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Simon Hands

Publications and source records attributed to Simon Hands.

At least 73 records · Page 4Linked to original sources
arXiv2013

Monte Carlo Study of Strongly-Interacting Degenerate Fermions: a Model for Voltage-Biased Bilayer Graphene

We formulate a model of N_f=4 flavors of relativistic fermion in 2+1d in the presence of a chemical potential mu coupled to two flavor doublets with opposite sign, akin to isopsin chemical potential in QCD. This is argued to be an effective theory for low energy electronic excitations in bilayer graphene, in which an applied voltage between the layers ensures equal populations of particles on one layer and holes on the other. The model is then reformulated on a spacetime lattice using staggered fermions, and in the absence of a sign problem, simulated using an orthodox hybrid Monte Carlo algorithm. With the coupling strength chosen to be close to a quantum critical point believed to exist for N_f<N_fc\approx4.8, it is found that there is a region below saturation where both the carrier density and a particle-hole "excitonic" condensate scale anomalously with increasing mu, much more rapidly that the corresponding quantities in free field theory, while the conventional chiral condensate is strongly suppressed. The corresponding ground state is speculated to be a strongly-correlated degenerate fermion system, with a remnant Fermi surface distorted by a superfluid excitonic condensate. The model thus shows qualitatively different behaviour to any model with mu=/=0 previously studied by lattice simulation.

hep-lat↗
arXiv2013

Towards the phase diagram of dense two-color matter

We study two-color QCD with two flavors of Wilson fermion as a function of quark chemical potential mu and temperature T. We find evidence of a superfluid phase at intermediate mu and low T where the quark number density and diquark condensate are both very well described by a Fermi sphere of nearly-free quarks disrupted by a BCS condensate. Our results suggest that the quark contribution to the energy density is negative (and balanced by a positive gauge contribution), although this result is highly sensitive to details of the energy renormalisation. We also find evidence that the chiral condensate in this region vanishes in the massless limit. This region gives way to a region of deconfined quark matter at higher T and mu, with the deconfinement temperature, determined from the renormalised Polyakov loop, decreasing only very slowly with increasing chemical potential. The quark number susceptibility chi_q does not exhibit any qualitative change at the deconfinement transition. We argue that this is because chi_q is not an appropriate measure of deconfinement for 2-color QCD at high density.

hep-lat↗
arXiv2012

Phase structure of QC2D at high temperature and density

We study two-color QCD with two flavors of Wilson fermion as a function of quark chemical potential mu and temperature T. We find evidence of a superfluid phase at intermediate mu and low T where the quark number density and diquark condensate are both very well described by a Fermi sphere of nearly-free quarks disrupted by a BCS condensate. This gives way to a region of deconfined quark matter at higher T and mu, with the deconfinement temperature decreasing only very slowly with increasing chemical potential. We find that heavy quarkonium bound states persist in the S-wave channels at all T and mu, with an energy reflecting the phase structure. P-wave states appear not to survive in the quarkyonic region.

hep-lat↗
arXiv2012

The Phase Diagram of Two Color QCD

I present recent results from lattice simulations of SU(2) gauge theory with Nf=2 Wilson quark flavors, at non-zero quark chemical potential. The thermodynamic equation of state is discussed along with the nature of the high density matter which forms. It is conjectured that deconfinement may mean different things for bulk and Fermi surface phenomena.

hep-lat↗
arXiv2012

Non-relativistic spectrum of two-color QCD at non-zero baryon density

The heavy quarkonium spectrum of Two Color QCD (QC$_2$D) at non-zero quark chemical potential $μ$ and temperature $T$ with $μ/T\gg1$ has been calculated in both $S$- and $P$-wave channels using a lattice non-relativistic formulation of QC$_2$D. As $μ$ is varied, the quarkonium spectra reveal three separate regions, corroborating previous findings that there are three distinct physical regimes of QC$_2$D at low temperature and high baryon density: hadronic matter, quark/quarkyonic matter, and deconfined matter. The results are interpreted in terms of the formation of heavy-light $Qq$ states in the two-color baryonic medium.

