arXiv subjects

Simon Hands

Publications and source records attributed to Simon Hands.

At least 91 records · Page 5Linked to original sources

arXiv2008

Quantum Phase Transition in a Graphene Model

We present results for the equation of state of a graphene-like model in an effort to understand the properties of its quantum phase transition. The N_f fermion species interact through a three dimensional instantaneous Coulomb potential. Since there are no reliable analytical tools that work for all values of N_f and the coupling constant g, we rely on Monte Carlo simulations to calculate the critical properties of the model near the phase transition. We consider the four-component formulation for the fermion fields, which arises naturally as the continuum limit of the staggered fermion construction in (2+1) dimensions. In the limit of infinitely strong Coulomb interaction, the system undergoes a quantum phase transition at a critical number of fermion species N_fc ~ 4.7. We also calculate the values of the critical exponents at the quantum phase transition.

cond-mat.str-el↗

arXiv2008

Quantum Critical Behaviour in a Graphene-like Model

We present the first results of numerical simulations of a 2+1 dimensional fermion field theory based on a recent proposal for a model of graphene, consisting of N_f four-component Dirac fermions moving in the plane and interacting via an instantaneous Coulomb interaction. In the strong-coupling limit we identify a critical number of flavors N_fc=4.8(2) separating an insulating from a conducting phase. This transition corresponds to the location of a quantum critical point, and we use a fit to the equation of state for the chiral order parameter to estimate the critical exponents. Next we simulate N_f=2 corresponding to real graphene, and approximately locate a transition from strong to weak coupling behaviour. Strong correlations are evident in the weak-coupling regime.

cond-mat.str-el↗

arXiv2007

Hadron Spectrum in a Two-Colour Baryon-Rich Medium

The hadron spectrum of SU(2) lattice gauge theory with two flavours of Wilson quark is studied on an 8^3x16 lattice using all-to-all propagators, with particular emphasis on the dependence on quark chemical potential mu. As mu is increased from zero the diquark states with non-zero baryon number B respond as expected, while states with B=0 remain unaffected until the onset of non-zero baryon density at mu=m_pi/2. Post onset the pi-meson mass increases in accordance with chiral perturbation theory while the rho becomes lighter. In the diquark sector a Goldstone state associated with a superfluid ground state can be identified. A further consequence of superfluidity is an approximate degeneracy between mesons and baryons with the same spacetime and isospin quantum numbers. Finally we find tentative evidence for the binding of states with kaon quantum numbers within the baryonic medium.

hep-lat↗

arXiv2007

Two Color Matter in the Quenched Approximation

We study a quenched SU(2) lattice gauge theory in 4d in which the spatial gauge ensemble $\{U_i\}$ is generated from a 3d gauge-Higgs model and the timelike link variables are ``reconstructed'' from the Higgs fields. The resulting ensemble is used to study quenched quark propagation with non-zero chemical potential $μ$. While it proves possible to alter the strength of the inter-quark interaction by changing the parameters of the dimensionally reduced model, there is no evidence for any region of parameter space where quarks exhibit deconfined behaviour or thermodynamic observables scale as if there were a Fermi surface.

hep-lat↗

arXiv2007

Can we study Quark Matter in the Quenched Approximation?

We study a quenched SU(2) lattice gauge theory in which, in an attempt to distinguish between timelike and spacelike gauge fields, the gauge ensemble {U_mu} is generated from a 3 dimensional gauge-Higgs model, the timelike link variables being "reconstructed" from the Higgs fields. The resulting ensemble is used to study quenched quark propagation with non-zero chemical potential mu; in particular, the quark density, chiral and superfluid condensates, meson, baryon and gauge-fixed quark propagators are all studied as functions of mu. While it proves possible to alter the strength of the inter-quark interaction by changing the parameters of the dimensionally reduced model, there is no evidence for any region of parameter space where quarks exhibit deconfined behaviour or thermodynamic observables scale as if there were a Fermi surface.

hep-lat↗

arXiv2007

Spectral functions at small energies and the electrical conductivity in hot, quenched lattice QCD

