Phase structure for lattice fermions with flavored chemical potential terms
Tatsuhiro Misumi
备注：
34 pages, 9 figures; extended discussion on Lorentz symmetry for general values of parameters, two figures added, references added, version to appear in JHEP
We discuss the chiral phase diagram in the parameter space of lattice QCD with minimal-doubling fermions, which can be seen as lattice fermions with flavored chemical potential terms. We study strong-coupling lattice QCD with the Karsten-Wilczek formulation, which has one relevant parameter $μ_{3}$ as well as gauge coupling and a mass parameter. We find a nontrivial chiral phase structure with a second-order phase transition between chiral symmetric and broken phases. To capture the whole structure of the phase diagram, we study the related lattice Gross-Neveu model. The result indicates that the chiral phase transition also exists in the weak-coupling region. From these results we speculate on the $μ_{3}$-$g^{2}$ chiral phase diagram in lattice QCD with minimal-doubling fermions, and discuss their application to numerical simulations.
I discuss minimally doubled fermions fermions as an ultra-local formulation on the lattice for sea quarks that realize a non-singlet chiral symmetry. I introduce a non-singlet mass term for Karsten-Wilczek fermions and identify the appropriate representation of the SU(2) flavor group at finite lattice spacing. I present an algebraic proof that the symmetry of the quark determinant under charge conjugation and reflections of the Euclidean axes is preserved for Karsten-Wilczek fermions as sea quarks. Finally, I discuss how the flavor components in meson correlation functions with Karsten-Wilczek…
We investigate the parity-broken phase structure for staggered and naive fermions in the Gross-Neveu model as a toy model of QCD. We consider a generalized staggered Gross-Neveu model including two types of four-point interactions. We use generalized mass terms to split the doublers for both staggered and naive fermions. The phase boundaries derived from the gap equations show that the mass splitting of tastes results in an Aoki phase both in the staggered and naive cases. We also discuss the continuum limit of these models and explore taking the chirally-symmetric limit by fine-tuning a mass …
By using the lattice Monte-Carlo simulation, we investigate the finite temperature (T) chiral phase transition at color SU(3) gauge theories with various species of fundamental fermions, and discuss the signal of the (pre-)conformality at large Nf (num. of flavors.) via their comparisons. As Nf increases, we observe stronger fermion screening effects which result from a larger fermion multiplicity. We investigate a finite T step-scaling associated with a uniqueness of the critical temperature (Tc) at each Nf, then the vanishing step-scaling indicates the emergence of the conformality around Nf…
We present a theoretical foundation for the index theorem in naive and minimally doubled lattice fermions by studying the spectral flow of a Hermitean version of Dirac operators. We utilize the point splitting method to implement flavored mass terms, which play an important role in constructing proper Hermitean operators. We show the spectral flow correctly detects the index of the would-be zero modes which is determined by gauge field topology and the number of species doublers. Using the flavored mass terms, we present new types of overlap fermions from the naive fermion kernels, with a numb…
We present a theoretical foundation for the Index theorem in naive and minimally doubled lattice fermions by studying the spectral flow of a Hermitean version of Dirac operators. We utilize the point splitting method to implement flavored mass terms, which play an important role in constructing proper Hermitean operators. We show the spectral flow correctly detects the index of the would-be zero modes which is determined by gauge field topology. Using the flavored mass terms, we present new types of overlap fermions from the naive fermion kernels, with a number of flavors that depends on the c…
We discuss recent progress in lattice QCD studies on various aspects involving strange quarks. Appropriate combinations of conserved net strange and net charm fluctuations and their correlations with other conserved charges provide evidence that in the hadronic phase so far unobserved hadrons contribute to the thermodynamics and need to be included in hadron resonance gas models. In the strange sector this leads to significant reductions of the chemical freeze-out temperature of strange hadrons. In this context, a discussion of data from heavy-ion collisions at SPS, RHIC and LHC on the chemica…
Different versions of improved staggered fermions can be used as valence quarks to reduce discretization effects in lattice QCD calculations while increasing statistics on existing staggered gauge ensembles. Such mixed-action simulations can be used to improve determinations of light quark masses, Gasser-Leutwyler couplings, decay constants, and other parameters relevant to particle phenomenology. We recall the generalization of ordinary, unmixed staggered chiral perturbation theory required to describe data from lattice calculations with a mixed action such as with HYP staggered valence quark…
Resonant scattering in two-flavored Sp(4) lattice gauge theories
Swansea University（斯旺西大学）；University of Graz（格拉茨大学）；Pusan National University（釜山国立大学）；University of Tsukuba（筑波大学）；Institute for Basic Science (IBS)（基础科学研究院）；National Yang Ming Chiao Tung University（国立阳明交通大学）；Chung-Yuan Christian University（中原大学）
We show that two recent independent proposals for regularizing a chiral gauge theory stem from one common trick. If the anomaly free complex representation carried by the right handed fermi--fields is $r$ one constructs a vector like theory with flavored right handed fermionic matter in $r+\bar r$ but with a mass matrix of the order of the cutoff and having an index equal to unity in an infinite dimensional flavor space. We present a Pauli--Villars realization of the trick that is likely to work to all orders in perturbation theory and a lattice version which is argued to produce the correct c…
We study a recently proposed formulation of overlap fermions at finite density. In particular we compute the energy density as a function of the chemical potential and the temperature. It is shown that overlap fermions with chemical potential reproduce the correct continuum behavior.
