We study positive and negative parity nucleons on the lattice using the chirally improved lattice Dirac operator. Our analysis is based on a set of three operators chi_i with the nucleon quantum numbers but in different representations of the chiral group and with different diquark content. We use a variational method to separate ground state and excited states and determine the mixing coefficients for the optimal nucleon operators in terms of the chi_i. We clearly identify the negative parity resonances N(1535) and N(1650) and their masses agree well with experimental data. The mass of the observed excited positive parity state is too high to be interpreted as the Roper state. Our results for the mixing coefficients indicate that chiral symmetry is important for N(1535) and N(1650) states. We confront our data for the mixing coefficients with quark models and provide insights into the physics of the nucleon system and the nature of strong decays.Comment: Tables added, small modifications in the tex

The Lee-Yang theorem for the zeroes of the partition function is not strictly applicable to quantum systems because the zeroes are defined in units of the fugacity e h∆τ , and the Euclidean-time lattice spacing ∆τ can be divergent in the infrared (IR). We recently presented analytic arguments describing how a new space-Euclidean time zeroes expansion can be defined, which reproduces Lee and Yang's scaling but avoids the unresolved branch points associated with the breaking of nonlocal symmetries such as parity. We now present a first numerical analysis for this new zeros approach for a quantum spin chain system. We use our scheme to quantify the renormalization group flow of the physical lattice couplings to the IR fixed point of this system. We argue that the generic Finite-Size Scaling (FSS) function of our scheme is identically the entanglement entropy of the lattice partition function and, therefore, that we are able to directly extract the central charge, c, of the quantum spin chain system using conformal predictions for the scaling of the entanglement entropy.

The reweighting scheme developed in Glasgow to circumvent the lattice action becoming complex at finite density suffers from a pathological onset transition thought to be due to the reweighting. We present a new reweighting scheme based on this approach in which we combine ensembles to alleviate the sampling bias we identify in the polynomial coefficients of the fugacity expansion.

We propose an exact renormalization group equation for Lattice Gauge Theories, that has no dependence on the lattice spacing. We instead relate the lattice spacing properties directly to the continuum convergence of the support of each local plaquette. Equivalently, this is formulated as a convergence prescription for a characteristic polynomial in the gauge coupling that allows the exact meromorphic continuation of a nonperturbative system arbitrarily close to the continuum limit.

We derive a lattice β-function for the 2d-Antiferromagnetic Heisenberg model, which allows the lattice interaction couplings of the nonperturbative Quantum Monte Carlo vacuum to be related directly to the zero-temperature fixed points of the nonlinear sigma model in the presence of strong interplanar and spin anisotropies. In addition to the usual renormalization of the gapful disordered state in the vicinity of the quantum critical point, we show that this leads to a chiral doubling of the spectra of excited states. PACS numbers: 75.10.Jm, 75.40.CxThe 2d-Antiferromagnetic Heisenberg model is a well studied system that has two RG fixed points that have been identified at zero temperature through various applications of the 2d nonlinear sigma model [1,2]. Dependening on the relative anisotropy of the exchange coupling, J, between the two spatial directions of the system, the groundstate of the 2d antiferromagnetic groundstate is found to be either Néel ordered and gapless, or a gapful quantum disordered state. Varying the anisotropy drives dynamical fluctuations causing a zero temperature phase transition between the two groundstates [3], whereby the system effectively crosses over from 2d to 3d [4]. Without the inclusion of a θ-term, the 2d nonlinear sigma model is used to give an effectively classical description of the Néel ordered groundstate, and the quantum nature of the disordered state arises in some nontrivial way through the dynamical scale evolution of the system. It has been questioned whether the inclusion of an explicit source term for quantum fluctuations would be of relevance in the Néel phase [5,6], in order to understand the mechanism of symmetry breaking, but the inclusion of such a θ-term provides an irrelevant perturbation. However, if no source term for quantum fluctuations is included, the renormalization scale of the system can only be defined through phenomenological input. This picture has been successfully verified in detail by comparing nonlinear sigma model predictions for the scaling of the correlation length in the Néel, and quantum disordered regimes, with numerics obtained from Quantum Monte Carlo (QMC) studies [7,8].

