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Uwe-Jens Wiese

Publications and source records attributed to Uwe-Jens Wiese.

32 records · Page 2Linked to original sources
arXiv2013

O(N) Models with Topological Lattice Actions

A variety of lattice discretisations of continuum actions has been considered, usually requiring the correct classical continuum limit. Here we discuss "weird" lattice formulations without that property, namely lattice actions that are invariant under most continuous deformations of the field configuration, in one version even without any coupling constants. It turns out that universality is powerful enough to still provide the correct quantum continuum limit, despite the absence of a classical limit, or a perturbative expansion. We demonstrate this for a set of O(N) models (or non-linear $σ$-models). Amazingly, such "weird" lattice actions are not only in the right universality class, but some of them even have practical benefits, in particular an excellent scaling behaviour.

hep-lat↗
arXiv2012

Study of theta-Vacua in the 2-d O(3) Model

We investigate the continuum limit of the step scaling function in the 2-d O(3) model with different theta-vacua. Since we find a different continuum value of the step scaling function for each value of theta, we can conclude that theta indeed is a relevant parameter of the theory and does not get renormalized non-perturbatively. Furthermore, we confirm the result of the conjectured exact S-matrix theory, which predicts the continuum value at theta = pi. To obtain high precision data, we use a modified Hasenbusch improved estimator and an action with an optimized constraint, which has very small cut-off effects. The optimized constraint action combines the standard action of the 2-d O(3) model with a topological action. The topological action constrains the angle between neighboring spins and is therefore invariant against small deformations of the field.

hep-lat↗
arXiv2012

Walking near a Conformal Fixed Point: the 2-d O(3) Model at theta near pi as a Test Case

Slowly walking technicolor models provide a mechanism for electroweak symmetry breaking whose nonperturbative lattice investigation is rather challenging. Here we demonstrate walking near a conformal fixed point considering the 2-d lattice O(3) model at vacuum angle $θ\approx π$. The essential features of walking technicolor models are shared by this toy model and can be accurately investigated by numerical simulations. We show results for the running coupling and the beta-function and we perform a finite size scaling analysis of the massgap close to the conformal point.

hep-lat↗
arXiv2011

Non-trivial θ-Vacuum Effects in the 2-d O(3) Model

We study θ-vacua in the 2-d lattice O(3) model using the standard action and an optimized constraint action with very small cut-off effects, combined with the geometric topological charge. Remarkably, dislocation lattice artifacts do not spoil the non-trivial continuum limit at θ non-zero, and there are different continuum theories for each value of θ. A very precise Monte Carlo study of the step scaling function indirectly confirms the exact S-matrix of the 2-d O(3) model at θ= π.

hep-lat↗
arXiv2011

Partition Functions of Strongly Correlated Electron Systems as "Fermionants"

We introduce a new mathematical object, the "fermionant" ${\mathrm{Ferm}}_N(G)$, of type $N$ of an $n \times n$ matrix $G$. It represents certain $n$-point functions involving $N$ species of free fermions. When N=1, the fermionant reduces to the determinant. The partition function of the repulsive Hubbard model, of geometrically frustrated quantum antiferromagnets, and of Kondo lattice models can be expressed as fermionants of type N=2, which naturally incorporates infinite on-site repulsion. A computation of the fermionant in polynomial time would solve many interesting fermion sign problems.

cond-mat.str-el↗
arXiv2008

Revisiting the deconfinement phase transition in SU(4) Yang-Mills theory in 2+1 dimensions

In order to deepen our understanding of the nature of the deconfinement phase transition for various gauge groups, we investigate SU(4) Yang-Mills theory in 2+1 dimensions. We find that the transition is weakly first order. We perform extensive Monte Carlo simulations on lattices with temporal extent N_t = 3, 4 and 5, and spatial sizes up to N_s = 20 N_t. We observe coexistence of confined and deconfined phases at the critical temperature, and finite-size scaling shows consistency with first order exponents. The continuum extrapolation of the latent heat yields L_h/T_c^3=0.188(17).