A new formulation of chiral fermions on the lattice is presented. It is a version of overlap fermions, but built from the computationally efficient staggered fermions rather than the previously used Wilson fermions. The construction reduces the four quark flavors described by the staggered fermion to two quark flavors; this pair can be taken as the up and down quarks in Lattice QCD. The exact flavored chiral symmetry of the staggered fermion gets converted into an unflavored Ginsparg-Wilson chiral symmetry of the new overlap fermion, which also has pairs of exact chiral zero-modes satisfying t…
We review the recent progress in new lattice fermion formulations. We focus on the following three types which have possibility of improving lattice simulations. (1) Flavored-mass fermions are a generalization of Wilson fermions with species-splitting mass terms. In particular, staggered-Wilson fermions initiated by Adams have possibilities of reducing numerical costs in overlap fermions and the influence of taste-breaking in staggered fermions. (2) Central-branch Wilson fermions, in which additive mass renormalization is forbidden by extra axial symmetry, could enable us to perform Wilson-fer…
Wilson Fermions with untwisted and twisted mass are widely used in lattice simulations. Therefore one important question is whether the twist angle and the lattice spacing affect the phase diagram. We briefly report on the study of the phase diagram of QCD in the parameter space of the degenerate quark masses, isospin chemical potential, lattice spacing, and twist angle by employing chiral perturbation theory. Moreover we calculate the pion masses and their dependence on these four parameters.
We study condensation in two-flavored, scalar QED with non-degenerate masses at finite chemical potential. The conventional formulation of the theory has a sign problem at finite density which can be solved using an exact reformulation of the theory in terms of dual variables. We perform a Monte Carlo simulation in the dual representation and observe a condensation at a critical chemical potential $μ_c$. After determining the low-energy spectrum of the theory we try to establish a connection between $μ_c$ and the mass of the lightest excitation of the system, which are naively expected to be e…
The three-dimensional four-fermion model with a Z_2 chiral symmetry and N=4 fermion species in the system is investigated numerically at non-zero temparature and chemical potential. The phase diagram in the (chemical potential, temperature) plane is mapped out quantitatively. A detailed finite size scaling analysis shows that the zero temperature and non-zero chemical potential chiral phase transition is first order, whereas the non-zero temperature and non-zero chemical potential transition remains second order down to very low temperatures. Quantitative results for the location of the end of…
Recently a formulation of overlap fermions at finite density based on an analytic continuation of the sign function was proposed. We study this proposal by analyzing the energy and number densities for free fermions as a function of the chemical potential and the temperature. Our results show that overlap fermions with chemical potential give rise to the correct continuum behavior.
Generalized susceptibilities of the net quark number have been proposed to be good probes for the transitions in the QCD phase diagram and for the search of a possible critical end point. In this article we explore a new strategy for computing quark number susceptibilities from lattice QCD via an expansion in the fugacity parameter $e^{μβ}$. All quark number related bulk observables are particularly easy to access in this approach and we present results for generalized quark number susceptibilities up to 4-th order. Ratios of these quantities are studied and compared with model calculations fo…
We present a phase diagram for SU(3) lattice gauge theory with 695 MeV dynamical staggered fermions, in the plane of temperature and chemical potential, obtained from effective Polyakov line actions. The derivation is via the method of relative weights, and the effective theories are solved at finite chemical potential by mean field theory.