In lattice QCD, the Maximum Entropy Method can be used to reconstruct spectral functions from euclidean correlators obtained in numerical simulations. We show that at finite temperature the most commonly used algorithm, employing Bryan's method, is inherently unstable at small energies and give a modification that avoids this. We demonstrate this approach using the vector current-current correlator obtained in quenched QCD at finite temperature. Our first results indicate a small electrical conductivity above the deconfinement transition.

hep-lat↗

arXiv2007

Simulating Dense Matter

I review the Sign Problem hindering lattice QCD simulations of dense baryonic matter, focussing where possible on its physical relevance. The possibility of avoiding the Sign Problem via a duality transformation is also briefly considered. Finally, I review evidence for deconfinement at non-zero quark density in recent simulations of Two Color QCD.

hep-lat↗

arXiv2007

Phase diagram of the three dimensional Thirring model - A Monte Carlo study

Certain approximate solutions of the continuum Schwinger-Dyson Equations (SDEs) predict chiral symmetry breaking in the 3d Thirring model when the number of fermion flavors N_f<4.32 whereas others predict symmetry breaking for all N_f. Our results from Monte Carlo simulations with N_f=6, predict a second order chiral phase transition. The critical coupling in this case corresponds to an ultra-violet fixed point of the renormalization group defining a non-trivial continuum limit. Further, our numerical simulations provide an estimate for the critical number of fermion flavors, N_fc \approx 6.5.

hep-lat↗

arXiv2007

Critical Flavor Number in the Three Dimensional Thirring Model

We present results of a Monte Carlo simulation of the three dimensional Thirring model with the number of fermion flavors N_f varied between 2 and 18. By identifying the lattice coupling at which the chiral condensate peaks, simulations are be performed at couplings g^2(N_f) corresponding to the strong coupling limit of the continuum theory. The chiral symmetry restoring phase transition is studied as N_f is increased, and the critical number of flavors estimated as N_{fc}=6.6(1). The critical exponents measured at the transition do not agree with self-consistent solutions of the Schwinger-Dyson equations; in particular there is no evidence for the transition being of infinite order. Implications for the critical flavor number in QED_3 are briefly discussed.

hep-lat↗

arXiv2006

Spectral functions at non-zero momentum in hot QCD

We present results for meson spectral functions at non-zero momentum at temperatures both below and above Tc, obtained in quenched simulations for a number of valence quark masses. For the lightest quark masses, a clear difference between the spectral functions on cold and hot lattices is observed.

hep-lat↗

arXiv2006

Chiral Symmetry Restoration in Anisotropic QED(3)

We present results from a Monte Carlo simulation of non-compact lattice QED in 3 dimensions in which an explicit anisotropy $κ$ between $x$ and $y$ hopping terms has been introduced into the action. Using a parameter set corresponding to broken chiral symmetry in the isotropic limit $κ=1$, we study the chiral condensate on $16^3$, $20^3$, and $24^3$ lattices as $κ$ is varied, and fit the data to an equation of state which incorporates anisotropic volume corrections. The value $κ_c$ at which chiral symmetry ispparently restored is strongly volume-dependent, suggesting that the transition may be a crossover rather than a true phase transition. In addition we present results on $16^3$ lattices for the scalar meson propagator, and for the Landau gauge-fixed fermion propagator. The scalar mass approaches the pion mass at large $κ$, consistent with chiral symmetry restoration, but the fermion remains massive at all values of $κ$ studied, suggesting that strong infra-red fluctuations persist into the chirally symmetric regime. Implications for models of high-$T_c$ superconductivity based on anisotropic QED$_3$ are discussed.

hep-lat↗

arXiv2006

Quark Matter in QC(2)D

Results are presented from a numerical study of lattice QCD with gauge group SU(2) and two flavors of Wilson fermion at non-zero quark chemical potential mu >> T. Studies of the equation of state, the superfluid condensate, and the Polyakov line all suggest that in addition to the low density phase of Bose-condensed diquark baryons, there is a deconfined phase at higher quark density in which quarks form a degenerate system, whose Fermi surface is only mildly disrupted by Cooper pair condensation.

