arXiv subjects

Simon Hands

Publications and source records attributed to Simon Hands.

At least 109 records · Page 6Linked to original sources

arXiv2005

Fermion propagators in QED3 with velocity anisotropies

QED3 with fermi and gap anisotropies is considered to be a candidate effective field theory of high temperature superconductors. Simulations of a variant of the theory have demonstrated that there is evidence consistent with a phase transition to a chirally restored phase as the velocity anisotropy increases, and that the correlation lengths of pions in spatial directions behave in a manner consistent with the anisotropy being a relevant parameter of the theory. We present the first measurements of the fermion propagator in Landau gauge for this theory and suggest that the structure of this theory is more complex than previously thought.

hep-lat↗

arXiv2005

Lattice Study of Anisotropic QED-3

We present results from a Monte Carlo simulation of non-compact lattice QED in 3 dimensions on a $16^3$ lattice in which an explicit anisotropy between $x$ and $y$ hopping terms has been introduced into the action. This formulation is inspired by recent formulations of anisotropic QED$_3$ as an effective theory of the non-superconducting portion of the cuprate phase diagram, with relativistic fermion degrees of freedom defined near the nodes of the gap function on the Fermi surface, and massless photon degrees of freedom reproducing the dynamics of the phase disorder of the superconducting order parameter. Using a parameter set corresponding to broken chiral symmetry in the isotropic limit, our results show that the renormalised anisotropy, defined in terms of the ratio of correlation lengths of gauge invariant bound states in the $x$ and $y$ directions, exceeds the explicit anisotropy $κ$ introduced in the lattice action, implying in contrast to recent analytic results that anisotropy is a relevant deformation of QED$_3$. There also appears to be a chiral symmetry restoring phase transition at $κ_c\simeq4.5$, implying that the pseudogap phase persists down to T=0 in the cuprate phase diagram.

hep-lat↗

arXiv2005

Two Color QCD beyond the BEC regime

We present results of simulations of Two Color QCD using two flavors of Wilson quark in the fundamental representation, at non-zero quark chemical potential mu, on an 8^3x16 lattice. Results for the quark number density, quark and gluon energy densities, and superfluid condensate are qualitatively distinct from the behaviour expected on the assumption that the dominant degrees of freedom are tightly bound scalar diquarks which Bose condense; rather the scaling with mu is more suggestive of a Fermi surface disrupted by a Cooper pair condensate. We also present evidence both for screening of the static potential, and color deconfinement, arising solely as a result of a non-zero quark density.

hep-lat↗

arXiv2004

The Lattice NJL Model at Non-zero Baryon and Isospin Densities

We present initial results of a numerical investigation of the chiral symmetry restoring transition in the (3+1)-dimensional Nambu -- Jona-Lasinio model with both non-zero baryon chemical potential (mu_B) and isospin chemical potential (mu_I). With non-zero isospin chemical potential, the model suffers from a sign problem. We proceed in two ways: (i) We perform ``partially quenched'' simulations in which mu_I is made non-zero only during the measurement of chiral observables; (ii) We perform full simulations with imaginary isospin chemical potential with the aim to analytically continue results to real mu_I.

hep-lat↗

arXiv2004

QED in 2+1 Dimensions with Fermi and Gap Anisotropies

QED in 2+1 dimensions has long been studied as a model field theory which exhibits both asymptotic freedom and non-trivial IR behaviour. There is also a trend towards viewing it as a candidate low energy effective theory for the pseudogap phase of high temperature superconductors. One feature of these theories is their lack of isotropy in the x and y directions (a common feature of Dirac theories in condensed matter systems). A model motivated by this work is outlined, and tentative evidence presented for chiral symmetry restoration as the relative anisotropy is increased.

