Tobias Rindlisbacher

Two-flavor lattice QCD with a finite density of heavy quarks: heavy-dense limit and “particle-hole” symmetry

A bstractWe investigate the properties of the half-filling point in lattice QCD (LQCD), in particular the disappearance of the sign problem and the emergence of an apparent particle-hole symmetry, and try to understand where these properties come from by studying the heavy-dense fermion determinant and the corresponding strong-coupling partition function (which can be integrated analytically). We then add in a first step an effective Polyakov loop gauge action (which reproduces the leading terms in the character expansion of the Wilson gauge action) to the heavy-dense partition function and try to analyze how some of the properties of the half-filling point change when leaving the strong coupling limit. In a second step, we take also the leading nearest-neighbor fermion hopping terms into account (including gauge interactions in the fundamental representation) and mention how the method could be improved further to incorporate the full set of nearest-neighbor fermion hoppings. Using our mean-field method, we also obtain an approximate (μ, T) phase diagram for heavy-dense LQCD at finite inverse gauge coupling β. Finally, we propose a simple criterion to identify the chemical potential beyond which lattice artifacts become dominant.

Euclidean Dynamical Triangulation revisited: is the phase transition really 1st order?

A bstractThe transition between the two phases of 4D Euclidean Dynamical Triangulation [1] was long believed to be of second order until in 1996 first order behavior was found for sufficiently large systems [5, 9]. However, one may wonder if this finding was affected by the numerical methods used: to control volume fluctuations, in both studies [5, 9] an artificial harmonic potential was added to the action and in [9] measurements were taken after a fixed number of accepted instead of attempted moves which introduces an additional error. Finally the simulations suffer from strong critical slowing down which may have been underestimated.In the present work, we address the above weaknesses: we allow the volume to fluctuate freely within a fixed interval; we take measurements after a fixed number of attempted moves; and we overcome critical slowing down by using an optimized parallel tempering algorithm [12]. With these improved methods, on systems of size up to N4 = 64k 4- simplices, we confirm that the phase transition is 1st order.In addition, we discuss a local criterion to decide whether parts of a triangulation are in the elongated or crumpled state and describe a new correspondence between EDT and the balls in boxes model. The latter gives rise to a modified partition function with an additional, third coupling.Finally, we propose and motivate a class of modified path-integral measures that might remove the metastability of the Markov chain and turn the phase transition into 2nd order.

Sampling of General Correlators in Worm-Algorithm Based Simulations

Abstract Using the complex ϕ 4 -model as a prototype for a system which is simulated by a worm algorithm, we show that not only the charged correlator 〈 ϕ ⁎ ( x ) ϕ ( y ) 〉 , but also more general correlators such as 〈 | ϕ ( x ) | | ϕ ( y ) | 〉 or 〈 arg ⁡ ( ϕ ( x ) ) arg ⁡ ( ϕ ( y ) ) 〉 , as well as condensates like 〈 | ϕ | 〉 , can be measured at every step of the Monte Carlo evolution of the worm instead of on closed-worm configurations only. The method generalizes straightforwardly to other systems simulated by worms, such as spin or sigma models.

Oscillating propagators in heavy-dense QCD

A bstractUsing Monte Carlo simulations and extended mean field theory calculations we show that the 3-dimensional ℤ3 spin model with complex external fields has non-monotonic spatial correlators in some regions of its parameter space. This model serves as a proxy for heavy-dense QCD in (3 + 1) dimensions. Non-monotonic spatial correlators are intrinsically related to a complex mass spectrum and a liquid-like (or crystalline) behavior. A liquid phase could have implications for heavy-ion experiments, where it could leave detectable signals in the spatial correlations of baryons.

Lattice simulation of the SU(2) chiral model at zero and non-zero pion density

We propose a flux representation based lattice formulation of the partition function corresponding to the SU(2) principal chiral Lagrangian, including a chemical potential and scalar/pseudo-scalar source terms. Lattice simulations are then used to obtain non-perturbative properties of the theory, in particular its mass spectrum at zero and non-zero pion density. We also sketch a method to efficiently measure general one- and two-point functions during the worm updates.

