arXiv subjects

Michael C. Ogilvie

Publications and source records attributed to Michael C. Ogilvie.

At least 19 recordsLinked to original sources

arXiv2025

Dilepton production from moaton quasiparticles

The phase diagram of QCD may contain a moat regime in a large region of temperature $T$ and chemical potential $μ\neq0$. A moat regime is characterized by quasiparticle moatons (pions) whose energy is minimal at nonzero spatial momentum. At $μ\neq 0$, higher mass dimension operators play a critical role in a moat regime. At dimension six, there are nine possible gauge invariant couplings between scalars and photons. For back-to-back dilepton production, only one operator contributes, which significantly enhances production near a moat threshold. This enhancement is an experimental signature of moatons.

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arXiv2025

Exotic phases in finite-density $\mathbb{Z}_3$ theories

Lattice $\mathbb{Z}_3$ theories with complex actions share many key features with finite-density QCD including a sign problem and $CK$ symmetry. Complex $\mathbb{Z}_3$ spin and gauge models exhibit a generalized Kramers-Wannier duality mapping them onto chiral $\mathbb{Z}_3$ spin and gauge models, which are simulatable with standard lattice methods in large regions of parameter space. The Migdal-Kadanoff real-space renormalization group (RG) preserves this duality, and we use it to compute the approximate phase diagram of both spin and gauge $\mathbb{Z}_3$ models in dimensions one through four. Chiral $\mathbb{Z}_3$ spin models are known to exhibit a Devil's Flower phase structure, with inhomogeneous phases which can be thought of as $\mathbb{Z}_3$ analogues of chiral spirals. Out of the large class of models we study, we find that only chiral spin models and their duals have a Devil's Flower structure with an infinite set of inhomogeneous phases, a result we attribute to Elitzur's theorem. We also find that different forms of the Migdal-Kadanoff RG produce different numbers of phases, a violation of the expectation for universal behavior from a real-space RG. We discuss extensions of our work to $\mathbb{Z}_N$ models, SU($N$) models and nonzero temperature.

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arXiv2021

Finite-density QCD, $\mathcal{PT}$ symmetry, and dual algorithms

Finite-density QCD and many other field theories with sign problems have a $\mathcal{PT}$-type symmetry. After a brief introduction to $\mathcal{PT}$-symmetric field theories, a real dual representation for $\mathcal{PT}$-symmetric scalar field theories with complex actions is derived. We show that $\mathcal{PT}$-symmetric field theories can exhibit exotic behavior, including sinusoidally modulated propagators, disorder lines, and spatially inhomogeneous pattern-forming phases. We discuss the interplay of duality, $\mathcal{PT}$-symmetry and pattern formation using a $ϕ^4$ model and $Z(N)$ spin model with sign problems as examples. These behaviors may occur in finite-density QCD and related models.

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arXiv2021

Finite-density QCD, $\mathcal{PT}$ symmetry, and exotic phases

We study the phase structure of effective models of finite-density QCD using analytic and lattice simulation techniques developed for the study of non-Hermitian and $\mathcal{PT}$-symmetric QFTs. Finite-density QCD is symmetric under the combined operation of the charge and complex conjugation operators $\mathcal{CK}$, which falls into the class of so-called generalized $\mathcal{PT}$ symmetries. We show that $\mathcal{PT}$-symmetric quantum field theories can support patterned ground-state field configurations in the vicinity of a critical endpoint. We apply our methods to a lattice heavy quark model at nonzero chemical potential that displays patterning behavior for a range of parameters. We derive a simple approximate criterion for the formation of these patterns, which can be used with lattice results.

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arXiv2021

$\mathcal PT$ symmetry, pattern formation, and finite-density QCD

A longstanding issue in the study of quantum chromodynamics (QCD) is its behavior at nonzero baryon density, which has implications for many areas of physics. The path integral has a complex integrand when the quark chemical potential is nonzero and therefore has a sign problem, but it also has a generalized $\mathcal PT$ symmetry. We review some new approaches to $\mathcal PT$-symmetric field theories, including both analytical techniques and methods for lattice simulation. We show that $\mathcal PT$-symmetric field theories with more than one field generally have a much richer phase structure than their Hermitian counterparts, including stable phases with patterning behavior. The case of a $\mathcal PT$-symmetric extension of a $ϕ^4$ model is explained in detail. The relevance of these results to finite density QCD is explained, and we show that a simple model of finite density QCD exhibits a patterned phase in its critical region.