Recently it was suggested that the problem of species doubling with Kogut-Susskind lattice fermions entails, at finite chemical potential, a confusion of particles with antiparticles. What happens instead is that the familiar correspondence of positive-energy spinors to particles, and of negative-energy spinors to antiparticles, ceases to hold for the Kogut-Susskind time derivative. To show this we highlight the role of the spinorial ``energy'' in the Osterwalder-Schrader reconstruction of the Fock space of non-interacting lattice fermions at zero temperature and nonzero chemical potential. We…
We propose a new framework for investigating two-flavor lattice QCD with finite temperature and density. We consider the Karsten-Wilczek fermion formulation, in which a species-dependent imaginary chemical potential term can reduce the number of species to two without losing chiral symmetry. This lattice discretization is useful for study on finite-($T$,$μ$) QCD since its discrete symmetries are appropriate for the case. To show its applicability, we study strong-coupling lattice QCD with temperature and chemical potential. We derive the effective potential of the scalar meson field and obtain…
A numerical technique is proposed for an efficient numerical determination of the average phase factor of the fermionic determinant continued to imaginary values of the chemical potential. The method is tested in QCD with eight flavors of dynamical staggered fermions. A direct check of the validity of analytic continuation is made on small lattices and a study of the scaling with the lattice volume is performed.
We consider the phase diagram of twisted mass Wilson fermions of two-flavor QCD in the parameter space of the quark mass, the isospin chemical potential, the twist angle and the lattice spacing. This work extends earlier studies in the continuum and those at zero chemical potential. We evaluate the phase diagram as well as the spectrum of the (pseudo-)Goldstone bosons using the chiral Lagrangian for twisted mass Wilson fermions at non-zero isospin chemical potential. The phases are obtained from a mean field analysis. At zero twist angle we find that already an infinitesimal isospin chemical p…
The staggered fermion determinant is complex when the quark chemical potential mu is nonzero. Its fourth root, used in simulations with dynamical fermions, will have phase ambiguities that become acute when Re mu is sufficiently large. We show how to resolve these ambiguities, but our prescription only works very close to the continuum limit. We argue that this regime is far from current capabilities. Other procedures require being even closer to the continuum limit, or fail altogether, because of unphysical discontinuities in the measure. At zero temperature the breakdown is expected when Re …
Standard lattice fermion algorithms run into the well-known sign problem at real chemical potential. In this paper we investigate the possibility of using imaginary chemical potential, and argue that it has advantages over other methods, particularly for probing the physics at finite temperature as well as density. As a feasibility study, we present numerical results for the partition function of the two-dimensional Hubbard model with imaginary chemical potential. We also note that systems with a net imbalance of isospin may be simulated using a real chemical potential that couples to I_3 with…
SU(2) lattice gauge theory with dynamical fermion at non-zero chemical potential and at finite temperature is studied. We focus on the influence of chemical potential for quark condensate and mass of pseudoscalar meson at finite temperature. Hybrid Monte Carlo simulations with $N_f=8$ staggered fermions are carried out on $12 \times 12\times 24 \times 4$ lattice. At $β=1.1$ and $m_{q}=$0.05,0.07,0.1, we calculate the quark condensate and masses of pseudoscalar meson consisting of light and heavier quarks for chemical potential $μ=$ 0.0,0.02,0.05,0.1,0.2.
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 $μ=0$ 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)criti…
We investigate the phase structure of the two-dimensional lattice Gross-Neveu model formulated with the Wilson fermion action to leading order of 1/N expansion. Structural change of the parity-broken phase under the influence of finite temperature and chemical potential is studied. The connection between the lattice phase structure and the chiral phase transition of the continuum theory is clarified.
We show that in the microscopic domain of QCD (also known as the $ε$-domain) at nonzero chemical potential the average phase factor of the fermion determinant is nonzero for $μ< m_π/2$ and is exponentially suppressed for larger values of the chemical potential. This follows from the chiral Lagrangian that describes the low-energy limit of the expectation value of the phase factor. Explicit expressions for the average phase factor are derived using a random matrix formulation of the zero momentum limit of this chiral Lagrangian.
We perform the first study of lattice QCD with overlap fermions at finite temperature $T$ and chemical potential $μ$. We start from the Taylor expanded overlap fermion action, and derive in the strong coupling limit the effective free energy by mean field approximation. On the ($μ,T$) plane and in the chiral limit, there is a tricritical point, separating the second order chiral phase transition line at small $μ$ and large $T$, and first order chiral phase transition line at large $μ$ and small $T$.