hep-lat↗

arXiv2004

Zero Lattice Sound

We study the N_f-flavor Gross-Neveu model in 2+1 dimensions with a baryon chemical potential mu, using both analytical and numerical methods. In particular, we study the self-consistent Boltzmann equation in the Fermi liquid framework using the quasiparticle interaction calculated to O(1/N_f), and find solutions for zero sound propagation for almost all mu > mu_c, the critical chemical potential for chiral symmetry restoration. Next we present results of a numerical lattice simulation, examining temporal correlation functions of mesons defined using a point-split interpolating operator, and finding evidence for phonon-like behaviour characterised by a linear dispersion relation in the long wavelength limit. We argue that our results provide the first evidence for a collective excitation in a lattice simulation.

hep-lat↗

arXiv2004

Numerical Portrait of a Relativistic BCS Gapped Superfluid

We present results of numerical simulations of the 3+1 dimensional Nambu - Jona-Lasinio (NJL) model with a non-zero baryon density enforced via the introduction of a chemical potential mu not equal to 0. The triviality of the model with a number of dimensions d>=4 is dealt with by fitting low energy constants, calculated analytically in the large number of colors (Hartree) limit, to phenomenological values. Non-perturbative measurements of local order parameters for superfluidity and their related susceptibilities show that, in contrast to the 2+1 dimensional model, the ground-state at high chemical potential and low temperature is that of a traditional BCS superfluid. This conclusion is supported by the direct observation of a gap in the dispersion relation for 0.5<=(mu a)<=0.85, which at (mu a)=0.8 is found to be roughly 15% the size of the vacuum fermion mass. We also present results of an initial investigation of the stability of the BCS phase against thermal fluctuations. Finally, we discuss the effect of splitting the Fermi surfaces of the pairing partners by the introduction of a non-zero isospin chemical potential.

hep-lat↗

arXiv2004

Quantum chaos in supersymmetric QCD at finite density

We investigate the distribution of the spacings of adjacent eigenvalues of the lattice Dirac operator. At zero chemical potential $μ$, the nearest-neighbor spacing distribution $P(s)$ follows the Wigner surmise of random matrix theory both in the confinement and in the deconfinement phase. This is indicative of quantum chaos. At nonzero chemical potential, the eigenvalues of the Dirac operator become complex and we discuss how $P(s)$ can be defined in the complex plane. Numerical results from an SU(2) simulation with staggered fermions in fundamental and adjoint representations are compared with predictions from non-hermitian random matrix theory, and agreement with the Ginibre ensemble is found for $μ\approx 0.5$.

hep-lat↗

arXiv2003

Lattice simulations of 2-colour QCD with Wilson fermions

We report on the status of our simulations of two-colour QCD with two flavours of Wilson quarks, at nonzero chemical potential and diquark source. Preliminary results are presented for the static quark potential, gluon propagator, and meson and diquark spectrum.

hep-lat↗

arXiv2003

High Density Effective Theory Confronts the Fermi Liquid

The high density effective theory recently introduced by Hong and Hsu to describe ultradense relativistic fermionic matter is used to calculate the tree-level forward scattering amplitude between two particles at the Fermi surface. While the direct term correctly reproduces that of the underlying gauge theory, the exchange term has the wrong sign. The physical consequences are discussed in the context of Landau's theoretical description of the Fermi liquid.

hep-ph↗

arXiv2003

A BCS Gap on the Lattice

Monte Carlo simulations of the 3+1 dimensional NJL model are performed with baryon chemical potential mu>0. For mu>Sigma_0, the constituent quark mass in vacuum, chiral symmetry is restored and a diquark condensate forms. We analyse the fermion propagator and find evidence for particle-hole mixing in the vicinity of the Fermi surface and an energy gap Delta>0, both of which provide evidence for superfluidity at high baryon density induced by a BCS mechanism. At (mu a)=0.8 the ratio between the BCS gap and the vacuum quark mass is Delta/Sigma_0=0.15(2).

