scholarly journals Complex Langevin calculations in QCD at finite density

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Yuta Ito ◽  
Hideo Matsufuru ◽  
Yusuke Namekawa ◽  
Jun Nishimura ◽  
Shinji Shimasaki ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Chemical Potential ◽  
Expansion Method ◽  
Finite Density ◽  
Fermi Sphere ◽  
Expectation Value ◽  
Sign Problem ◽  
Zero Momentum ◽  
Effective Theories ◽  
Severe Sign

Abstract We demonstrate that the complex Langevin method (CLM) enables calculations in QCD at finite density in a parameter regime in which conventional methods, such as the density of states method and the Taylor expansion method, are not applicable due to the severe sign problem. Here we use the plaquette gauge action with β = 5.7 and four-flavor staggered fermions with degenerate quark mass ma = 0.01 and nonzero quark chemical potential μ. We confirm that a sufficient condition for correct convergence is satisfied for μ/T = 5.2 − 7.2 on a 83 × 16 lattice and μ/T = 1.6 − 9.6 on a 163 × 32 lattice. In particular, the expectation value of the quark number is found to have a plateau with respect to μ with the height of 24 for both lattices. This plateau can be understood from the Fermi distribution of quarks, and its height coincides with the degrees of freedom of a single quark with zero momentum, which is 3 (color) × 4 (flavor) × 2 (spin) = 24. Our results may be viewed as the first step towards the formation of the Fermi sphere, which plays a crucial role in color superconductivity conjectured from effective theories.

scholarly journals Complex Langevin simulation of QCD at finite density and low temperature using the deformation technique

2018 ◽  
Vol 175 ◽  
pp. 07017 ◽  
Author(s):  
Keitro Nagata ◽  
Jun Nishimura ◽  
Shinji Shimasaki
Keyword(s):  
Low Temperature ◽  
Deformation Parameter ◽  
Original System ◽  
Baryon Number ◽  
Finite Density ◽  
Clear Sign ◽  
Sign Problem ◽  
Singular Drift ◽  
Langevin Simulation ◽  
Severe Sign

We study QCD at finite density and low temperature by using the complex Langevin method. We employ the gauge cooling to control the unitarity norm and intro-duce a deformation parameter in the Dirac operator to avoid the singular-drift problem. The reliability of the obtained results are judged by the probability distribution of the magnitude of the drift term. By making extrapolations with respect to the deformation parameter using only the reliable results, we obtain results for the original system. We perform simulations on a 43 × 8 lattice and show that our method works well even in the region where the reweighing method fails due to the severe sign problem. As a result we observe a delayed onset of the baryon number density as compared with the phase-quenched model, which is a clear sign of the Silver Blaze phenomenon.

scholarly journals A study of QCD at finite density using complex Langevin dynamics

2017 ◽  
Author(s):  
◽  
Felipe Attanasio ◽  
Keyword(s):  
Phase Diagram ◽  
Chemical Potential ◽  
Sampling Methods ◽  
Phase Diagram Of Qcd ◽  
Finite Density ◽  
Boltzmann Weight ◽  
Numerical Studies ◽  
Dynamic Stabilisation ◽  
Sign Problem ◽  
Standard Tool

Numerical simulations are a standard tool to investigate field theories in non-perturbative regimes. Typical algorithms used to evaluate path integrals in Euclidean space rely on importance sampling methods; i.e., a probabilistic interpretation of the Boltzmann weight eS. However, many theories of interest suffer from the infamous sign problem: the action is complex and the Boltzmann weight cannot be used as a probability distribution. Complex Langevin simulations allow numerical studies of theories that exhibit the sign problem, such as QCD at finite density. In this thesis, we study methods to investigate the phase diagram of QCD in the temperature{chemical potential plane, using the complex Langevin method. We provide results on the phase diagram for the heavy-denseapproximation of QCD (HDQCD) for three spatial volumes, using complex Langevin and the gauge cooling technique. We also present polynomial fits of the critical temperature as function of the chemical potential for each volume. Subsequently, we discuss instabilities encountered during this study, which motivated a novel technique, named Dynamic Stabilisation, which will be introduced and the theoretical ideas behind it, explained. Dynamic stabilisation was, then, used in an investigation of the dependency of the critical chemical potential on the hopping parameter. The two previous studies were used to guide a second examination of the HDQCD phase diagram, focussed around the phase boundary. Lastly, we present preliminary results on the phase diagram of QCD with fully dynamical quarks at high temperatures. This shows that complex Langevin, augmented with gauge cooling and dynamic stabilisation, is suited for investigating QCD at finite chemical potential.