We have recently given a construction of the overlap Dirac operator at nonzero quark chemical potential. Here, we introduce a quark chemical potential in the domain-wall fermion formalism and show that our earlier result is reproduced if the extent of the fifth dimension is taken to infinity and its lattice spacing is taken to zero. We also extend this result to include a bare quark mass, consider its continuum limit, and prove a number of properties of the overlap operator at nonzero quark chemical potential. In particular, we show that the relation between the anomaly and the index of the ov…
We investigate the real and imaginary chemical-potential dependence of pion and $ρ$-meson screening masses in both the confinement and the deconfinement region by using two-flavor lattice QCD. The spatial meson correlators are calculated in the imaginary chemical potential region with lattice QCD simulations. We extract pion and $ρ$-meson screening masses from the correlators. The obtained meson screening masses are extrapolated to the real chemical potential region by assuming some analytic function. In the real chemical potential region, the resulting pion and $ρ$-meson screening masses mono…
A dimensionally reduced expression for the QCD fermion determinant at finite temperature and chemical potential is derived which sheds light on the determinant's dependence on these quantities. This is done via a partial zeta regularisation, formally applying a general formula for the zeta-determinant of a differential operator in one variable with operator-valued coefficients. The resulting expression generalises the known one for the free fermion determinant, obtained via Matsubara frequency summation, to the case of general background gauge field; moreover there is no undetermined overall f…
We study the phase structure of imaginary chemical potential. We calculate the Polyakov loop using clover-improved Wilson action and renormalization improved gauge action. We obtain a two-state signals indicating the first order phase transition for $β= 1.9, μ_I = 0.2618, κ=0.1388$ on $8^3\times 4$ lattice volume We also present a result of the matrix reduction formula for the Wilson fermion.
Using Wilson fermions, we study SU(2) lattice QCD with the chemical potential at $β=1.6$. The ratio of fermion determinants is evaluated at each Metropolis link update step. We calculate the baryon number density, the Polyakov loops and the pseudoscalar and vector masses on $4^4$ and $4^3\times 8$ lattices. Preliminary data show the pseudoscalar meson becomes massive around $μ=0.4$, which indicates the chiral symmetry restoration. The calculation is broken down when approaching to the transition region. We analyze the behavior of the fermion determinant and eigen value distributions of the det…
We present a reduction method for Wilson Dirac fermions with non-zero chemical potential which generates a dimensionally reduced fermion matrix. The size of the reduced fermion matrix is independent of the temporal lattice extent and the dependence on the chemical potential is factored out. As a consequence the reduced matrix allows a simple evaluation of the Wilson fermion determinant for any value of the chemical potential and hence the exact projection to the canonical partition functions.
We give another derivation of quark confinement in QCD from the viewpoint of the low-energy effective Abelian gauge theory of QCD obtained via Abelian projection. It is based on the recently discovered Berezinskii-Kosterlitz-Thouless phase transition in the four-dimensional Abelian gauge theory. Moreover, we show that there exists a critical gauge coupling constant in QCD, above which confinement set in and below which there is no confinement. In a SU(N) gauge theory with $N_f$ flavored fermions, we argue that this leads to a critical value of fermion flavors $N_f^c$ for the confinement as wel…
For QCD with Wilson fermions at isospin chemical potential we study the finite phase transition on an $8^3\times4$ lattice at $κ=0.15$. We use two gauge actions: Wilson action and DBW2 action. Both actions give the same results. The phase diagram is qualitatively similar to the one obtained for QCD at small baryon chemical potential. We also calculate the number density for various isospin chemical potentials.
We present results from an ongoing study of the phase diagram of (2+1)-flavor QCD using the HISQ action with smaller than physical light quark masses in the Roberge-Weiss (RW) plane on lattices with temporal extent $N_τ=4$. We find that the endpoint of the $1^{st}$ order RW transition line remains $2^{nd}$ order at least down to light quark masses corresponding to Goldstone pion masses of $55$ MeV. Furthermore, we show that the chiral condensate is sensitive to the RW transition and may serve as a energy-like operator characterizing universal behavior close to the RW endpoint.
