Publications (85)
Phase Diagram of Dynamical Twisted Mass Wilson Fermions at Finite Isospin Chemical Potential
Oliver Janssen, Mario Kieburg, K. Splittorff +2
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 la…
Subsets and the canonical partition functions
Jacques Bloch, Falk Bruckmann, Mario Kieburg +2
We explain the physical nature of the subset solution to the sign problem in chiral random matrix theory: The subset sum is shown to project out the canonical determinant with zero…
Spectral Sum Rules of the Dirac operator and Partially Quenched Chiral Condensates
P. H. Damgaard, K. Splittorff
Exploiting Virasoro constraints on the effective finite-volume partition function, we derive generalized Leutwyler-Smilga spectral sum rules of the Dirac operator to high order. By…
The QCD sign problem as a total derivative
Jeff Greensite, Joyce C. Myers, K. Splittorff
We consider the distribution of the complex phase of the fermion determinant in QCD at nonzero chemical potential and examine the physical conditions under which the distribution t…
Quantum Phase Estimation and the Aharonov-Bohm effect
K. Splittorff
We consider the time evolution of a particle on a ring with a long solenoid through and show that due to the Aharonov-Bohm effect this system naturally makes up a physical implemen…
Logarithmic Universality in Random Matrix Theory
K. Splittorff
Universality in unitary invariant random matrix ensembles with complex matrix elements is considered. We treat two general ensembles which have a determinant factor in the weight.…
Universal distributions from non-Hermitian Perturbation of Zero-Modes
M. Kieburg, A. Mielke, M. Rud +1
Hermitian operators with exact zero modes subject to non-Hermitian perturbations are considered. Specific focus is on the average distribution of the initial zero modes of the Herm…
Lattice QCD and dense quark matter
M. P. Lombardo, K. Splittorff, J. J. M. Verbaarschot
This talk summarizes recent progress in lattice QCD for dense quark matter. The emphasis is on the insights obtained from analytical results derived within chiral perturbation theo…
Impossibility of spontaneously breaking local symmetries and the sign problem
K. Splittorff
Elitzur's theorem stating the impossibility of spontaneous breaking of local symmetries in a gauge theory is reexamined. The existing proofs of this theorem rely on gauge invarianc…
Unquenched QCD Dirac Operator Spectra at Nonzero Baryon Chemical Potential
G. Akemann, J. C. Osborn, K. Splittorff +1
The microscopic spectral density of the QCD Dirac operator at nonzero baryon chemical potential for an arbitrary number of quark flavors was derived recently from a random matrix m…
The zeros of the QCD partition function
A. D. Jackson, C. B. Lang, M. Oswald +1
We establish a relationship between the zeros of the partition function in the complex mass plane and the spectral properties of the Dirac operator in QCD. This relation is derived…
Chiral Symmetry Breaking at Nonzero Chemical Potential
J. C. Osborn, K. Splittorff, J. J. M. Verbaarschot
We consider chiral symmetry breaking at nonzero chemical potential and discuss the relation with the spectrum of the Dirac operator. We solve the so called Silver Blaze Problem tha…
The Superfluid and Conformal Phase Transitions of Two-Color QCD
J. T. Lenaghan, F. Sannino, K. Splittorff
The phase structure of two-color QCD is examined as a function of the chemical potential and the number of light quark flavors. We consider effective Lagrangians for two-color QCD…
The Sign Problem via Imaginary Chemical Potential
K. Splittorff, B. Svetitsky
We calculate an analogue of the average phase factor of the staggered fermion determinant at imaginary chemical potential. Our results from the lattice agree well with the analytic…
Progress on the Microscopic Spectrum of the Dirac Operator for QCD with Wilson Fermions
K. Splittorff, J. J. M. Verbaarschot
Starting from the chiral Lagrangian for Wilson fermions at nonzero lattice spacing we have obtained compact expressions for all spectral correlation functions of the Hermitian Wils…
Melting the Diquark Condensate in Two-Color QCD: A Renormalization Group Analysis
J. Wirstam, J. T. Lenaghan, K. Splittorff
We use a Landau theory and the epsilon expansion to study the superfluid phase transition of two-color QCD at nonzero temperature, T, and baryonic chemical potential, mu. At low T,…
Extracting from small lattices: unquenched results
P. H. Damgaard, U. M. Heller, K. Splittorff +2
We calculate the response of the microscopic Dirac spectrum to an imaginary isospin chemical potential for QCD with two dynamical flavors in the chiral limit. This extends our prev…
The Dirac spectrum in Complex Langevin Simulations of QCD
