44,945 research outputs found
Quantum dislocations: the fate of multiple vacancies in two dimensional solid 4He
Defects are believed to play a fundamental role in the supersolid state of
4He. We have studied solid 4He in two dimensions (2D) as function of the number
of vacancies n_v, up to 30, inserted in the initial configuration at rho =
0.0765 A^-2, close to the melting density, with the exact zero temperature
Shadow Path Integral Ground State method. The crystalline order is found to be
stable also in presence of many vacancies and we observe two completely
different regimes. For small n_v, up to about 6, vacancies form a bound state
and cause a decrease of the crystalline order. At larger n_v, the formation
energy of an extra vacancy at fixed density decreases by one order of magnitude
to about 0.6 K. In the equilibrated state it is no more possible to recognize
vacancies because they mainly transform into quantum dislocations and
crystalline order is found almost independent on how many vacancies have been
inserted in the initial configuration. The one--body density matrix in this
latter regime shows a non decaying large distance tail: dislocations, that in
2D are point defects, turn out to be mobile, their number is fluctuating, and
they are able to induce exchanges of particles across the system mainly
triggered by the dislocation cores. These results indicate that the notion of
incommensurate versus commensurate state loses meaning for solid 4He in 2D,
because the number of lattice sites becomes ill defined when the system is not
commensurate. Crystalline order is found to be stable also in 3D in presence of
up to 100 vacancies
Central extensions of classical and quantum q-Viraroso algebras
We investigate the central extensions of the q-deformed (classical and
quantum) Virasoro algebras constructed from the elliptic quantum algebra
A_{q,p}[sl(N)_c]. After establishing the expressions of the cocycle conditions,
we solve them, both in the classical and in the quantum case (for sl(2)). We
find that the consistent central extensions are much more general that those
found previously in the literature.Comment: Latex2e, needs amsfonts and amssymb package
Deformed W_N algebras from elliptic sl(N) algebras
We extend to the sl(N) case the results that we previously obtained on the
construction of W_{q,p} algebras from the elliptic algebra
A_{q,p}(\hat{sl}(2)_c). The elliptic algebra A_{q,p}(\hat{sl}(N)_c) at the
critical level c=-N has an extended center containing trace-like operators
t(z). Families of Poisson structures indexed by N(N-1)/2 integers, defining
q-deformations of the W_N algebra, are constructed. The operators t(z) also
close an exchange algebra when (-p^1/2)^{NM} = q^{-c-N} for M in Z. It becomes
Abelian when in addition p=q^{Nh} where h is a non-zero integer. The Poisson
structures obtained in these classical limits contain different q-deformed W_N
algebras depending on the parity of h, characterizing the exchange structures
at p \ne q^{Nh} as new W_{q,p}(sl(N)) algebras.Comment: LaTeX2e Document - packages subeqn,amsfonts,amssymb - 30 page
From quantum to elliptic algebras
It is shown that the elliptic algebra at the
critical level c=-2 has a multidimensional center containing some trace-like
operators t(z). A family of Poisson structures indexed by a non-negative
integer and containing the q-deformed Virasoro algebra is constructed on this
center. We show also that t(z) close an exchange algebra when p^m=q^{c+2} for m
integer, they commute when in addition p=q^{2k} for k integer non-zero, and
they belong to the center of when k is odd. The
Poisson structures obtained for t(z) in these classical limits contain the
q-deformed Virasoro algebra, characterizing the structures at generic values of
p, q and m as new algebras.Comment: LaTeX2e Document - packages subeqn,amsfont
Universal construction of W_{p,q} algebras
We present a direct construction of abstract generators for q-deformed W_N
algebras. This procedure hinges upon a twisted trace formula for the elliptic
algebra A_{q,p}(sl(N)_c) generalizing the previously known formulae for quantum
groups.Comment: packages amsfonts, amssym
On lattice chiral gauge theories
The Smit-Swift-Aoki formulation of a lattice chiral gauge theory is presented. In this formulation the Wilson and other non invariant terms in the action are made gauge invariant by the coupling with a nonlinear auxilary scalar field, omega. It is shown that omega decouples from the physical states only if appropriate parameters are tuned so as to satisfy a set of BRST identities. In addition, explicit ghost fields are necessary to ensure decoupling. These theories can give rise to the correct continuum limit. Similar considerations apply to schemes with mirror fermions. Simpler cases with a global chiral symmetry are discussed and it is shown that the theory becomes free at decoupling. Recent numerical simulations agree with those considerations
Exact ground state Monte Carlo method for Bosons without importance sampling
Generally ``exact'' Quantum Monte Carlo computations for the ground state of
many Bosons make use of importance sampling. The importance sampling is based,
either on a guiding function or on an initial variational wave function. Here
we investigate the need of importance sampling in the case of Path Integral
Ground State (PIGS) Monte Carlo. PIGS is based on a discrete imaginary time
evolution of an initial wave function with a non zero overlap with the ground
state, that gives rise to a discrete path which is sampled via a Metropolis
like algorithm. In principle the exact ground state is reached in the limit of
an infinite imaginary time evolution, but actual computations are based on
finite time evolutions and the question is whether such computations give
unbiased exact results. We have studied bulk liquid and solid 4He with PIGS by
considering as initial wave function a constant, i.e. the ground state of an
ideal Bose gas. This implies that the evolution toward the ground state is
driven only by the imaginary time propagator, i.e. there is no importance
sampling. For both the phases we obtain results converging to those obtained by
considering the best available variational wave function (the Shadow wave
function) as initial wave function. Moreover we obtain the same results even by
considering wave functions with the wrong correlations, for instance a wave
function of a strongly localized Einstein crystal for the liquid phase. This
convergence is true not only for diagonal properties such as the energy, the
radial distribution function and the static structure factor, but also for
off-diagonal ones, such as the one--body density matrix. From this analysis we
conclude that zero temperature PIGS calculations can be as unbiased as those of
finite temperature Path Integral Monte Carlo.Comment: 11 pages, 10 figure
On the Quasi-Hopf structure of deformed double Yangians
We construct universal twists connecting the centrally extended double
Yangian DY(sl(2))_c with deformed double Yangians DY_r(sl(2))_c, thereby
establishing the quasi-Hopf structures of the latter.Comment: 11 page
Quantized vortices in two dimensional solid 4He
Diagonal and off-diagonal properties of 2D solid 4He systems doped with a
quantized vortex have been investigated via the Shadow Path Integral Ground
State method using the fixed-phase approach. The chosen approximate phase
induces the standard Onsager-Feynman flow field. In this approximation the
vortex acts as a static external potential and the resulting Hamiltonian can be
treated exactly with Quantum Monte Carlo methods. The vortex core is found to
sit in an interstitial site and a very weak relaxation of the lattice positions
away from the vortex core position has been observed. Also other properties
like Bragg peaks in the static structure factor or the behavior of vacancies
are very little affected by the presence of the vortex. We have computed also
the one-body density matrix in perfect and defected 4He crystals finding that
the vortex has no sensible effect on the off-diagonal long range tail of the
density matrix. Within the assumed Onsager Feynman phase, we find that a
quantized vortex cannot auto-sustain itself unless a condensate is already
present like when dislocations are present. It remains to be investigated if
backflow can change this conclusion.Comment: 4 pages, 3 figures, LT26 proceedings, accepted for publication in
Journal of Physics: Conference Serie
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