arXiv subjects

Robert Lohmayer

Publications and source records attributed to Robert Lohmayer.

At least 19 recordsLinked to original sources

arXiv2026

Order-separated tensor-network method for QCD in the strong-coupling expansion

We introduce the order-separated Grassmann higher-order tensor renormalization group (OS-GHOTRG) method for QCD with staggered quarks in the strong-coupling expansion. The method allows us to determine the expansion coefficients of the partition function, from which we can obtain the strong-coupling expansions of thermodynamical observables. We use the method in two dimensions to compute the free energy, the particle-number density, and the chiral condensate as a function of the chemical potential up to third order in the inverse coupling $\beta$. Although near the phase transition the expansion is only a good approximation to the full theory at small $\beta$, we show that the range of applicability can be greatly extended by fits to judiciously chosen transition functions.

hep-lat↗

arXiv2025

Tensor-network formulation of QCD in the strong-coupling expansion

We present a tensor-network formulation for the strong-coupling expansion of QCD with staggered quarks at nonzero chemical potential, for arbitrary number of dimensions, colors, and flavors. We integrate out the gauge and quark degrees of freedom and rewrite the partition function as the complete trace of a tensor network. This network consists of local tensors that contain a numerical and a Grassmann part. We truncate the initial tensor at a fixed order in the inverse coupling $\beta$ and compute analytical results for the partition function, the free energy, and the chiral condensate on a $2\times2$ lattice up to order $\beta^4$. In a follow-up paper we will introduce an enhanced tensor-network method, order-separated GHOTRG, to explicitly compute the expansion coefficients of the partition function for larger lattices. To demonstrate its potential, first results obtained with this new method are already presented here.

hep-lat↗

arXiv2025

Grassmann tensor approach for two-dimensional QCD in the strong-coupling expansion

We present a tensor-network approach for the strong-coupling expansion of two-dimensional QCD with staggered quarks at non-zero chemical potential. After expanding the Boltzmann factor in the gauge and fermion actions, all gauge fields can be integrated out exactly and the partition function can be evaluated using the Grassmann higher-order tensor renormalization group approach. The method is modified to compute the $\mu$ dependence of the quark number density and the chiral condensate up to order $\beta^3$ with complete absence of higher-order terms infiltrating the result. Although the expansion itself is only a good approximation to the full theory at small $\beta<0.1$, the range can be extended, by using judiciously chosen fits. Moreover, these fits also yield a valuable expansion in $\beta$ for the critical chemical potential.

hep-lat↗

arXiv2023

Grassmann tensor-network method for strong-coupling QCD

We present a tensor-network method for strong-coupling QCD with staggered quarks at nonzero chemical potential. After integrating out the gauge fields at infinite coupling, the partition function can be written as a full contraction of a tensor network consisting of coupled local numeric and Grassmann tensors. To evaluate the partition function and to compute observables, we develop a Grassmann higher-order tensor renormalization group method, specifically tailored for this model. We apply the method to the two-dimensional case and validate it by comparing results for the partition function, the chiral condensate and the baryon density with exact analytical expressions on small lattices up to volumes of $4\times4$. For larger two-dimensional volumes, we present tensor results for the chiral condensate as a function of the mass and volume, and observe that the chiral symmetry is not broken dynamically in two dimensions. Furthermore, our results for the number density as a function of the chemical potential hint at a first-order phase transition. Finally, we present some preliminary tensor results for three-dimensional strong-coupling QCD.

hep-lat↗

arXiv2022

Improved local truncation schemes for the higher-order tensor renormalization group method

The higher-order tensor renormalization group is a tensor-network method providing estimates for the partition function and thermodynamical observables of classical and quantum systems in thermal equilibrium. At every step of the iterative blocking procedure, the coarse-grid tensor is truncated to keep the tensor dimension under control. For a consistent tensor blocking procedure, it is crucial that the forward and backward tensor modes are projected on the same lower dimensional subspaces. In this paper we present two methods, the SuperQ and the iterative SuperQ method, to construct tensor truncations that reduce or even minimize the local approximation errors, while satisfying this constraint.

hep-lat↗

arXiv2022

Grassmann higher-order tensor renormalization group approach for two-dimensional strong-coupling QCD