K. Splittorff
We show that the spectrum of the Dirac operator in complex Langevin simulations of QCD at non-zero chemical potential must behave in a way which is radically different from the one…
Thermodynamics of chiral symmetry at low densities
K. Splittorff, D. Toublan, J. J. M. Verbaarschot
The phase diagram of two-color QCD as a function of temperature and baryon chemical potential is considered. Using a low-energy chiral Lagrangian based on the symmetries of the mic…
The Wilson Dirac Spectrum for QCD with Dynamical Quarks
K. Splittorff, J. J. M. Verbaarschot
All microscopic correlation functions of the spectrum of the Hermitian Wilson Dirac operator with any number of flavors with equal masses are computed. In particular, we give expli…
The density in the density of states method
Jeff Greensite, Joyce C. Myers, K. Splittorff
It has been suggested that for QCD at finite baryon density the distribution of the phase angle, i.e. the angle defined as the imaginary part of the logarithm of the fermion determ…
Chiral Symmetry Breaking and the Dirac Spectrum at Nonzero Chemical Potential
J. C. Osborn, K. Splittorff, J. J. M. Verbaarschot
The relation between the spectral density of the QCD Dirac operator at nonzero baryon chemical potential and the chiral condensate is investigated. We use the analytical result for…
Surprises for QCD at Nonzero Chemical Potential
K. Splittorff, J. J. M. Verbaarschot
In this lecture we compare different QCD-like partition functions with bosonic quarks and fermionic quarks at nonzero chemical potential. Although it is not a surprise that the gro…
The Realization of the Sharpe-Singleton Scenario
M. Kieburg, K. Splittorff, J. J. M. Verbaarschot
The microscopic spectral density of the Wilson Dirac operator for two flavor lattice QCD is analyzed. The computation includes the leading order a^2 corrections of the chiral Lagra…
Diquark Condensate in QCD with Two Colors at Next-to-Leading Order
K. Splittorff, D. Toublan, J. J. M. Verbaarschot
We study QCD with two colors and quarks in the fundamental representation at finite baryon density in the limit of light quark masses. In this limit the free energy of this theory…
The Ginsparg-Wilson relation and local chiral random matrix theory
K. Splittorff, A. D. Jackson
A chiral random matrix model with locality is constructed and examined. The Nielsen-Ninomiya no-go theorem is circumvented by the use of a generally applicable modified Dirac opera…
Phase of the Fermion Determinant at Nonzero Chemical Potential
K. Splittorff, J. J. M. Verbaarschot
We show that in the microscopic domain of QCD (also known as the -domain) at nonzero chemical potential the average phase factor of the fermion determinant is nonzero for $μ<…
The gradient flow of the Dirac spectrum
Alexander S. Christensen, K. Splittorff, J. J. M. Verbaarschot
We construct chiral perturbation theory for the gradient flow of the microscopic Dirac eigenvalues and compute the density of and correlations between the microscopic eigenvalues a…
Finite-Volume Scaling of the Wilson-Dirac Operator Spectrum
P. H. Damgaard, U. M. Heller, K. Splittorff
The microscopic spectral density of the Hermitian Wilson-Dirac operator is computed numerically in quenched lattice QCD. We demonstrate that the results given for fixed index of th…
Phase Diagram of the Dirac Spectrum at Nonzero Chemical Potential
J. C. Osborn, K. Splittorff, J. J. M. Verbaarschot
The Dirac spectrum of QCD with dynamical fermions at nonzero chemical potential is characterized by three regions, a region with a constant eigenvalue density, a region where the e…
QCD with Bosonic Quarks at Nonzero Chemical Potential
K. Splittorff, J. J. M. Verbaarschot
We formulate the low energy limit of QCD like partition functions with bosonic quarks at nonzero chemical potential. The partition functions are evaluated in the parameter domain t…
Statistical QCD with non-positive measure
J. C. Osborn, K. Splittorff, J. J. M. Verbaarschot
In this talk we discuss the microscopic limit of QCD at nonzero chemical potential. In this domain, where the QCD partition function is under complete analytical control, we uncove…
The Replica Method and Toda Lattice Equations for QCD_3
T. Andersson, P. H. Damgaard, K. Splittorff
We consider the epsilon-regime of QCD in 3 dimensions. It is shown that the leading term of the effective partition function satisfies a set of Toda lattice equations, recursive in…
Degenerate distributions in complex Langevin dynamics: one-dimensional QCD at finite chemical potential
Gert Aarts, K. Splittorff
We demonstrate analytically that complex Langevin dynamics can solve the sign problem in one-dimensional QCD in the thermodynamic limit. In particular, it is shown that the contrib…