nucl-th↗

arXiv2006

Meson spectral functions at nonzero momentum in hot QCD

We present preliminary results for meson spectral functions at nonzero momentum, obtained from quenched lattice QCD simulations at finite temperature using the Maximal Entropy Method. Twisted boundary conditions are used to have access to many momenta p~T. For light quarks, we observe a drastic modification when heating the system from below to above Tc. In particular, for the vector spectral density we find a nonzero spectral weight at all energies.

hep-lat↗

arXiv2006

Deconfinement in dense 2-color QCD

We study SU(2) lattice gauge theory with two flavors of Wilson fermion at non-zero chemical potential mu and low temperature on a 8^3x16 system. We identify three regimes along the mu-axis. For mu<~m_pi/2 the system remains in the vacuum phase, and all physical observables considered remain essentially unchanged. The intermediate regime is characterised by a non-zero diquark condensate and an associated increase in the baryon density, consistent with what is expected for Bose-Einstein condensation of tightly bound diquarks. We also observe screening of the static quark potential here. In the high-density deconfined regime we find a non-zero Polyakov loop and a strong modification of the gluon propagator, including significant screening in the magnetic sector in the static limit, which must have a non-perturbative origin. The behaviour of thermodynamic observables and the superfluid order parameter are consistent with a Fermi surface disrupted by a BCS diquark condensate. The energy per baryon as a function of mu exhibits a minimum in the deconfined regime, implying that macroscopic objects such as stars formed in this theory are largely composed of quark matter.

hep-lat↗

arXiv2005

On the Interplay of Fermions and Monopoles in Compact QED_3

The infra-red properties of three-dimensional abelian lattice gauge theory are known to be governed by a neutral plasma of magnetic monopole excitations. We address the fate of these monopoles in the presence of light dynamical fermions, using a lattice formulation of compact QED_3 with N_f=4 fermion flavors supplemented by a four-fermi contact term permitting numerical Monte Carlo simulations in the chiral limit. Our data hint at a restoration of chiral symmetry above a critical value of the (inverse) coupling beta. By performing simulations in a sector of non-vanishing magnetic charge, we are able to study the response of the theory to an external magnetic test charge. Our results suggest that the monopole plasma persists even once chiral symmetry is restored, and hence survives the continuum limit.

hep-lat↗

arXiv2005

The onset and deconfinement transitions in two-colour QCD

We study two-colour QCD with two flavours of Wilson fermion at non-zero chemical potential mu and zero temperature. We find evidence of two separate transitions: an onset transition at mu ~ m_pi/2 where quark number and energy densities increase from zero; and a deconfinement transition at higher mu. The mu-dependence of the number and energy densities and the diquark condensate indicate that a Fermi surface is formed and that BCS rather than Bose-Einstein condensation dominates at the quark mass considered here, especially beyond the deconfinement transition.

hep-lat↗

arXiv2005

Supercurrent Flow in NJL_{2+1} at High Baryon Density

We present results of numerical simulations of the 2+1d Nambu -- Jona-Lasinio model with non-zero baryon chemical potential mu and spatially-varying complex diquark source strength j. By choosing arg(j) to vary smoothly through 2 pi across the spatial extent of the lattice, a baryon number current is induced which in the high density phase remains non-vanishing as |j|->0; we are hence able to extract a quantity characteristic of a superfluid known as the helicity modulus. We also study supercurrent flow at non-zero temperature and estimate the critical temperature at which the normal phase is restored, which is consistent with the conventional picture for thin-film superfluids in which the transition is viewed in terms of vortex -- anti-vortex unbinding.

hep-lat↗

arXiv2005

On meson spectral functions at high temperature and nonzero momentum

In the high-temperature phase of QCD meson spectral functions at nonzero momentum are expected to have a nontrivial and interesting structure. In order to provide a reference point for lattice studies employing e.g. the Maximal Entropy Method, we discuss several characteristics of meson spectral functions in the infinite-temperature limit. We report on ongoing work in quenched QCD with staggered fermions.

hep-lat↗