We derive the lattice β-function for quantum spin chains, suitable for relating finite temperature Monte Carlo data to the zero temperature fixed points of the continuum nonlinear sigma model.Our main result is that the asymptotic freedom of this lattice β-function is responsible for the nonintegrable singularity in θ, that prevents analytic continuation between θ = 0 and θ = π.1 Haldane's conjecture for antiferromagnetic (AFM) spin chains predicts the existence of a nonvanishing gap for the groundstate of integer spin chains, and a vanishing gap for halfinteger spin chain systems [1]. For a bond-alternating integer chain, for example, different topological realisations of the gapped groundstate are seen, separated by critical features driven by quantum fluctuations [2]. The low-energy effective model for the groundstate of these spin chain systems is the 2d O(3) model with a θ-term. In the derivation of this effective action from the spin Hamiltonian in [1] the θ-parameter is a function of both the lattice interaction couplings and the nonperturbative dynamics. At θ = 0 the results of the 2d O(3) nonlinear sigma model are in found to be in agreement with predictions for integer systems, through numerical analysis. However, if we vary the lattice interaction couplings to drive the quantum fluctuations it also drives nonlocal fluctuations of the vacuum, and the physics at θ = π can be difficult to investigate numerically because of the complex action problem. A similar difficulty is found in investigations of the 2d O(3) model in [3]. Although quantum fluctuations are not relevant in this case, the experimentally relevant results derived for the scaling of the correlation length, are only defined through the cutoff scale for the nonlocal fluctuations. As such, the constants that appear in the nonlinear sigma model action (spin stiffness, spin wave velocity etc.) can only determined from phenomenological input, which serves to quantify the scale of the nonlocal fluctuations. Perturbatively, it is possible to treat expansions around θ = π via deformations of the Sine-Gordon model with an irrelevant nonlinear term [4] to quantify the renormalization scale of the quantum fluctuations. However, is is only recently that the effect of nonlocal fluctuations has been considered in addition to quantum fluctuations for quantum spin chains [5][6]. This has lead to the introduction of a double Sine-Gordon model description of the quantum spin chains in the vicinity of θ = π which leads to a change of the perturbation. What we want to consider in this article is what happens if the couplings of the perturbative expansion in [4] become strong due to nonlocal fluctuations, is it then possible to define a nonperturbative renormalization program.The nonlinear sigma model, as a continuum theory, is known to be integrable at only two points θ = 0 and θ = π [7]. The nonintegrable singularities found as a function of varying θ mean that the changes of the groundstate topology cannot properly be described analytically as a function of v...

We disprove the Vafa-Witten theorem on the impossibility of spontaneously breaking parity in vector-like gauge field theories, identifying a mechanism driven by quantum fluctuations. With the introduction of a meromorphic Lattice formulation, defined over 5 dimensions, we demonstrate that the minima of the free energy can be distinct from the maxima of the partition function : identifying and evaluating a suitable contour for the partition function defined such that asymptotic behaviour of the complex action is non-oscillatory.PACS numbers: 73.43. Nq, 11.15.Ha, 11.10.Gh. Recently attempts have been made to determine the properties of the Grand Canonical Partition Function of QCD at nonzero baryon densities using numerical Lattice QCD approaches [1]. These results are directly relevant for determining the equation of state of QCD for experimental Heavy Ion Collider results. These efforts are frustrated numerically by the difficulties in constructing efficient sampling algorithms at finite baryon densities. One faces the problem of a complex-valued Lattice action, whose phase oscillates rapidly as a function of the configuration within a Lattice statistical ensemble. This then prevents the effective use of importance sampling methods. All recent sampling improvement treatments in this vein appear now to suffer from the same generic flaw of an unphysical light pseudo-baryonic transition [2,3].To gain understanding of this feature an analytic treatment of partition function zeroes for QCD and QCD-like theories with a complex action problem was recently proposed [4,5]. Here the properties of the zeroes are identified as relating directly to specific regions of parameter space in the continuum where the partition function is itself ill-defined. This is linked in the discussion to the Vafa-Witten Theorem on the impossibility of spontaneously breaking parity symmetry in QCD [6]. A local bosonic parity breaking source term in the action is shown to generate a similarly pathologically ill-defined continuum partition function. This is demonstrated explicitly through the properties of the zeroes, and is used to justify the main theorem result. Although not included in this specific zeroes analysis the Vafa-Witten theorem result is understood to represent a wider pathology in Lattice simulation [7,8]. Bosonic terms with substructure in the Vafa-Witten formalism give rise to unphysical diagrammatic contributions to the Lattice QCD partition function. For example, in N f = 2 QCD with a four fermion operator source [9], or the Aoki phase with Wilson fermions [10,11,12]. * Electronic address: crompton@itp.uni-leipzig. de We now apply a new quantum system partition function zeroes treatment to this problem, and show that in contrast it is possible to give a well-defined continuum partition function for all generic complex action problems (of those of the form in the Vafa-Witten discussion) for all parameter space regions. Under the proviso, that, the local source term has a highly nonlocal component for which the continuum ...

We identify the leading corrections to Finite-Size Scaling relations for the correlation length and twist order parameter of three mixed-spin quantum spin chains for the critical feature that develops at, θ = π, corresponding to a change in the topological realisation of the groundstates.