The Approach to the Thermodynamic Limit in Lattice QCD at μ\neq0
K. Splittorff, J. J. M. Verbaarschot
The expectation value of the complex phase factor of the fermion determinant is computed to leading order in the -expansion of the chiral Lagrangian. The computation is valid fo…
The Fluctuations of the Quark Number and of the Chiral Condensate
M. P. Lombardo, K. Splittorff, J. J. M. Verbaarschot
The distributions of the quark number and chiral condensate over the gauge fields are computed for QCD in Euclidean space at nonzero quark chemical potential. As both operators are…
Baryon Number Dirac Spectrum in QCD
J. R. Ipsen, K. Splittorff
The relation between the baryon number in QCD at nonzero chemical potential and the spectral density of the baryon number Dirac operator, , is examined. We show that ext…
Phase Diagram of Wilson and Twisted Mass Fermions at finite isospin chemical potential
M. Kieburg, K. Splittorff, J. J. M. Verbaarschot +1
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 t…
The QCD Sign Problem for Small Chemical Potential
K. Splittorff, J. J. M. Verbaarschot
The expectation value of the complex phase factor of the fermion determinant is computed in the microscopic domain of QCD at nonzero chemical potential. We find that the average ph…
New Ways to Determine Low-Energy Constants with Wilson Fermions
P. H. Damgaard, U. M. Heller, K. Splittorff
We show how the leading physical and Wilson low-energy constants associated with Wilson fermions in lattice gauge theory can be determined individually by using spectral informatio…
Distribution of Canonical Determinants in QCD
Andrei Alexandru, C. Gattringer, H. -P. Schadler +2
The distribution of canonical determinants in QCD is determined by means of chiral perturbation theory. For a non-zero quark charge the canonical determinants take complex values.…
QCD Dirac Spectra and the Toda Lattice
K. Splittorff, J. J. M. Verbaarschot
We discuss the spectrum of the QCD Dirac operator both at zero and at nonzero baryon chemical potential. We show that, in the ergodic domain of QCD, the Dirac spectrum can be obtai…
Full simulation of chiral Random Matrix Theory at non-zero chemical potential by Complex Langevin
A. Mollgaard, K. Splittorff
It is demonstrated that the complex Langevin method can simulate chiral random matrix theory at non-zero chemical potential. The successful match with the analytic prediction for t…
QCD-like Theories at Finite Baryon and Isospin Density
K. Splittorff, D. T. Son, M. A. Stephanov
We use 2-color QCD as a model to study the effects of simultaneous presence of chemical potentials for isospin charge, , and for baryon number, . We determine the phase…
Lessons from Random Matrix Theory for QCD at Finite Density
K. Splittorff, J. J. M. Verbaarschot
In this lecture we discuss various aspects of QCD at nonzero chemical potential, including its phase diagram and the Dirac spectrum, and summarize what chiral random matrix theory…
Microscopic Spectrum of the Wilson Dirac Operator
P. H. Damgaard, K. Splittorff, J. J. M. Verbaarschot
We calculate the leading contribution to the spectral density of the Wilson Dirac operator using chiral perturbation theory where volume and lattice spacing corrections are given b…
Fluctuations, correlations and the sign problem in QCD
M. P. Lombardo, K. Splittorff, J. J. M. Verbaarschot
We study the distribution of the phase angle and the magnitude of the fermion determinant as well as its correlation with the chiral condensate and the baryon number for QCD at non…
Chiral Condensate at Nonzero Chemical Potential in the Microscopic Limit of QCD
J. C. Osborn, K. Splittorff, J. J. M. Verbaarschot
The chiral condensate in QCD at zero temperature does not depend on the quark chemical potential (up to one third the nucleon mass), whereas the spectral density of the Dirac opera…
How the Quark Number fluctuates in QCD at small chemical potential
M. P. Lombardo, K. Splittorff, J. J. M. Verbaarschot
We discuss the distribution of the quark number over the gauge fields for QCD at nonzero quark chemical potential. As the quark number operator is non-hermitian, the distribution i…
Replica Limit of the Toda Lattice Equation
K. Splittorff, J. J. M. Verbaarschot
In a recent breakthrough Kanzieper showed that it is possible to obtain exact nonperturbative Random Matrix results from the replica limit of the corresponding Painlevé equation.…
Supersymmetric Quenching of the Toda Lattice Equation
K. Splittorff, J. J. M. Verbaarschot
The average of the ratio of powers of the spectral determinants of the Dirac operator in the -regime of QCD is shown to satisfy a Toda lattice equation. The quenched limit of t…
