In particular, when the quench stops at the critical point, nonlinear oscillations of magnetization occur. They are characterized by a period and an amplitude that are inversely proportional. If we keep driving the condensate far away from the critical point through the unmagnetized ``symmetric'' polar phase, the amplitude of magnetization oscillations slowly decreases reaching a non-zero asymptotic value. That process is described by the equation that can be mapped onto the classical mechanical problem of a particle moving under the influence of harmonic and ``anti-friction'' forces whose interplay leads to surprisingly simple fixed-amplitude oscillations. We obtain several scaling results relating the condensate magnetization to the quench rate, and verify numerically all analytical predictions.Comment: 15 pages, 11 figures, final version accepted in NJP (slight changes with respect to the former submission

AdS_2/CFT_1, Canonical Transformations and Superconformal Mechanics

We propose a simple conformal mechanics model which is classically equivalent to a charged massive particle propagating near the AdS_2\times S^2 horizon of an extreme Reissner-Nordstr\"om black hole. The equivalence holds for any finite value of the black hole mass and with both the radial and angular degrees of freedom of the particle taken into account. It is ensured by the existence of a canonical transformation in the Hamiltonian formalism. Using this transformation, we construct the Hamiltonian of a N=4 superparticle on AdS_2\times S^2 background.Comment: 10 pages, LaTe

Gauging N=4 supersymmetric mechanics II: (1,4,3) models from the (4,4,0) ones

Exploiting the gauging procedure developed by us in hep-th/0605211, we study the relationships between the models of N=4 mechanics based on the off-shell multiplets (4,4,0) and (1,4,3). We make use of the off-shell N=4, d=1 harmonic superspace approach as most adequate for treating this circle of problems. We show that the most general sigma-model type superfield action of the multiplet (1,4,3) can be obtained in a few non-equivalent ways from the (4,4,0) actions invariant under certain three-parameter symmetries, through gauging the latter by the appropriate non-propagating gauge multiplets. We discuss in detail the gauging of both the Pauli-Gursey SU(2) symmetry and the abelian three-generator shift symmetry. We reveal the (4,4,0) origin of the known mechanisms of generating potential terms for the multiplet (1,4,3), as well as of its superconformal properties. A new description of this multiplet in terms of unconstrained harmonic analytic gauge superfield is proposed. It suggests, in particular, a novel mechanism of generating the (1,4,3) potential terms via coupling to the fermionic off-shell N=4 multiplet (0,4,4).Comment: 27 page

Quantization in a General Light-front Frame

In this paper, we study the question of quantization of quantum field theories in a general light-front frame. We quantize scalar, fermion as well as gauge field theories in a systematic manner carrying out the Hamiltonian analysis carefully. The decomposition of the fields into positive and negative frequency terms needs to be done carefully after which we show that the (anti) commutation relations for the quantum operators become frame independent. The frame dependence is completely contained in the functions multiplying these operators in the field decomposition. We derive the propagators from the vacuum expectation values of the time ordered products of the fields.Comment: 14 pages, revtex, version to be published in Phys. Rev. D with the discussion of Abelian field quantization replaced by the non-Abelian field and some comments added on the Mandelstam-Liebbrandt prescriptio

Conformal and Superconformal Mechanics Revisited

We find, at the Lagrangian off-shell level, the explicit equivalence transformation which relates the conformal mechanics of De Alfaro, Fubini and Furlan to the conformal mechanics describing the radial motion of the charged massive particle in the Bertotti-Robinson AdS$_2\times S^2$ background. Thus we demonstrate the classical equivalence of these two systems which are usually regarded as essentially different ``old'' and ``new'' conformal mechanics models. We also construct a similar transformation for N=2, $SU(1,1|1)$ superconformal mechanics in N=2 superfield formulation. Performing this transformation in the action of the N=2 superconformal mechanics, we find an off-shell superfield action of N=2 superextension of Bertotti-Robinson particle. Such an action has not been given before. We show its on-shell equivalence to the AdS$_2$ superparticle action derived from the spontaneous partial breaking of $SU(1,1|1)$ superconformal symmetry treated as the N=2 AdS$_2$ supersymmetry.Comment: LaTeX, 15 page

Infinite Symmetry in the Fractional Quantum Hall Effect

We have generalized recent results of Cappelli, Trugenberger and Zemba on the integer quantum Hall effect constructing explicitly a ${\cal W}_{1+\infty}$ for the fractional quantum Hall effect such that the negative modes annihilate the Laughlin wave functions. This generalization has a nice interpretation in Jain's composite fermion theory. Furthermore, for these models we have calculated the wave functions of the edge excitations viewing them as area preserving deformations of an incompressible quantum droplet, and have shown that the ${\cal W}_{1+\infty}$ is the underlying symmetry of the edge excitations in the fractional quantum Hall effect. Finally, we have applied this method to more general wave functions.Comment: 15pp. LaTeX, BONN-HE-93-2

Black Hole Entropy from a Highly Excited Elementary String

Suggested correspondence between a black hole and a highly excited elementary string is explored. Black hole entropy is calculated by computing the density of states for an open excited string. We identify the square root of oscillator number of the excited string with Rindler energy of black hole to obtain an entropy formula which, not only agrees at the leading order with the Bekenstein-Hawking entropy, but also reproduces the logarithmic correction obtained for black hole entropy in the quantum geometry framework. This provides an additional supporting evidence for correspondence between black holes and strings.Comment: revtex, 4 page