We present a tensor-network approach for two-dimensional strong-coupling QCD with staggered quarks at nonzero chemical potential. After integrating out the gauge fields at infinite coupling, the partition function can be written as a full contraction of a tensor network consisting of coupled local numeric and Grassmann tensors. To evaluate the partition function and to compute observables, we develop a Grassmann higher-order tensor renormalization group method, specifically tailored for this model. During the coarsening procedure, the blocking of adjacent Grassmann tensors is performed analytically, and the total number of Grassmann variables in the tensor network is reduced by a factor of two at each coarsening step. The coarse-site numeric tensors are truncated using higher-order singular value decompositions. The method is validated by comparing the partition function, the chiral condensate and the baryon density computed with the tensor method with exact analytical results on small lattices up to volumes of $4\times4$. For larger volumes, we present first tensor results for the chiral condensate as a function of the mass and volume, and observe that the chiral symmetry is not broken dynamically in two dimensions. We also present tensor results for the number density as a function of the chemical potential, which hint at a first-order phase transition.

hep-lat↗

arXiv2022

BITES: Balanced Individual Treatment Effect for Survival data

Estimating the effects of interventions on patient outcome is one of the key aspects of personalized medicine. Their inference is often challenged by the fact that the training data comprises only the outcome for the administered treatment, and not for alternative treatments (the so-called counterfactual outcomes). Several methods were suggested for this scenario based on observational data, i.e.~data where the intervention was not applied randomly, for both continuous and binary outcome variables. However, patient outcome is often recorded in terms of time-to-event data, comprising right-censored event times if an event does not occur within the observation period. Albeit their enormous importance, time-to-event data is rarely used for treatment optimization. We suggest an approach named BITES (Balanced Individual Treatment Effect for Survival data), which combines a treatment-specific semi-parametric Cox loss with a treatment-balanced deep neural network; i.e.~we regularize differences between treated and non-treated patients using Integral Probability Metrics (IPM). We show in simulation studies that this approach outperforms the state of the art. Further, we demonstrate in an application to a cohort of breast cancer patients that hormone treatment can be optimized based on six routine parameters. We successfully validated this finding in an independent cohort. BITES is provided as an easy-to-use python implementation.

stat.ME↗

arXiv2021

Tensor-network simulation of the strong-coupling $U(N)$ model

We apply tensor network methods to study the strong-coupling $U(N)$ model in its dimer formulation. In three and four dimensions, we investigate the chiral condensate as a function of the quark mass and the degree of the symmetry group, and find good agreement with Monte Carlo simulations. Particularly interesting is the study of chiral symmetry breaking as a function of the mass and the volume, which clearly shows that this symmetry is spontaneously broken in the limit of infinite volume and zero mass.

hep-lat↗

arXiv2021

Tensor-network study of the 3d $O(2)$ model at non-zero chemical potential and temperature

We present results of tensor-network simulations of the three-dimensional $O(2)$ model at non-zero chemical potential and temperature, which were computed using the higher-order tensor-renormalization-group method (HOTRG). This necessitated enhancements to the HOTRG blocking procedure to reduce the truncation error in the case of anisotropic tensors. Moreover, the construction of the truncated vector spaces was adapted to strongly reduce the effect of systematic errors in the computation of observables using the finite-difference method. Our (improved) HOTRG results for the evolution of the number density with the chemical potential are in agreement with results obtained with the worm algorithm, and both the Silver Blaze phenomenon at zero temperature and the temperature dependence of the number density can be adequately reproduced.

hep-lat↗

arXiv2021

Effective $\mathbb{Z}_{3}$ model for finite-density QCD with tensor networks

The tensor renormalization group is a promising numerical method used to study lattice statistical field theories. However, this approach is computationally expensive in 2+1 and 3+1 dimensions. Here we use tensor renormalization group methods to study an effective three-dimensional $\mathbb{Z}_{3}$ model for the heavy-quark, high-temperature, strong-coupling limit of single-flavor 3+1 dimensional quantum chromodynamics. Our results are cross-checked using the worm Monte Carlo algorithm. We present the phase diagram of the model through the measurement of the Polyakov loop, the nearest-neighbor Polyakov loop correlator, and their susceptibilities. The tensor renormalization group results are in good agreement with the literature

hep-lat↗

arXiv2021

Tensor renormalization group study of the 3d $O(2)$ model

We calculate thermodynamic potentials and their derivatives for the three-dimensional $O(2)$ model using tensor-network methods to investigate the well-known second-order phase transition. We also consider the model at non-zero chemical potential to study the Silver Blaze phenomenon, which is related to the particle number density at zero temperature. Furthermore, the temperature dependence of the number density is explored using asymmetric lattices. Our results for both zero and non-zero magnetic field, temperature, and chemical potential are consistent with those obtained using other methods.

