20 research outputs found
The partition function zeroes of quantum critical points
The Lee–Yang theorem for the zeroes of the partition function is not strictly applicable to quantum systems because the zeroes are defined in units of the fugacity ehΔτ, and the Euclidean-time lattice spacing Δτ can be divergent in the infrared (IR). We recently presented analytic arguments describing how a new space-Euclidean time zeroes expansion can be defined, which reproduces Lee and Yang's scaling but avoids the unresolved branch points associated with the breaking of nonlocal symmetries such as Parity. We now present a first numerical analysis for this new zeroes approach for a quantum spin chain system. We use our scheme to quantify the renormalization group flow of the physical lattice couplings to the IR fixed point of this system. We argue that the generic Finite-Size Scaling (FSS) function of our scheme is identically the entanglement entropy of the lattice partition function and, therefore, that we are able to directly extract the central charge, c, of the quantum spin chain system using conformal predictions for the scaling of the entanglement entropy
Composite reweighting with Imaginary Chemical Potentials in SU(3)
We review the overlap pathology of the Glasgow reweighting method for finite
density QCD, and discuss the sampling bias that effects the determination of
the ensemble-averaged fugacity polynomial expansion coefficients that form the
Grand Canonical Partition function. The expectation of the difference in free
energies between canonical partition functions generated with different
measures is presented as an indicator of a systematic quark number dependent
biasing in the reweighting approach. The advantages of building up an unbiased
polynomial expansion for the Grand Canonical Partition function through a
series of parallel ensembles generated by reweighting with imaginary chemical
potentials are then contrasted with addressing the overlap pathology through a
secondary reweighting.Comment: 3 pages, 1 figure, Lattice2002(nonzerot
Finite Size Scaling, Fisher Zeroes and N=4 Super Yang-Mills
We investigate critical slowing down in the local updating continuous-time
Quantum Monte Carlo method by relating the finite size scaling of Fisher Zeroes
to the dynamically generated gap, through the scaling of their respective
critical exponents. As we comment, the nonlinear sigma model representation
derived through the hamiltonian of our lattice spin model can also be used to
give a effective treatment of planar anomalous dimensions in N=4 SYM. We
present scaling arguments from our FSS analysis to discuss quantum corrections
and recent 2-loop results, and further comment on the prospects of extending
this approach for calculating higher twist parton distributions.Comment: Lattice 2004(spin), Fermilab, June 21-26, 2004; 3 pages, 4 figure
Composite reweighting SU(2) QCD at Finite Temperature
The Glasgow reweighting method is evaluated for SU(2) lattice gauge theory at
nonzero \mu and finite T. We establish that the ' overlap problem' of SU(3)
measurements, in which the transition points determined from thermodynamic
observables have an unphysical dependence on the value of \mu used in the
reweighting persists for SU(2). By combining the information from different
lattice ensembles we alleviate sampling bias in the fugacity expansion, and
identify the Lee-Yang zeros associated with the transition to a high density
phase that can plausibly be associated with diquark condensation. We also
confirm the existence of a line of first order transitions above a critical
point in the T-\mu plane previously identified by effective chiral lagrangian
calculations.Comment: 8 pages, 7 figure
Lattice QCD at finite isospin density at zero and finite temperature
We simulate lattice QCD with dynamical and quarks at finite chemical
potential, , for the third component of isospin (), at both zero
and at finite temperature. At zero temperature there is some ,
say, above which and parity are spontaneously broken by a charged pion
condensate. This is in qualitative agreement with the prediction of effective
(chiral) Lagrangians which also predict . This transition appears
to be second order, with scaling properties consistent with the mean-field
predictions of such effective Lagrangian models. We have also studied the
restoration of symmetry at high temperature for . For
sufficiently large, this finite temperature phase transition appears to
be first order. As is decreased it becomes second order connecting
continuously with the zero temperature transition.Comment: 23 pages, Revtex, 9 figures. Major revision of sections 3 and 4 to
include new analyses of critical scaling which we now find to be in the
universality class of mean-field theor
The pseudo-Goldstone spectrum of 2-colour QCD at finite density
We examine the spectrum of 2-colour lattice QCD with 4 continuum flavours at
a finite chemical potential () for quark-number, on a
lattice. First we present evidence that the system undergoes a transition to a
state with a diquark condensate, which spontaneously breaks quark number at
, and that this transition is mean field in nature. We then
examine the 3 states that would be Goldstone bosons at for zero Dirac
and Majorana quark masses. The predictions of chiral effective Lagrangians give
a good description of the behaviour of these masses for . Except
for the heaviest of these states, these predictions diverge from our
measurements, once is significantly greater than . However, the
qualitative behaviour of these masses, indicates that the physics is very
similar to that predicted by these effective Lagrangians, and there is some
indication that at least part of these discrepancies is due to saturation, a
lattice artifact.Comment: 32 pages LaTeX/Revtex, 8 Postscript figure
Remarks on the multi-parameter reweighting method for the study of lattice QCD at non-zero temperature and density
We comment on the reweighting method for the study of finite density lattice
QCD. We discuss the applicable parameter range of the reweighting method for
models which have more than one simulation parameter. The applicability range
is determined by the fluctuations of the modification factor of the Boltzmann
weight. In some models having a first order phase transition, the fluctuations
are minimized along the phase transition line if we assume that the pressure in
the hot and the cold phase is balanced at the first order phase transition
point. This suggests that the reweighting method with two parameters is
applicable in a wide range for the purpose of tracing out the phase transition
line in the parameter space. To confirm the usefulness of the reweighting
method for 2 flavor QCD, the fluctuations of the reweighting factor are
measured by numerical simulations for the cases of reweighting in the quark
mass and chemical potential directions. The relation with the phase transition
line is discussed. Moreover, the sign problem caused by the complex phase
fluctuations is studied.Comment: 20 page, 6 figure
Real and imaginary chemical potential in 2-color QCD
In this paper we study the finite temperature SU(2) gauge theory with
staggered fermions for non-zero imaginary and real chemical potential. The
method of analytical continuation of Monte Carlo results from imaginary to real
chemical potential is tested by comparison with simulations performed {\em
directly} for real chemical potential. We discuss the applicability of the
method in the different regions of the phase diagram in the temperature --
imaginary chemical potential plane.Comment: 15 pages, 7 figures; a few comments added; version published on Phys.
Rev.