hep-lat↗
arXiv2011

Quark number susceptibility at finite density and low temperature

We study the quark number susceptibility in SU(2) lattice gauge theory with two Wilson quark flavours at non-zero chemical potential and low temperature. We present some technical aspects of the issue and numerical results obtained at different lattices and different parameters. We discuss what this observable can teach us about the phase diagram of the model and in particular about the relation between susceptibility and Polyakov loop

hep-lat↗
arXiv2011

Monte Carlo simulation of monolayer graphene at non-zero temperature

We present results from lattice simulations of a monolayer graphene model at non-zero temperature. At low temperatures for sufficiently strong coupling the model develops an excitonic condensate of particle-hole pairs corresponding to an insulating phase. The Berezinskii-Kosterlitz-Thouless phase transition temperature is associated with the value of the coupling where the critical exponent delta governing the response of the order parameter at criticality to an external source has a value close to 15. The critical coupling on a lattice with temporal extent N_t=32 (T=1/(N_t a_t) where a_t is the temporal lattice spacing) and spatial extent N_s=64 is very close to infinite coupling. The value of the transition temperature normalized with the zero temperature fermion mass gap Delta_0 is given by T_BKT/Delta_0=0.055(2). This value provides an upper bound on the transition temperature, because simulations closer to the continuum limit where the full U(4) symmetry is restored may result in an even lower value. In addition, we measured the helicity modulus Upsilon and the fermion thermal mass Delta_T(T), the later providing evidence for a pseudogap phase with Delta_T>0 extending to arbitrarily high T.

cond-mat.str-el↗
arXiv2011

Magnetic monopole plasma phase in (2+1)d compact quantum electrodynamics with fermionic matter

We present the first evidence from lattice simulations that the magnetic monopoles in three dimensional compact quantum electrodynamics (cQED3) with N_f=2 and N_f= 4 four-component fermion flavors are in a plasma phase. The evidence is based mainly on the divergence of the monopole susceptibility (polarizability) with the lattice size at weak gauge couplings. A weak four-Fermi term added to the cQED3 action enabled simulations with massless fermions. The exact chiral symmetry of the interaction terms forbids symmetry breaking lattice discretization counterterms to appear in the theory's effective action. It is also shown that the scenario of a monopole plasma does not depend on the strength of the four-Fermi coupling. Other observables such as the densities of "isolated" dipoles and monopoles and the so-called specific heat show that a crossover from a dense monopole plasma to a dilute monopole gas occurs at strong couplings. The implications of our results on the stability of U(1) spin liquids in two spatial dimensions are also discussed.

hep-lat↗
arXiv2011

Lattice Study of Dense Matter with Two Colors and Four Flavors

We present results from a simulation of SU(2) lattice gauge theory with N_f=4 flavors of Wilson fermion and non-zero quark chemical potential mu, using the same 12^3x24 lattice, bare gauge coupling, and pion mass in cut-off units as a previous study with N_f=2. The string tension for N_f=4 is found to be considerably smaller implying smoother gauge field configurations. Thermodynamic observables and order parameters for superfluidity and color deconfinement are studied, and comparisons drawn between the two theories. Results for quark density and pressure as functions of mu are qualitatively similar for N_f=2 and N_f=4; in both cases there is evidence for a phase in which baryonic matter is simultaneously degenerate and confined. Results for the stress-energy tensor, however, suggest that while N_f=2 has a regime where dilute matter is non-relativistic and weakly-interacting, N_f=4 matter is relativistic and strongly-interacting for all values of mu above onset.

hep-lat↗
arXiv2011

Topological Fluctuations in Dense Matter with Two Colors

We study the topological charge fluctuations of an SU(2) lattice gauge theory containing both N_f=2 and 4 flavors of Wilson fermion, at low temperature with non-zero chemical potential $μ$. The topological susceptibility, chi_T, is used to characterize differing physical regimes as mu is varied between the onset of matter at mu_o and and color deconfinement at mu_d. Suppression of instantons by matter via Debye screening is also investigated, revealing effects not captured by perturbative predictions. In particular, the breaking of scale invariance leads to the mean instanton size rho becoming mu-dependent in the regime between onset and deconfinement, with a scaling rho~1/mu^2 over the range mu_o<mu<mu_d, resulting in an enhancement of chi_T immediately above onset.

hep-lat↗
arXiv2010

QCD with chemical potential on S^1 x S^3

In this proceedings we summarize our calculation of the phase diagram of QCD at non-zero temperature and chemical potential on S^1 x S^3 from one-loop perturbation theory [1], which is valid in the limit R << 1/Lambda, where R is the radius of S^3. We calculate several observables including the Polyakov lines and the quark number, for large number of colors N and large number of quark flavors Nf, on S^1 x S^3, and compare with results for the same system with N = 3, and with results for N=2 lattice QCD. For N > 2 the action is complex and the dominant contributions to the path integral occur in the space of complexified gauge field configurations. This results in the expectation values of the eigenvalues of the Polyakov line lying off the unit circle and out in the complex plane. This is an important issue for the lattice, and also for the calculation on S^1 x S^3 in the large N limit where we obtain analytical results using the saddle point approximation. It is thus necessary to adapt available techniques to locate the stationary solutions in the complexified gauge field configuration space.

