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We carried out a calculation of the Roper state with the Sequential Empirical Bayesian (SEB) method with overlap valence fermion on 2+1-flavor domain-wall fermion configurations on the 24^3 x 64 lattice with a^{-1} = 1.73 GeV. The light sea quark mass corresponds to a pion mass of 330 MeV. The mass of the Roper, chirally extrapolated to the physical pion mass, is 1404(112) MeV which is consistent with the experimental value at 1440 MeV. When compared to the Roper state calculation with variational method for Clover and twisted mass fermions, it is found that the Roper states from SEB with overlap fermion are systematically lower by 400 - 800 MeV for all the quark masses ranging from light to the strange mass region. We study the origin of the difference by exploring the size of the interpolation field in relation to the radial wavefunction of the Roper and also the dynamical influence of the higher Fock space., Comment: 7 pages, 6 figures, presented at the 31st International Symposium on Lattice Field Theory (LATTICE 2013), 29 July - 3 August 2013, Mainz, Germany

We present renormalization constants of overlap quark bilinear operators on 2+1-flavor domain wall fermion configurations. Both overlap and domain wall fermions have chiral symmetry on the lattice. The scale independent renormalization constant for the local axial vector current is computed using a Ward Identity. The renormalization constants for the scalar, pseudoscalar and vector current are calculated in the RI-MOM scheme. Results in the MS-bar scheme are obtained by using perturbative conversion ratios. The analysis uses in total six ensembles with lattice sizes 24^3x64 and 32^3x64., 7 pages, 10 figures, presented at the 31st International Symposium on Lattice Field Theory (LATTICE 2013), 29 July - 3 August 2013, Mainz, Germany

We investigate the phase diagram in the temperature, imaginary chemical potential plane for QCD with three degenerate quark flavors using Wilson type fermions. While more expensive than the staggered fermions used in past studies in this area, Wilson fermions can be used safely to simulate systems with three quark flavors. In this talk, we focus on the (pseudo)critical line that extends from $\mu=0$ in the imaginary chemical potential plane, trace it to the Roberge-Weiss line, and determine its location relative to the Roberge-Weiss transition point. In order to smoothly follow the (pseudo)critical line in this plane we perform a multi-histogram reweighting in both temperature and chemical potential. To perform reweighting in the chemical potential we use the compression formula to compute the determinants exactly. Our results are compatible with the standard scenario., Comment: 7 pages, 5 figures. Proceedings of the 31st International Symposium on Lattice Field Theory (Lattice 2013), 29 July - 3 August 2013, Mainz, Germany

A direct calculation of the mixed action parameter ${\ensuremath{\Delta}}_{\mathrm{mix}}$ with valence overlap fermions on a domain-wall fermion sea is presented. The calculation is performed on four ensembles of the $2+1$ flavor domain-wall gauge configurations: ${24}^{3}\ifmmode\times\else\texttimes\fi{}64$ ($a{m}_{l}=0.005$, $a=0.114\text{ }\text{ }\mathrm{fm}$) and ${32}^{3}\ifmmode\times\else\texttimes\fi{}64$ ($a{m}_{l}=0.004$, 0.006, 0.008, $a=0.085\text{ }\text{ }\mathrm{fm}$). For pion masses close to 300 MeV we find ${\ensuremath{\Delta}}_{\mathrm{mix}}=0.030(6)\text{ }\text{ }{\mathrm{GeV}}^{4}$ at $a=0.114\text{ }\text{ }\mathrm{fm}$ and ${\ensuremath{\Delta}}_{\mathrm{mix}}=0.033(12)\text{ }\text{ }{\mathrm{GeV}}^{4}$ at $a=0.085\text{ }\text{ }\mathrm{fm}$. The results are quite independent of the lattice spacing and they are significantly smaller than the results for valence domain-wall fermions on asqtad sea or those of valence overlap fermions on clover sea. Combining the results extracted from these two ensembles, we get ${\ensuremath{\Delta}}_{\mathrm{mix}}=0.030(6)(5)\text{ }\text{ }{\mathrm{GeV}}^{4}$, where the first error is statistical and the second is the systematic error associated with the fitting method.