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arXiv2021

Universality of Pattern Formation

We study a $\mathcal PT$-symmetric scalar Euclidean field theory with a complex action, using both theoretical analysis and lattice simulations. This model has a rich phase structure that exhibits pattern formation in the critical region. Analytical results and simulations associate pattern formation with tachyonic instabilities in the homogeneous phase. Monte Carlo simulation shows that pattern morphologies vary smoothly, without distinct microphases. We suggest that pattern formation in this model may be regarded as a form of arrested spinodal decomposition. We extend our theoretical analysis to multicomponent $\mathcal PT$-symmetric Euclidean scalar field theories and show that they give rise to new universality classes of local field theories that exhibit patterned behavior in the critical region. QCD at finite temperature and density is a member of the $Z(2)$ universality class when the Polyakov loop is used to distinguish confined and deconfined phases. This suggests the possibility of the formation of patterns of confined and deconfined matter in QCD in the critical region in the $μ-T$ plane.

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arXiv2018

Simulation of Scalar Field Theories with Complex Actions

Many scalar field theory models with complex actions are invariant under the antilinear ($PT$) symmetry operation $L^{\ast}(-χ)=L(χ)$. Models in this class include the $iϕ^{3}$ model, the Bose gas at finite density and Polyakov loop spin models at finite density. This symmetry may be used to obtain a dual representation where weights in the functional integral are real but not necessarily positive. For a subclass of models satisfying a dual positive weight condition, the partition function is manifestly positive. The sign problem is eliminated; such models are easily simulated by a simple local algorithm in any number of dimensions. Simulations of models in this subclass show a rich set of behaviors. Propagators may exhibit damped oscillations, indicating a clear violation of spectral positivity. Pattern formation may also occur, with both stripe and bubble morphologies possible. The existence of a positive representation is constrained by Lee-Yang zeros: a positive representation cannot exist everywhere in the neighborhood of such a zero. Simulation results raise the possibility that pattern-forming behavior may occur in finite density QCD in the vicinity of the critical line.

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arXiv2017

Simulation of Scalar Field Theories with Complex Actions

We develop a method for the simulation of scalar field theories with complex actions which is local, simple to implement and can be used in any number of space-time dimensions. For model systems satisfying the $\mathcal{PT}$ symmetry condition $L^{*}(ϕ)=L(-ϕ)$, the complex weight problem is reduced to a sign problem. The sign problem is eliminated completely for a large subclass of these models; this class includes models within the $iϕ^{3}$ universality class, and also models with nonzero chemical potential. Simulations of models from this subclass show a rich set of behaviors. Propagators may exhibit damped oscillations, indicating a clear violation of spectral positivity. Modulated phases occur in some models, exhibiting striping and other pattern-forming behaviors. These field theory models are connected to complex systems where pattern formation occurs because of competition between interactions at two different length scales.

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arXiv2016

Liquid-Gas Phase Transitions and $\mathcal{CK}$ Symmetry in Quantum Field Theories

A general field-theoretic framework for the treatment of liquid-gas phase transitions is developed. Starting from a fundamental four-dimensional field theory at nonzero temperature and density, an effective three-dimensional field theory with a sign problem is derived. Although charge conjugation $\mathcal{C}$ is broken at finite density, there remains a symmetry under $\mathcal{CK}$, where $\mathcal{K}$ is complex conjugation. We consider four models: relativistic fermions, nonrelativistic fermions, static fermions and classical particles. The thermodynamic behavior is extracted from $\mathcal{CK}$-symmetric complex saddle points of the effective field theory at tree level. The relativistic and static fermions show a liquid-gas transition, manifesting as a first-order line at low temperature and high density, terminated by a critical end point. In the cases of nonrelativistic fermions and classical particles, we find no first-order liquid-gas transitions at tree level. The mass matrix controlling the behavior of correlation functions is obtained from fluctuations around the saddle points. Due to the $\mathcal{CK}$ symmetry of the models, the eigenvalues of the mass matrix can be complex. This leads to the existence of disorder lines, which mark the boundaries where the eigenvalues go from purely real to complex. The regions where the mass matrix eigenvalues are complex are associated with the critical line. In the case of static fermions, a powerful duality between particles and holes allows for the analytic determination of both the critical line and the disorder lines. Depending on the values of the parameters, either zero, one or two disorder lines are found. Numerical results for relativistic fermions give a very similar picture.