We study chemical-potential dependence of confinement and mass gap in QCD with adjoint fermions in spacetime with one spatial compact direction. By calculating the one-loop effective potential for the Wilson line in the presence of chemical potential, we show that a center-symmetric phase and a center-broken phase alternate when the chemical potential in unit of the compactification scale is increased. In the center-symmetric phase we use semiclassical methods to show that photons in the magnetic bion plasma acquire a mass gap that grows with the chemical potential as a result of anisotropic i…
We study the two dimensional lattice Thirring model in the presence of a fermion chemical po- tential. Our model is asymptotically free, contains massive fermions that mimic a baryon and light bosons that mimic pions. Hence it is a useful toy model for QCD, especially since it too suffers from a sign problem in the auxiliary field formulation in the presence of a fermion chemical potential. In this work we formulate the model in both the world line and fermion-bag representations and show that the sign problem can be completely eliminated with open boundary conditions when the fermions are mas…
The order of the thermal transition in the chiral limit of QCD with two dynamical flavours of quarks is a long-standing issue. Still, it is not definitely known whether the transition is of first or second order in the continuum limit. Which of the two scenarios is realized has important implications for the QCD phase diagram and the existence of a critical endpoint at finite densities. Settling this issue by simulating at successively decreased pion mass was not conclusive yet. Recently, an alternative approach was proposed, extrapolating the first order phase transition found at imaginary ch…
A connection between the operator fermionic currents $\hatJ$ and corresponding `Grassmannian' currents $J$ in the functional integral formalism is studied. The QCD action with non--zero chemical potential $μ$ is derived. A connection between the fermionic Fock space and boundary conditions along the forth direction is discussed.
The order of the thermal phase transition in the chiral limit of Quantum Chromodynamics (QCD) with two dynamical flavors of quarks is a long-standing issue and still not known in the continuum limit. Whether the transition is first or second order has important implications for the QCD phase diagram and the existence of a critical endpoint at finite densities. We follow a recently proposed approach to explicitly determine the region of first order chiral transitions at imaginary chemical potential, where it is large enough to be simulated, and extrapolate it to zero chemical potential with kno…
In this lecture we discuss various properties of the phase factor of the fermion determinant for QCD at nonzero chemical potential. Its effect on physical observables is elucidated by comparing the phase diagram of QCD and phase quenched QCD and by illustrating the failure of the Banks-Casher formula with the example of one-dimensional QCD. The average phase factor and the distribution of the phase are calculated to one-loop order in chiral perturbation theory. In quantitative agreement with lattice QCD results, we find that the distribution is Gaussian with a width $\sim μT \sqrt V$ (for $m_π…
In QCD the spontaneous breaking of chiral symmetry and the U(1) axial anomaly can be understood considering instantons as the gauge configurations mediating quark-quark interaction. The existence of an exact zero mode solution of the Dirac equation in the field of a single instanton is the fundamental ingredient of this analysis. Explicit expressions for psi_0 are available for T different from 0 and mu=0, and mu different from 0 and T=0. In this paper we derive the solution for the most general case T different from 0 and mu different from 0. This new result opens the possibility of investiga…
Complex action problems coming from either a chemical potential or a topological term have been solved for several models in recent years by mapping them to so-called dual degrees of freedom. In terms of these dual variables the partition sum has only real and positive contributions such that a Monte Carlo simulation is possible. In this paper we discuss a dual representation for massless staggered fermions in two dimensions coupled to a U(1) gauge field. We include a topological term, and for the case of several flavors with vanishing total charge also a chemical potential. We show that the r…
The QCD phase diagram is studied in the lattice QCD simulation with the imaginary chemical potential approach. We employ a clover-improved Wilson fermion action of two-flavors and a renormalization-group improved gauge action, and perform the simulation at an intermediate quark mass on a $8^3\times 4$ lattice. The QCD phase diagram in the imaginary chemical potential $μ_I$ region is investigated by performing the simulation for more than 150 points on the $(β,μ_I)$ plane. We find that the Roberge-Weiss phase transition at $μ_I/T=π/3$ is first order and its endpoint is second order, which are i…
We discuss simulation strategies for the massless lattice Schwinger model with a topological term and finite chemical potential. The simulation is done in a dual representation where the complex action problem is solved and the partition function is a sum over fermion loops, fermion dimers and plaquette-occupation numbers. We explore strategies to update the fermion loops coupled to the gauge degrees of freedom and check our results with conventional simulations (without topological term and at zero chemical potential), as well as with exact summation on small volumes. Some physical implicatio…
Recently, it has been suggested that large-Nc orbifold equivalences may be applicable to certain theories with chemical potentials, including QCD, in certain portions of their phase diagram. When valid, such an equivalence offers the possibility of relating large-Nc QCD at non-zero baryon chemical potential, a theory with a complex fermion determinant, to a related theory whose fermion determinant is real and positive. In this paper, we provide a test of this large Nc equivalence using a holographic realization of a supersymmetric theory with baryon chemical potential and a related theory with…
We study the expectation value of the phase of the fermion determinant for Wilson lattice fermions with chemical potential. We use quenched SU(3) ensembles and implement a recently proposed exact dimensional reduction of the fermion determinant. Ensembles at several temperatures below and above the phase transition are studied and we analyze the role of the quark mass, the temperature, the volume and the topological sectors. We compare our numerical results to predictions from chiral perturbation theory.