hep-lat↗
arXiv2005

A new efficient Cluster Algorithm for the Ising Model

Using D-theory we construct a new efficient cluster algorithm for the Ising model. The construction is very different from the standard Swendsen-Wang algorithm and related to worm algorithms. With the new algorithm we have measured the correlation function with high precision over a surprisingly large number of orders of magnitude.

hep-lat↗
arXiv2005

The Status of D-Theory

Field theories are usually quantized by performing a path integral over configurations of classical fields. This is the case both in perturbation theory and in Wilson's nonperturbative lattice field theory. D-theory is an alternative nonperturbative formulation of field theory in which classical fields emerge from the low-energy collective dynamics of discrete quantum variables (quantum spins and their gauge analogs -- quantum links) which undergo dimensional reduction. D-theory was developed some time ago as a discrete approach to U(1) and SU(2) pure gauge theories, extended to SU(N) gauge theories and full QCD, and also applied to a variety of other models. On the practical side, D-theory provides a framework for the development of efficient numerical methods, such as cluster algorithms. For example, in the D-theory formulation of CP(N-1) models one can simulate efficiently at non-zero chemical potential or at non-zero vacuum angle theta. On the conceptual side, D-theory offers a natural solution for the nonperturbative hierarchy problem of chiral symmetry in QCD. We also take a broader nonperturbative view on fundamental physics and speculate that D-theory variables -- i.e. quantum spins and quantum links -- may be promising candidates for the physical degrees of freedom that Nature has chosen to regularize the standard model physics at ultra-short distances.

hep-lat↗
arXiv2004

Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations

Quantum Monte Carlo simulations, while being efficient for bosons, suffer from the "negative sign problem'' when applied to fermions - causing an exponential increase of the computing time with the number of particles. A polynomial time solution to the sign problem is highly desired since it would provide an unbiased and numerically exact method to simulate correlated quantum systems. Here we show, that such a solution is almost certainly unattainable by proving that the sign problem is NP-hard, implying that a generic solution of the sign problem would also solve all problems in the complexity class NP (nondeterministic polynomial) in polynomial time.

cond-mat.stat-mech↗
arXiv2000

SO(10) Unification of Color Superconductivity and Chiral Symmetry Breaking?

Motivated by the SO(5) theory of high-temperature superconductivity and antiferromagnetism, we ask if an SO(10) theory unifies color superconductivity and chiral symmetry breaking in QCD. The transition to the color superconducting phase would then be analogous to a spin flop transition. While the spin flop transition generically has a unified SO(3) description, the SO(5) and SO(10) symmetric fixed points are unstable, at least in (4 - epsilon) dimensions, and require the fine-tuning of one additional relevant parameter. If QCD is near the SO(10) fixed point, it has interesting consequences for heavy ion collisions and neutron stars.

hep-ph↗
arXiv1999

Meron-Cluster Solution of Fermion Sign Problems

We present a general strategy to solve the notorious fermion sign problem using cluster algorithms. The method applies to various systems in the Hubbard model family as well as to relativistic fermions. Here it is illustrated for non-relativistic lattice fermions. A configuration of fermion world-lines is decomposed into clusters that contribute independently to the fermion permutation sign. A cluster whose flip changes the sign is referred to as a meron. Configurations containing meron-clusters contribute 0 to the path integral, while all other configurations contribute 1. The cluster representation describes the partition function as a gas of clusters in the zero-meron sector.

cond-mat.stat-mech↗
arXiv1992

Bosonization and Cluster Updating of Lattice Fermions

A lattice fermion model is formulated in Fock space using the Jordan-Wigner representation for the fermion creation and annihilation operators. The resulting path integral is a sum over configurations of lattice site occupation numbers $n(x,t) = 0,1$ which may be viewed as bosonic Ising-like variables. However, as a remnant of Fermi statistics a nonlocal sign factor arises for each configuration. When this factor is included in measured observables the bosonic occupation numbers interact locally, and one can use efficient cluster algorithms to update the bosonized variables.

hep-lat↗
arXiv1992

Gauge Fixing on the Lattice without Ambiguity

A new gauge fixing condition is discussed, which is (lattice) rotation invariant, has the `smoothness' properties of the Landau gauge but can be efficiently computed and is unambiguous for almost all lattice gauge field configurations.

hep-lat↗