Lattice four-fermion models containing $N$ flavors of staggered fermions, that are invariant under $Z_2$ and U(1) chiral symmetries, are known to suffer from sign problems when formulated using the auxiliary field approach. Although these problems have been ignored in previous studies, they can be severe. Here we show that the sign problems disappear when the models are formulated in the fermion bag approach, allowing us to solve them rigorously for the first time., references added

The recently proposed fermion bag approach is a powerful technique to solve some four-fermion lattice field theories. Due to the existence of a duality between strong and weak couplings, the approach leads to efficient Monte Carlo algorithms in both these limits. The new method allows us for the first time to accurately compute quantities close to the quantum critical point in the three dimensional lattice Thirring model with massless fermions on large lattices. The critical exponents at the quantum critical point are found to be $\nu=0.85(1)$, $\eta = 0.65(1)$ and $\eta_\psi = 0.37(1)$., Comment: 5 pages, 2 figures and 1 table, published version

A canonical ensemble algorithm is employed to study the phase diagram of Nf ¼ 3 QCD using lattice simulations. We lock in the desired quark number sector using an exact Fourier transform of the fermion determinant. We scan the phase space below Tc and look for an S-shape structure in the chemical potential, which signals the coexistence phase of a first order phase transition in finite volume. Applying Maxwell construction, we determine the boundaries of the coexistence phase at three temperatures and extrapolate them to locate the critical point. Using an improved gauge action and improved Wilson fermions on lattices with a spatial extent of 1.8 fm and quark masses close to that of the strange, we find the critical point at TE ¼ 0:925ð5ÞTc and baryon chemical potentialE ¼ 2:60ð8ÞTc. QCD is expected to have a rich phase diagram at finite temperature and finite density. Current lattice calculations have shown that the transition from the hadronic phase to QGP phase is a rapid crossover (1,2). For large baryon chemical potential and very low temperature, a number of models suggest that the transition is a first order. If this is the case, when the chemical potential is lowered and temperature raised, this first order phase transition is ex- pected to end as a second order phase transition point—the critical point. However, lattice QCD simulations with chemical potential are difficult due to the notorious ''sign problem''. The majority of current simulations are focus- ing on small chemical potential regionq=T � 1 where the ''sign problem'' appears to be under control. Up to now, all the Nf ¼ 3 or 2 þ 1 simulations are based on the grand canonical ensemble (T, � B as parameters) with staggered fermions. The results from the multiparameter reweighting (3), Taylor expansion with small � (4,5) and the curvature of the critical surface (6) are not settled and need to be cross-checked. Even the existence of the critical point is in question (6). We employ an algorithm, which is not re- stricted to small chemical potential because of the mitiga- tion of the sign problem under the current parameter settings, to study this problem. In this letter, we adopt an exact Monte Carlo algorithm (7-9) based on the canonical partition function (10-15) which is designed to alleviate the determinant fluctuation problems. As it turns out, the sign fluctuations are not serious on the lattices used in the present study, as we shall see later. In the canonical ensemble simulations in finite volume, the coexistence phase of a first order phase tran- sition has a characteristic S-shape as a function of density due to the surface tension. This finite-volume property has been exploited successfully to identify the phase bounda- ries via the Maxwell construction in studies of phase transition with the staggered fermions (14,15) and clover fermions (16) for the Nf ¼ 4casewhich is known to have a first order phase transition at � ¼ 0. In these benchmark studies the boundaries were identified at three temperatures below Tc, and they were extrapolated in density and tem- perature to show that the intersecting point indeed coin- cides with the independently identified first order transition point at T c and � ¼ 0 (16). In view of the success of the N f ¼ 4 study, we extend this method to the more realistic Nf ¼ 3 case (17,18). Although the real world contains two light quarks and one heavier strange quark, the three degenerate flavor case has a similar phase structure. Our primary goal in this study is to determine whether a first order phase transition exists for Nf ¼ 3 and where the critical point is located. With the aid of recently developed matrix reduction technique (19-21), we scan the chemical potential as a function of baryon number for four temperatures below Tc which is determined at zero chemical potential, and we observe clear signals for a first order phase transition for temperatures below 0:93Tc. The phase boundaries of the coexistence phase are determined and then extrapolated in temperature and density to locate the critical point at TE ¼ 0:927ð5ÞTc andE ¼ 2:60ð8ÞTc. Our results are based on simulations on 6 3 � 4 lattices with clover fer- mion action with quark masses which correspond to the pion mass from 750 MeV for the lowest temperature to 775 MeV for the highest temperature. The canonical partition function in lattice QCD can be derived from the fugacity expansion of the grand canonical partition function, ZðV; T; � Þ¼ X k ZCðV; T; kÞek=T ; (1)