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arXiv2016

Schwinger Pair Production at Finite Temperature

Thermal corrections to Schwinger pair production are potentially important in particle physics, nuclear physics and cosmology. However, the lowest-order contribution, arising at one loop, has proved difficult to calculate unambiguously. We show that this thermal correction may be calculated for charged scalars using the worldline formalism, where each term in the decay rate is associated with a worldline instanton. We calculate all finite-temperature worldline instantons, their actions and fluctuations prefactors, thus determining the complete one-loop decay rate at finite temperature. The thermal contribution to the decay rate becomes nonzero at a threshold temperature $T=eE/2m$, above which it dominates the zero temperature result. This is the lowest of an infinite set of thresholds at $T=neE/2m$. The decay rate is singular at each threshold as a consequence of the failure of the quadratic approximation to the worldline path integral. We argue that that higher-order effects will make the decay rates finite everywhere, and model those effects by the inclusion of hard thermal loop damping rates. We also demonstrate that the formalism developed here generalizes to the case of finite-temperature pair production in inhomogeneous fields.

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arXiv2016

Complex spectrum of finite-density lattice QCD with static quarks at strong coupling

We calculate the spectrum of transfer matrix eigenvalues associated with Polyakov loops in finite-density lattice QCD with static quarks. These eigenvalues determine the spatial behavior of Polyakov loop correlations functions. Our results are valid for all values of the gauge coupling in $1+1$ dimensions, and valid in the strong-coupling region for any number of dimensions. When the quark chemical potential $μ$ is nonzero, the spatial transfer matrix $T_s$ is non-Hermitian. The appearance of complex eigenvalues in $T_s$ is a manifestation of the sign problem in finite-density QCD. The invariance of finite-density QCD under the combined action of charge conjugation $\mathcal{C}$ and complex conjugation $\mathcal{K}$ implies that the eigenvalues of $T_s$ are either real or part of a complex pair. Calculation of the spectrum confirms the existence of complex pairs in much of the temperature-chemical potential plane. Many features of the spectrum for static quarks are determined by a particle-hole symmetry. For $μ$ small compared to the quark mass $M$, we typically find real eigenvalues for the lowest lying states. At somewhat larger values of $μ,$ pairs of eigenvalues may form complex-conjugate pairs, leading to damped oscillatory behavior in Polyakov loop correlation functions. However, near $μ=M$, the low-lying spectrum becomes real again. This is a direct consequence of the approximate particle-hole symmetry at $μ=M$ for heavy quarks. This behavior of the eigenvalues should be observable in lattice simulations and can be used as a test of lattice algorithms. Our results provide independent confirmation of results we have previously obtained in PNJL models using complex saddle points.

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arXiv2015

Complex saddle points in finite-density QCD

We consider complex saddle points in QCD at finite temperature and density, which are constrained by symmetry under charge and complex conjugations. This approach naturally incorporates color neutrality, and the Polyakov loop and the conjugate loop at the saddle point are real but not identical. Moreover, it can give rise to a complex mass matrix associated with the Polyakov loops, reflecting oscillatory behavior in color-charge densities. This aspect of the phase structure appears to be sensitive to the origin of confinement, as modeled in the effective potential.

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arXiv2014

Complex Saddle Points and Disorder Lines in QCD at finite temperature and density

The properties and consequences of complex saddle points are explored in phenomenological models of QCD at non-zero temperature and density. Such saddle points are a consequence of the sign problem, and should be considered in both theoretical calculations and lattice simulations. Although saddle points in finite-density QCD are typically in the complex plane, they are constrained by a symmetry that simplifies analysis. We model the effective potential for Polyakov loops using two different potential terms for confinement effects, and consider three different cases for quarks: very heavy quarks, massless quarks without modeling of chiral symmetry breaking effects, and light quarks with both deconfinement and chiral symmetry restoration effects included in a pair of PNJL models. In all cases, we find that a single dominant complex saddle point is required for a consistent description of the model. This saddle point is generally not far from the real axis; the most easily noticed effect is a difference between the Polyakov loop expectation values $\left\langle {\rm Tr}_{F}P\right\rangle $ and $\left\langle {\rm Tr}_{F}P^{\dagger}\right\rangle $, and that is confined to small region in the $μ-T$ plane. In all but one case, a disorder line is found in the region of critical and/or crossover behavior. The disorder line marks the boundary between exponential decay and sinusoidally modulated exponential decay of correlation functions. Disorder line effects are potentially observable in both simulation and experiment. Precision simulations of QCD in the $μ-T$ plane have the potential to clearly discriminate between different models of confinement.