hep-lat↗
arXiv2010

Numerical Study of the Two Color Attoworld

We consider QCD at very low temperatures and non-zero quark chemical potential from lattice Monte Carlo simulations of the two-color theory in a very small spatial volume (the attoscale). In this regime the quark number rises in discrete levels in qualitative agreement with what is found analytically at one loop on S3xS1 with radius R_S3 << 1/Λ_QCD. The detailed level degeneracy, however, cannot be accounted for using weak coupling arguments. At each rise in the quark number there is a corresponding spike in the Polyakov line, also in agreement with the perturbative results. In addition the quark number susceptibility shows a similar behaviour to the Polyakov line and appears to be a good indicator of a confinement-deconfinement type of transition.

hep-lat↗
arXiv2010

QCD with Chemical Potential in a Small Hyperspherical Box

To leading order in perturbation theory, we solve QCD, defined on a small three sphere in the large N and Nf limit, at finite chemical potential and map out the phase diagram in the (mu,T) plane. The action of QCD is complex in the presence of a non-zero quark chemical potential which results in the sign problem for lattice simulations. In the large N theory, which at low temperatures becomes a conventional unitary matrix model with a complex action, we find that the dominant contribution to the functional integral comes from complexified gauge field configurations. For this reason the eigenvalues of the Polyakov line lie off the unit circle on a contour in the complex plane. We find at low temperatures that as mu passes one of the quark energy levels there is a third-order Gross-Witten transition from a confined to a deconfined phase and back again giving rise to a rich phase structure. We compare a range of physical observables in the large N theory to those calculated numerically in the theory with N=3. In the latter case there are no genuine phase transitions in a finite volume but nevertheless the observables are remarkably similar to the large N theory.

hep-th↗
arXiv2010

A Quarkyonic Phase in Dense Two Color Matter?

We present results from simulations of Two Color QCD with two Wilson quark flavors in the presence of a quark chemical potential mu at two different lattice spacings. The equation of state, conformal anomaly, superfluid order parameter and Polyakov line are all discussed. Our results suggest that the transition from hadronic to quark matter, and that from confined to deconfined matter occur at distinct values of mu, consistent with the existence of a quarkyonic phase in this model.

hep-lat↗
arXiv2009

Monte Carlo Simulation of the Semimetal-Insulator Phase Transition in Monolayer Graphene

A 2+1 dimensional fermion field theory is proposed as a model for the low-energy electronic excitations in monolayer graphene. The model consists of N=2 four-component Dirac fermions moving in the plane and interacting via a contact interaction between charge densities. For strong couplings there is a continuous transition to a Mott insulting phase. We present results of an extensive numerical study of the model's critical region, including the order parameter, its associated susceptibility, and for the first time the quasiparticle propagator. The data enables an extraction of the critical exponents at the transition, including the dynamical critical exponent, which are hypothesised to be universal features of a quantum critical point. The relation of our model with others in the literature is discussed, along with the implications for physical graphene following from our value of the critical coupling.

cond-mat.str-el↗
arXiv2009

Lattice Simulations near the Semimetal-Insulator Phase Transition of Graphene

We present results from Monte Carlo simulations of a three dimensional fermionic field theory which can be derived from a model of graphene in which electrons interact via a screened Coulomb potential. For our simulations we employ lattice gauge theory methods used in elementary particle physics. We show that the theory undergoes a second order phase transition and we provide estimates for the critical exponents. The estimated value of the physical critical coupling implies that graphene in vacuum is an insulator. We also present the first results for the quasiparticle dispersion relation.

cond-mat.str-el↗
arXiv2009

Topological Aspects of Fermions on a Honeycomb Lattice

We formulate a model of relativistic fermions moving in two Euclidean dimensions based on a tight-binding model of graphene. The eigenvalue spectrum of the resulting Dirac operator is solved numerically in smooth U(1) gauge field backgrounds carrying an integer-valued topological charge Q, and it is demonstrated that the resulting number of zero-eigenvalue modes is in accord with the Atiyah-Singer index theorem applied to two continuum flavors. A bilinear but gauge non-invariant chirality operator appropriate for distinguishing the topological zero modes is identified. When this operator is used to calculate Q, it is found that the maximum topological charge capable of being measured in this fashion scales with the perimeter of the lattice. Some concluding remarks compare these results to what is known for staggered lattice fermions.

hep-lat↗