We present a new approach to some four-fermion lattice field theories which we call the generalized fermion bag approach. The basic idea is to identify unpaired fermionic degrees of freedom that cause sign problems and collect them in a bag. Paired fermions usually act like bosons and do not lead to sign problems. A resummation of all unpaired fermion degrees of freedom inside the bag is sufficient to solve the fermion sign problem in a variety of interesting cases. Using a concept of duality we then argue that the size of the fermion bags is small both at strong and weak couplings. This allows us to construct efficient algorithms in both these limits. Using the fermion bag approach, we study the quantum phase transition of the 3D massless lattice Thirrring model which is of interest in the context of Graphene. Using our method we are able to solve the model on lattices as large as $40^3$ with moderate computational resources. We obtain the precise location of the quantum critical point and the values of the critical exponents through this study., Comment: 14 pages, 5 figures, 1 table, contribution to Lattice 2011, July 10-16, 2011, Squaw Valley, Lake Tahoe, California, USA

We study a strongly coupled $Z_2$ lattice gauge theory with two flavors of quarks, invariant under an exact $\mathrm{SU}(2)\times \mathrm{SU}(2) \times \mathrm{U}_A(1) \times \mathrm{U}_B(1)$ symmetry which is the same as QCD with two flavors of quarks without an anomaly. The model also contains a coupling that can be used to break the $\mathrm{U}_A(1)$ symmetry and thus mimic the QCD anomaly. At low temperatures $T$ and small baryon chemical potential $\mu_B$ the model contains massless pions and massive bosonic baryons similar to QCD with an even number of colors. In this work we study the $T-\mu_B$ phase diagram of the model and show that it contains three phases : (1) A chirally broken phase at low $T$ and $\mu_B$, (2) a chirally symmetric baryon superfluid phase at low $T$ and high $\mu_B$, and (3) a symmetric phase at high $T$. We find that the nature of the finite temperature chiral phase transition and in particular the location of the tricritical point that seperates the first order line from the second order line is affected significantly by the anomaly., Comment: 22 pages, 16 figures, 5 tables, references added

In a progress toward searching for the QCD critical point, we study the finite density phase transition of ${N}_{f}=4$ and 2 lattice QCD at finite temperature with the canonical ensemble approach. We develop a winding number expansion method to accurately project out the particle number from the fermion determinant which greatly extends the applicable range of baryon number sectors to make the study feasible. Our lattice simulation was carried out with the clover fermions and improved gauge action. For a given temperature, we calculate the baryon-chemical potential from the canonical approach to look for the mixed phase as a signal for the first-order phase transition. In the case of ${N}_{f}=4$, we observe an ``S-shape'' structure in the chemical potential-density plane due to the surface tension of the mixed phase in a finite volume which is a signal for the first-order phase transition. We use the Maxwell construction to determine the phase boundaries for three temperatures below ${T}_{c}$. The intersecting point of the two extrapolated boundaries turns out to be at the expected first-order transition point at ${T}_{c}$ with $\ensuremath{\mu}=0$. This serves as a check for our method of identifying the critical point. We also studied the ${N}_{f}=2$ case, but do not see a signal of the mixed phase for temperature as low as $0.83{T}_{c}$.