Quantum Determinant Estimation
J. Agerskov, K. Splittorff
A quantum algorithm for computing the determinant of a unitary matrix is given. The algorithm requires no preparation of eigenstates of and estimates the phase of t…
Universal Distribution of Would-be Topological Zero Modes in Coupled Chiral Systems
Adam Mielke, K. Splittorff
We consider two quenched, chiral ensembles which are coupled in such a way that a combined chiral symmetry is preserved. The coupling also links the topology of the two systems suc…
Complex Langevin Dynamics for chiral Random Matrix Theory
A. Mollgaard, K. Splittorff
We apply complex Langevin dynamics to chiral random matrix theory at nonzero chemical potential. At large quark mass the simulations agree with the analytical results while incorre…
The Sign Problem is the Solution
J. C. Osborn, K. Splittorff, J. J. M. Verbaarschot
The unquenched spectral density of the Dirac operator at is complex and has oscillations with a period inversely proportional to the volume and an amplitude that grows ex…
Microscopic eigenvalue correlations in QCD with imaginary isospin chemical potential
P. H. Damgaard, U. M. Heller, K. Splittorff +2
We consider the chiral limit of QCD subjected to an imaginary isospin chemical potential. In the epsilon-regime of the theory we can perform precise analytical calculations based o…
Dashen's Phenomenon in Gauge Theories with Spontaneously Broken Chiral Symmetries
G. Akemann, J. T. Lenaghan, K. Splittorff
We examine Dashen's phenomenon in the Leutwyler--Smilga regime of QCD with any number of colors and quarks in either the fundamental or adjoint representations of the gauge group.…
Investigating corrections to a Gaussian distribution of the complex phase
Jeff Greensite, Joyce C. Myers, K. Splittorff
It has been suggested that the density of states approach to performing lattice simulations in QCD with nonzero chemical potential can be modified to improve the signal to noise ra…
Partially Quenched Chiral Perturbation Theory and the Replica Method
P. H. Damgaard, K. Splittorff
We describe a novel framework for partially quenched chiral perturbation theory based on the replica method. The computational rules are exceedingly simple. We illustrate these rul…
Effects of dynamical quarks on the spectrum of the Wilson Dirac operator
G. Akemann, P. H. Damgaard, K. Splittorff +1
Effects of dynamical quarks on the microscopic spectrum of the Wilson Dirac operator are analyzed by means of effective field theory. We consider the distributions of the real mode…
Factorization of Correlation Functions and the Replica Limit of the Toda Lattice Equation
K. Splittorff, J. J. M. Verbaarschot
Exact microscopic spectral correlation functions are derived by means of the replica limit of the Toda lattice equation. We consider both Hermitian and non-Hermitian theories in th…
Universal Broadening of Zero Modes: A General Framework and Identification
M. Kieburg, A. Mielke, K. Splittorff
We consider the smallest eigenvalues of perturbed Hermitian operators with zero modes, either topological or system specific. To leading order for small generic perturbation we sho…
Investigating the Sharpe-Singleton scenario on the lattice by direct eigenvalue computation
Joni M. Suorsa, T. Rantalaiho, K. Rummukainen +2
We investigate the phase structure of lattice QCD with dynamical Wilson fermions. Wilson chiral perturbation theory predicts that the Aoki phase and the Sharpe-Singleton scenario m…
Random Matrix Theory at Nonzero and
K. Splittorff, J. J. M. Verbaarschot
We review applications of random matrix theory to QCD at nonzero temperature and chemical potential. The chiral phase transition of QCD and QCD-like theories is discussed in terms…
Wilson Fermions, Random Matrix Theory and the Aoki Phase
G. Akemann, P. H. Damgaard, K. Splittorff +1
The QCD partition function for the Wilson Dirac operator, , at nonzero lattice spacing can be expressed in terms of a chiral Lagrangian as a systematic expansion in the qu…
Bosonic Partition Functions
M. Kellerstein, K. Splittorff, J. J. M. Verbaarschot
The behavior of quenched Dirac spectra of two-dimensional lattice QCD is consistent with spontaneous chiral symmetry breaking which is forbidden according to the Coleman-Mermin-Wag…
A new Chiral Two-Matrix Theory for Dirac Spectra with Imaginary Chemical Potential
G. Akemann, P. H. Damgaard, J. C. Osborn +1
We solve a new chiral Random Two-Matrix Theory by means of biorthogonal polynomials for any matrix size . By deriving the relevant kernels we find explicit formulas for all $(n,…
Triage of the Sign Problem
K. Splittorff, J. J. M. Verbaarschot