We investigate the possibility of coupling a chemical potential only to the physical chiral fermions on the lattice starting from the many body state description of overlap fermions. After developing the formalism for a chiral gauge theory, we focus our attention on the case of free fermions coupled to a vector like chemical potential and discuss the issue of zero temperature divergences.
We present results on the curvature of the critical line of QCD with 2+1 HISQ fermions at nonzero temperature and quark density obtained by analytic continuation from imaginary chemical potentials. Monte Carlo simulations are performed by means of the MILC code, suitably modified to include a nonzero imaginary baryon chemical potential. We set the chemical potential at the same value for the three quark species and work on the line of constant physics with a light to strange mass ratio of 1/20 as determined in Ref.~\cite{Bazavov:2011nk}.
We construct a lattice theory describing a system of interacting nonrelativistic spin s=1/2 fermions at nonzero chemical potential. The theory is applicable whenever the interparticle separation is large compared to the range of the two-body potential, and does not suffer from a sign problem. In particular, the theory could be useful in studying the thermodynamic limit of fermion systems for which the scattering length is much larger than the interparticle spacing, with applications to realistic atomic systems and dilute neutron gases.
We propose a new method to investigate the thermal properties of QCD with a small chemical potential $(μ)$. The derivatives of the phase transition point with respect to $μ$ are computed for 2 flavors of p4-improved staggered fermions. We moreover comment on the complex phase of the fermion determinant in finite-density QCD.
We investigate high density state of SU(2) QCD in the case of the Wilson fermions with Iwasaki improved action. Based on the Woodbery formula, the ratio of fermion determinants is evaluated at each step of the Metropolis link update. At $β=0.7$, for $κ= 0.150$, and $κ= 0.175$, we calculate thermodynamical quantities, such as, baryon number density, Polyakov line, and the energy density of gluon sector with chemical potential $μ$=0 to 0.9 on the $4^{3} \times 8$ lattice. The susceptibility of the Polyakov line to the chemical potential shows peak at around $μ= 0.7$ which indicates the deconfine…
We present a method of simulating lattice QCD at nonzero chemical potential in the chiral limit. By adding a weak four-fermi interaction to the standard staggered fermion SU(3) QCD action, we produce an algorithm in which the limit of massless fermions is well-behaved and physical. Using configurations at zero chemical potential, and an exact fugacity expansion of the fermion determinant, we can simulate QCD at nonzero chemical potential and evade the notorious problem of the complex action. Small lattice simulations give physical results: At strong gauge coupling the critical chemical potenti…
The QCD phase diagram at imaginary chemical potential exhibits a rich structure and studying it can constrain the phase diagram at real values of the chemical potential. Moreover, at imaginary chemical potential standard numerical techniques based on importance sampling can be applied, since no sign problem is present. In the last decade, a first understanding of the QCD phase diagram at purely imaginary chemical potential has been developed, but most of it is so far based on investigations on coarse lattices ($N_τ=4$, $a=0.3\:$fm). Considering the $N_f=2$ case, at the Roberge-Weiss critical v…
We clarify the relation between the improvement of dispersion relations in the fermion sector of lattice regularized QCD and the improvement of bulk thermodynamic observables. We show that in the infinite temperature limit the cut-off dependence in dispersion relations can be eliminated up to O(a^n) corrections, if the quark propagator is chosen to be rotationally invariant up to this order. In bulk thermodynamic observables this eliminates cut-off effects up to the same order at vanishing as well as non-vanishing chemical potential. We furthermore show, that in the infinite temperature, ideal…