Worm Algorithm for CP(N-1) Model

Abstract The C P N − 1 model in 2D is an interesting toy model for 4D QCD as it possesses confinement, asymptotic freedom and a non-trivial vacuum structure. Due to the lower dimensionality and the absence of fermions, the computational cost for simulating 2D C P N − 1 on the lattice is much lower than that for simulating 4D QCD. However, to our knowledge, no efficient algorithm for simulating the lattice C P N − 1 model for N > 2 has been tested so far, which also works at finite density. To this end we propose a new type of worm algorithm which is appropriate to simulate the lattice C P N − 1 model in a dual, flux-variables based representation, in which the introduction of a chemical potential does not give rise to any complications. In addition to the usual worm moves where a defect is just moved from one lattice site to the next, our algorithm additionally allows for worm-type moves in the internal variable space of single links, which accelerates the Monte Carlo evolution. We use our algorithm to compare the two popular C P N − 1 lattice actions and exhibit marked differences in their approach to the continuum limit.

arXiv : Spin models in complex magnetic fields: a hard sign problem

Coupling spin models to complex external fields can give rise to interesting phenomena like zeroes of the partition function (Lee-Yang zeroes, edge singularities) or oscillating propagators. Unfortunately, it usually also leads to a severe sign problem that can be overcome only in special cases; if the partition function has zeroes, the sign problem is even representation-independent at these points. In this study, we couple the N-state Potts model in different ways to a complex external magnetic field and discuss the above mentioned phenomena and their relations based on analytic calculations (1D) and results obtained using a modified cluster algorithm (general D) that in many cases either cures or at least drastically reduces the sign-problem induced by the complex external field.

Worm algorithm for the CPN−1 model

Abstract The C P N − 1 model in 2D is an interesting toy model for 4D QCD as it possesses confinement, asymptotic freedom and a non-trivial vacuum structure. Due to the lower dimensionality and the absence of fermions, the computational cost for simulating 2D C P N − 1 on the lattice is much lower than that for simulating 4D QCD. However, to our knowledge, no efficient algorithm for simulating the lattice C P N − 1 model for N > 2 has been tested so far, which also works at finite density. To this end we propose a new type of worm algorithm which is appropriate to simulate the lattice C P N − 1 model in a dual, flux-variables based representation, in which the introduction of a chemical potential does not give rise to any complications. In addition to the usual worm moves where a defect is just moved from one lattice site to the next, our algorithm additionally allows for worm-type moves in the internal variable space of single links, which accelerates the Monte Carlo evolution. We use our algorithm to compare the two popular C P N − 1 lattice actions and exhibit marked differences in their approach to the continuum limit.

Worm algorithm for the CPN−1CPN−1 model

Abstract The C P N − 1 model in 2D is an interesting toy model for 4D QCD as it possesses confinement, asymptotic freedom and a non-trivial vacuum structure. Due to the lower dimensionality and the absence of fermions, the computational cost for simulating 2D C P N − 1 on the lattice is much lower than that for simulating 4D QCD. However, to our knowledge, no efficient algorithm for simulating the lattice C P N − 1 model for N > 2 has been tested so far, which also works at finite density. To this end we propose a new type of worm algorithm which is appropriate to simulate the lattice C P N − 1 model in a dual, flux-variables based representation, in which the introduction of a chemical potential does not give rise to any complications. In addition to the usual worm moves where a defect is just moved from one lattice site to the next, our algorithm additionally allows for worm-type moves in the internal variable space of single links, which accelerates the Monte Carlo evolution. We use our algorithm to compare the two popular C P N − 1 lattice actions and exhibit marked differences in their approach to the continuum limit.

Elsevier : Worm algorithm for the CP

Abstract The C P N − 1 model in 2D is an interesting toy model for 4D QCD as it possesses confinement, asymptotic freedom and a non-trivial vacuum structure. Due to the lower dimensionality and the absence of fermions, the computational cost for simulating 2D C P N − 1 on the lattice is much lower than that for simulating 4D QCD. However, to our knowledge, no efficient algorithm for simulating the lattice C P N − 1 model for N > 2 has been tested so far, which also works at finite density. To this end we propose a new type of worm algorithm which is appropriate to simulate the lattice C P N − 1 model in a dual, flux-variables based representation, in which the introduction of a chemical potential does not give rise to any complications. In addition to the usual worm moves where a defect is just moved from one lattice site to the next, our algorithm additionally allows for worm-type moves in the internal variable space of single links, which accelerates the Monte Carlo evolution. We use our algorithm to compare the two popular C P N − 1 lattice actions and exhibit marked differences in their approach to the continuum limit.