hep-lat↗

arXiv2003

Fermi Surface Phenomena in the (2+1)d Four-Fermi Model

We study the Gross-Neveu model in 2+1 dimensions with a baryon chemical potential mu using both analytical and numerical methods. For mu greater than a critical value the model is chirally symmetric and has a Fermi surface with Fermi momentum ~mu. We have calculated the particle interaction in medium due to scalar meson exchange to leading order in 1/N, where N is the number of flavors, in the hard dense loop approach. The result has been used to calculate the relation between mu and the Fermi momentum and velocity in the resulting Fermi liquid to O(1/N). Simulation results from a 32^2x48 lattice for fermion and meson dispersion relations and meson wavefunctions are then presented, showing qualitative and in some cases quantitative agreement with analytic predictions. In particular, the simulations show clear evidence for the in-medium modification of the scalar propagator, oscillatory behaviour in the wavefunction consistent with a sharp Fermi surface, and tentative evidence for a massless pole in the vector meson channel resembling zero sound.

hep-lat↗

arXiv2002

A BCS Condensate in NJL_3+1 ?

We present results from a lattice Monte Carlo study of the Nambu - Jona-Lasinio model in 3+1 dimensions with a baryon chemical potential mu=/=0. As mu is increased there is a transition from a chirally-broken phase to relativistic quark matter, in which baryon number symmetry appears spontaneously broken by a diquark condensate at the Fermi surface, implying a superfluid ground state. Finite volume corrections to this relativistic BCS scenario, however, are anomalously large.

hep-ph↗

arXiv2002

Evidence for BCS Diquark Condensation in the 3+1d Lattice NJL Model

We present results of numerical simulations of the 3+1d Nambu - Jona-Lasinio model with a non-zero baryon chemical potential mu, with particular emphasis on the superfluid diquark condensate and associated susceptibilities. The results, when extrapolated to the zero diquark source limit, are consistent with the existence of a non-zero BCS condensate at high baryon density. The nature of the infinite volume and zero temperature limits are discussed.

hep-lat↗

arXiv2001

Diquark condensation in dense SU(2) matter

We report on a lattice study of two-color QCD with adjoint staggered fermions at high density. We find that the model has no early onset and we report on results for diquark condensation, from simulations with and without a diquark source term.

hep-lat↗

arXiv2001

The Lattice Fermi Surface

The Nambu - Jona-Lasinio model in 2+1 dimensions is simulated for non-zero baryon chemical potential with a diquark source term. No evidence for a BCS condensate or gap is seen at high density; rather, critical behaviour with novel exponents is observed, suggesting that 2d superfluidity as first described by Kosterlitz and Thouless is realised, but with the universality class determined by the presence of relativistic fermions.

hep-lat↗

arXiv2001

Lattice Matter

I review recent developments in the study of strongly interacting field theories with non-zero chemical potential mu. In particular I focus on (a) the determination of the QCD critical endpoint in the (mu,T) plane; (b) superfluid condensates in Two Color QCD; and (c) Fermi surface effects in the NJL model. Some remarks are made concerning the relation of superconductivity with the sign problem.

hep-lat↗

arXiv2001

Numerical Portrait of a Relativistic Thin Film BCS Superfluid

We present results of numerical simulations of the 2+1d Nambu - Jona-Lasinio model with a non-zero baryon chemical potential mu including the effects of a diquark source term. Diquark condensates, susceptibilities and masses are measured as functions of source strength j. The results suggest that diquark condensation does not take place in the high density phase mu>mu_c, but rather that the condensate scales non-analytically with j implying a line of critical points and long range phase coherence. Analogies are drawn with the low temperature phase of the 2d XY model. The spectrum of the spin-1/2 sector is also studied yielding the quasiparticle dispersion relation. There is no evidence for a non-zero gap; rather the results are characteristic of a normal Fermi liquid with Fermi velocity less than that of light. We conclude that the high density phase of the model describes a relativistic gapless thin film BCS superfluid.

hep-lat↗