hep-lat↗

arXiv2019

Induced QCD II: Numerical results

We numerically explore an alternative discretization of continuum $\text{SU}(N_c)$ Yang-Mills theory on a Euclidean spacetime lattice, originally introduced by Budzcies and Zirnbauer for gauge group $\text{U}(N_c)$. This discretization can be reformulated such that the self-interactions of the gauge field are induced by a path integral over $N_b$ auxiliary bosonic fields, which couple linearly to the gauge field. In the first paper of the series we have shown that the theory reproduces continuum $\text{SU}(N_c)$ Yang-Mills theory in $d=2$ dimensions if $N_b$ is larger than $N_c-\frac{3}{4}$ and conjectured, following the argument of Budzcies and Zirnbauer, that this remains true for $d>2$. In the present paper, we test this conjecture by performing lattice simulations of the simplest nontrivial case, i.e., gauge group $\text{SU}(2)$ in three dimensions. We show that observables computed in the induced theory, such as the static $q\bar q$ potential and the deconfinement transition temperature, agree with the same observables computed from the ordinary plaquette action up to lattice artifacts. We also find that the bound for $N_b$ can be relaxed to $N_c-\frac{5}{4}$ as conjectured in our earlier paper. Studies of how the new discretization can be used to change the order of integration in the path integral to arrive at dual formulations of QCD are left for future work.

hep-lat↗

arXiv2016

Induced QCD I: Theory

We explore an alternative discretization of continuum SU(N_c) Yang-Mills theory on a Euclidean spacetime lattice, originally introduced by Budzcies and Zirnbauer. In this discretization the self-interactions of the gauge field are induced by a path integral over N_b auxiliary boson fields, which are coupled linearly to the gauge field. The main progress compared to earlier approaches is that N_b can be as small as N_c. In the present paper we (i) extend the proof that the continuum limit of the new discretization reproduces Yang-Mills theory in two dimensions from gauge group U(N_c) to SU(N_c), (ii) derive refined bounds on N_b for non-integer values, and (iii) perform a perturbative calculation to match the bare parameter of the induced gauge theory to the standard lattice coupling. In follow-up papers we will present numerical evidence in support of the conjecture that the induced gauge theory reproduces Yang-Mills theory also in three and four dimensions, and explore the possibility to integrate out the gauge fields to arrive at a dual formulation of lattice QCD.

hep-lat↗

arXiv2015

Induced YM theory with auxiliary bosons

We study pure SU(N) lattice gauge theory with a plaquette weight factor given by an inverse determinant which can be written as an integral over auxiliary bosonic fields (modifying a proposal of Budczies and Zirnbauer). We derive conditions for the existence of a continuum limit and its equivalence to Yang-Mills theory. Furthermore, we perturbatively compute the relation between the coupling constants of the `induced' gauge action and the familiar Wilson gauge action using the background-field technique. The perturbative relation agrees well with numerical results for N=2 in three dimensions.

hep-lat↗

arXiv2015

QPACE 2 and Domain Decomposition on the Intel Xeon Phi

We give an overview of QPACE 2, which is a custom-designed supercomputer based on Intel Xeon Phi processors, developed in a collaboration of Regensburg University and Eurotech. We give some general recommendations for how to write high-performance code for the Xeon Phi and then discuss our implementation of a domain-decomposition-based solver and present a number of benchmarks.

cs.DC↗

arXiv2013

Single site model of large N gauge theories coupled to adjoint fermions

We consider a single site large N gauge theory coupled to adjoint fermions at weak coupling. We study the distribution of the eigenvalues of the link variables using a four-dimensional density function. We show that it is possible to recover the infinite-volume continuum limit for a certain range of fermion flavors if we use fermions with a bare mass of zero.

hep-lat↗

arXiv2013

Phase structure of two-dimensional QED at zero temperature with flavor-dependent chemical potentials and the role of multidimensional theta functions

We consider QED on a two-dimensional Euclidean torus with $f$ flavors of massless fermions and flavor-dependent chemical potentials. The dependence of the partition function on the chemical potentials is reduced to a $(2f-2)$-dimensional theta function. At zero temperature, the system can exist in an infinite number of phases characterized by certain values of traceless number densities and separated by first-order phase transitions. Furthermore, there exist many points in the $(f-1)$-dimensional space of traceless chemical potentials where two or three phases can coexist for $f=3$ and two, three, four or six phases can coexist for $f=4$. We conjecture that the maximal number of coexisting phases grows exponentially with increasing $f$.

hep-th↗

arXiv2013

Many-flavor Schwinger model at finite chemical potential

We study thermodynamic properties of the Schwinger model on a torus with f flavors of massless fermions and flavor-dependent chemical potentials. Generalizing the two-flavor case, we present a representation of the partition function in the form of a multidimensional theta function and show that the model exhibits a rich phase structure at zero temperature. The different phases, characterized by certain values of the particle numbers, are separated by first-order phase transitions. We work out the phase structure in detail for three and four fermion flavors and conjecture, based on an exploratory investigation of the five, six, and eight flavor case, that the maximal number of coexisting phases at zero temperature grows exponentially with increasing f.

hep-lat↗