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arXiv2014

Confinement on $R^{3}\times S^{1}$: continuum and lattice

There has been substantial progress in understanding confinement in a class of four-dimensional SU(N) gauge theories using semiclassical methods. These models have one or more compact directions, and much of the analysis is based on the physics of finite-temperature gauge theories. The topology $R^{3}\times S^{1}$ has been most often studied, using a small compactification circumference $L$ such that the running coupling $g^{2}\left(L\right)$ is small. The gauge action is modified by a double-trace Polyakov loop deformation term, or by the addition of periodic adjoint fermions. The additional terms act to preserve $Z(N)$ symmetry and thus confinement. An area law for Wilson loops is induced by a monopole condensate. In the continuum, the string tension can be computed analytically from topological effects. Lattice models display similar behavior, but the theoretical analysis of topological effects is based on Abelian lattice duality rather than on semiclassical arguments. In both cases the key step is reducing the low-energy symmetry group from $SU(N)$ to the maximal Abelian subgroup $U(1)^{N-1}$ while maintaining $Z(N)$ symmetry.

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arXiv2014

Complex saddle points in QCD at finite temperature and density

The sign problem in QCD at finite temperature and density leads naturally to the consideration of complex saddle points of the action or effective action. The global symmetry $\mathcal{CK}$ of the finite-density action, where $\mathcal{C}$ is charge conjugation and $\mathcal{K}$ is complex conjugation, constrains the eigenvalues of the Polyakov loop operator $P$ at a saddle point in such a way that the action is real at a saddle point, and net color charge is zero. The values of $Tr_{F}P$ and $Tr_{F}P^{\dagger}$ at the saddle point, are real but not identical, indicating the different free energy cost associated with inserting a heavy quark versus an antiquark into the system. At such complex saddle points, the mass matrix associated with Polyakov loops may have complex eigenvalues, reflecting oscillatory behavior in color-charge densities. We illustrate these properties with a simple model which includes the one-loop contribution of gluons and massless quarks moving in a constant Polyakov loop background. Confinement-deconfinement effects are modeled phenomenologically via an added potential term depending on the Polyakov loop eigenvalues. For sufficiently large $T$ and $μ$, the results obtained reduce to those of perturbation theory at the complex saddle point. These results may be experimentally relevant for the CBM experiment at FAIR.

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arXiv2013

The sign problem and Abelian lattice duality

For a large class of Abelian lattice models with sign problems, including the case of non-zero chemical potential, duality maps models with complex actions into dual models with real actions. For extended regions of parameter space, calculable for each model, duality resolves the sign problem for both analytic methods and computer simulations. Explicit duality relations are given for models for spin and gauge models based on Z(N) and U(1) symmetry groups. The dual forms are generalizations of the Z(N) chiral clock model and the lattice Frenkel-Kontorova model, respectively. From these equivalences, rich sets of spatially-modulated phases are found in the strong-coupling region of the original models.

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arXiv2013

The Sign Problem, PT Symmetry and Abelian Lattice Duality

Lattice field theories with complex actions are not easily studied using conventional analytic or simulation methods. However, a large class of these models are invariant under CT, where C is charge conjugation and T is time reversal, including models with non-zero chemical potential. For Abelian models in this class, lattice duality maps models with complex actions into dual models with real actions. For extended regions of parameter space, calculable for each model, duality resolves the sign problem for both analytic methods and computer simulations. Explicit duality relations are given for models for spin and gauge models based on Z(N) and U(1) symmetry groups. The dual forms are generalizations of the Z(N) chiral clock model and the lattice Frenkel-Kontorova model, respectively. From these equivalences, rich sets of spatially-modulated phases are found in the strong-coupling region of the original models.

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arXiv2012

Phases of Gauge Theories

One of the most fundamental questions we can ask about a given gauge theory is its phase diagram. In the standard model, we observe three fundamentally different types of behavior: QCD is in a confined phase at zero temperature, while the electroweak sector of the standard model combines Coulomb and Higgs phases. Our current understanding of the phase structure of gauge theories owes much to the modern theory of phase transitions and critical phenomena, but has developed into a subject of extensive study. After reviewing some fundamental concepts of phase transitions and finite-temperature gauge theories, we discuss some recent work that broadly extends our knowledge of the mechanisms that determine the phase structure of gauge theories. A new class of models with a rich phase structure has been discovered, generalizing our understanding of the confinement-deconfinement transition in finite-temperature gauge theories. Models in this class have space-time topologies with one or more compact directions. On R^3 x S^1, the addition of double-trace deformations or periodic adjoint fermions to a gauge theory can yield a confined phase in the region where the S^1 circumference L is small, so that the coupling constant is small, and semiclassical methods are applicable. In this region, Euclidean monopole solutions, which are constituents of finite-temperature instantons, play a crucial role in the calculation of a non-perturbative string tension. We review the techniques use to analyze this new class of models and the results obtained so far, as well as their application to finite-temperature phase structure, conformal phases of gauge theories and the large-N limit.

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