We discuss the sign problem in QCD at nonzero chemical potential and its relation with chiral symmetry breaking and the spectrum of the Dirac operator using the framework of chiral…
Vector condensation in QCD
K. Splittorff
The response of the QCD vacuum to quark chemical potentials on the order of the pion mass is studied within the context of chiral perturbation theory. For two colour QCD diquark co…
New term in effective field theory at fixed topology
M. Kieburg, M. Lauritzen, B. T. Søgaard +1
A random matrix model for lattice QCD which takes into account the positive definite nature of the Wilson term is introduced. The corresponding effective theory for fixed index of…
Distributions of the Phase Angle of the Fermion Determinant in QCD
M. P. Lombardo, K. Splittorff, J. J. M. Verbaarschot
The distribution of the phase angle and the magnitude of the fermion determinant as well as its correlations with the baryon number and the chiral condensate are studied for QCD at…
The sign problem in the -regime of QCD
K. Splittorff
QCD in the -regime at nonzero baryon chemical potential is reviewed. The focus is on aspects of the sign problem which are relevant for lattice QCD. It is discussed how sp…
The -regime of dilaton chiral perturbation theory
Taro V. Brown, Maarten Golterman, Svend Krøjer +2
The -regime of dilaton chiral perturbation theory is introduced. We compute the dilaton mass, the chiral condensate and the topological susceptibility in the -regime, as a…
Chiral Dynamics With Wilson Fermions
K. Splittorff
Close to the continuum the lattice spacing affects the smallest eigenvalues of the Wilson Dirac operator in a very specific manner determined by the way in which the discretization…
The van der Waals interaction in one, two and three dimensions
A. C. Ipsen, K. Splittorff
The van der Waals interaction between two polarizable atoms is considered. In three dimensions the standard form with an attractive potential is obtained from second-orde…
Spectrum of the Wilson Dirac Operator at Finite Lattice Spacings
G. Akemann, P. H. Damgaard, K. Splittorff +1
We consider the effect of discretization errors on the microscopic spectrum of the Wilson Dirac operator using both chiral Perturbation Theory and chiral Random Matrix Theory. A gr…
Microscopic Universality and the Chiral Phase Transition in two Flavor QCD
F. Farchioni, Ph. de Forcrand, I. Hip +2
We re-analyze data from available finite-temperature QCD simulations near the chiral transition, with the help of Chiral Random Matrix Theory (chRMT). Statistical properties of the…
Fluctuation Induced Critical Behavior at Non-Zero Temperature and Chemical Potential
K. Splittorff, J. T. Lenaghan, J. Wirstam
We discuss phase transitions in relativistic systems as a function of both chemical potential and temperature. The presence of a chemical potential explicitly breaks Lorentz invari…
The microscopic Twisted Mass Dirac spectrum and the spectral determination of the LECs of Wilson -PT
Krzysztof Cichy, Elena Garcia-Ramos, K. Splittorff +1
We present the comparison of the analytical microscopic spectral density for lattice QCD with twisted mass fermions with the one obtained on the lattice utilizing con…
A New Method for Determining on the Lattice
P. H. Damgaard, Urs M. Heller, K. Splittorff +1
We derive the two-point spectral correlation function of the Dirac operator with a specific external source in the -regime of QCD. This correlation function has a unique and st…
Lattice simulations of QCD with versus phase quenched QCD
K. Splittorff
Previously published lattice results for QCD at are compared to analytic predictions for phase quenched QCD. We observe that the strength of the sign problem in QCD is…
Discretization Effects in the Domain of QCD
Mario Kieburg, K. Splittorff, Jacobus J. M. Verbaarschot +1
At nonzero lattice spacing the QCD partition function with Wilson quarks undergoes either a second order phase transition to the Aoki phase for decreasing quark mass or shows a fir…
The Microscopic Twisted Mass Dirac Spectrum
K. Splittorff, J. J. M. Verbaarschot
The microscopic spectral density for lattice QCD with two flavors and maximally twisted mass is computed. The results are given for fixed index of the Dirac operator and include th…
Nonhermitian Supersymmetric Partition Functions: the case of one bosonic flavor
K. Splittorff, J. J. M. Verbaarschot, M. R. Zirnbauer
We discuss the supersymmetric formulation of the nonhermitian random matrix partition function with one bosonic flavor. This partition function is regularized by adding one…
Phase of the Fermion Determinant for QCD at Finite Chemical Potential
K. Splittorff, J. J. M. Verbaarschot
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…