The existence of the QCD critical point at non-zero baryon density is not only of great interest for experimental physics but also a challenge for the theory. We use lattice simulations based on the canonical ensemble method to explore the finite baryon density region and look for the critical point. We scan the phase diagram of QCD with three degenerate quark flavors using clover fermions with m π ≈ 700 MeV on 6 3 × 4 lattices. We measure the baryon chemical potential as we increase the density and we see the characteristic “S-shape” that signals the first order phase transition. We determine the phase boundary by Maxwell construction and report our preliminary results for the location of critical point.

The overlap fermion propagator is calculated on 2+1 flavor domain wall fermion gauge configurations on 16^3 x 32, 24^3 x 64 and 32^3 x 64 lattices. With HYP smearing and low eigenmode deflation, it is shown that the inversion of the overlap operator can be expedited by ~ 20 times for the 16^3 x 32 lattice and ~ 80 times for the 32^3 x 64 lattice. Through the study of hyperfine splitting, we found that the O(m^2a^2) error is small and these dynamical fermion lattices can adequately accommodate quark mass up to the charm quark. The low energy constant \Delta_{mix} which characterizes the discretization error of the pion made up of a pair of sea and valence quarks in this mixed action approach is calculated via the scalar correlator with periodic and anti-periodic boundary conditions. It is found to be small which shifts a 300 MeV pion mass by ~ 10 to 19 MeV on these sets of lattices. We have studied the signal-to-noise issue of the noise source for the meson and baryon. It is found that the many-to-all meson and baryon correlators with Z_3 grid source and low eigenmode substitution is efficient in reducing errors for the correlators of both mesons and baryons. With 64-point Z_3 grid source and low-mode substitution, it can reduce the statistical errors of the light quark (m_{\pi} ~ 200 - 300 MeV) meson and nucleon correlators by a factor of ~ 3-4 as compared to the point source. The Z_3 grid source itself can reduce the errors of the charmonium correlators by a factor of ~ 3., Comment: 30 pages, 18 figures, replaced with the version to be published in PRD

We explore the sign problem in strongly coupled lattice QED with one flavor of Wilson fermions in four dimensions using the fermion bag formulation. We construct rules to compute the weight of a fermion bag and show that even though the fermions are confined into bosons, fermion bags with negative weights do exist. By classifying fermion bags as either simple or complex, we find numerical evidence that complex bags with positive and negative weights come with almost equal probabilities and this leads to a severe sign problem. On the other hand simple bags mostly have a positive weight. Since the complex bags almost cancel each other, we suggest that eliminating them from the partition function may be a good approximation. This modified partition function suffers only from a mild sign problem. We also find a simpler model which does not suffer from any sign problem and may still be a good approximation at small and intermediate values of the hopping parameter. We also prove that when the hopping parameter is strictly infinite all fermion bags are non-negative., Comment: 17 pages, 4 figures, 5 tables

The existence of the QCD critical point at non-zero baryon density is not only of great interest for experimental physics but also a challenge for the theory. We use lattice simulations based on the canonical ensemble method to explore the finite baryon density region and look for the critical point. We scan the phase diagram of QCD with three degenerate quark flavors using clover fermions with $m_\pi \approx 700{MeV}$ on $6^3\times4$ lattices. We measure the baryon chemical potential as we increase the density and we see the characteristic "S-shape" that signals the first order phase transition. We determine the phase boundary by Maxwell construction and report our preliminary results for the location of critical point., Comment: 2 pages, 2 figures - To appear in the conference proceedings for Quark Matter 2009, March 30 - April 4, Knoxville, Tennessee

Finite density simulations require dynamical fermions which are computationally demanding. We employ Ferrenberg and Swendsen reweighting method to reduce the number of ensembles needed. We use their method to do a combined reweighting in both $\beta$ and quark number $k$ on an ensemble generated by the Kentucky group.

In her 3 July Perspective, “Earth's inner core: Is the rotation real?,” A. Souriau ([1][1]) notes that several different estimates of the inner core rotation rate have been published since the appearance of the original results of Song and Richards ([2][2]). She discusses problems with the