scholarly journals Aspects of quantum information in finite density field theory

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Lucas Daguerre ◽  
Raimel Medina ◽  
Mario Solís ◽  
Gonzalo Torroba
Keyword(s):  
Field Theory ◽  
Quantum Information ◽  
Mutual Information ◽  
Fermi Surface ◽  
Relative Entropy ◽  
Chemical Potential ◽  
Operator Product ◽  
Dirac Fermions ◽  
Long Distance ◽  
Finite Density

Abstract We study different aspects of quantum field theory at finite density using methods from quantum information theory. For simplicity we focus on massive Dirac fermions with nonzero chemical potential, and work in 1 + 1 space-time dimensions. Using the entanglement entropy on an interval, we construct an entropic c-function that is finite. Unlike what happens in Lorentz-invariant theories, this c-function exhibits a strong violation of monotonicity; it also encodes the creation of long-range entanglement from the Fermi surface. Motivated by previous works on lattice models, we next calculate numerically the Renyi entropies and find Friedel-type oscillations; these are understood in terms of a defect operator product expansion. Furthermore, we consider the mutual information as a measure of correlation functions between different regions. Using a long-distance expansion previously developed by Cardy, we argue that the mutual information detects Fermi surface correlations already at leading order in the expansion. We also analyze the relative entropy and its Renyi generalizations in order to distinguish states with different charge and/or mass. In particular, we show that states in different superselection sectors give rise to a super-extensive behavior in the relative entropy. Finally, we discuss possible extensions to interacting theories, and argue for the relevance of some of these measures for probing non-Fermi liquids.

scholarly journals Chemical potential and quantum Hall ferromagnetism in bilayer graphene

Science ◽  
2014 ◽  
Vol 345 (6192) ◽  
pp. 58-61 ◽  
Author(s):  
Kayoung Lee ◽  
Babak Fallahazad ◽  
Jiamin Xue ◽  
David C. Dillen ◽  
Kyounghwan Kim ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Chemical Potential ◽  
Hexagonal Boron Nitride ◽  
Quantum Hall ◽  
Bilayer Graphene ◽  
Zero Magnetic Field ◽  
High Magnetic Fields ◽  
Complex Interplay ◽  
Electron Hole ◽  
Quantum Hall State

Bilayer graphene has a distinctive electronic structure influenced by a complex interplay between various degrees of freedom. We probed its chemical potential using double bilayer graphene heterostructures, separated by a hexagonal boron nitride dielectric. The chemical potential has a nonlinear carrier density dependence and bears signatures of electron-electron interactions. The data allowed a direct measurement of the electric field–induced bandgap at zero magnetic field, the orbital Landau level (LL) energies, and the broken-symmetry quantum Hall state gaps at high magnetic fields. We observe spin-to-valley polarized transitions for all half-filled LLs, as well as emerging phases at filling factors ν = 0 and ν = ±2. Furthermore, the data reveal interaction-driven negative compressibility and electron-hole asymmetry in N = 0, 1 LLs.

scholarly journals Sign problem via imaginary chemical potential

2007 ◽  
Vol 75 (11) ◽  
Author(s):  
K. Splittorff ◽  
B. Svetitsky
Keyword(s):  
Chemical Potential ◽  
Sign Problem

scholarly journals Hybrid Numerical-Experimental Model Update Based on Correlation Approach for Turbine Components

2020 ◽  
Author(s):  
Zeeshan Saeed ◽  
Christian Maria Firrone ◽  
Teresa Maria Berruti
Keyword(s):  
Degrees Of Freedom ◽  
Expansion Method ◽  
Hybrid Models ◽  
Impact Testing ◽  
Equivalent Model ◽  
Correlated Channels ◽  
Model Update ◽  
Model Mixing ◽  
Fatigue Failures

Abstract Bladed-disks in turbo-machines experience high cycle fatigue failures due to high vibration amplitudes. Therefore, it is important to accurately predict their dynamic characteristics including the mechanical joints at blade-disk (root joint) or blade-blade (shroud) interfaces. These joints help in dampening the vibration amplitudes. Before the experimental identification of these joints, it is of paramount importance to accurately measure the interface degrees-of-freedom (DoF). However, they are largely inaccessible for the measurements. For this reason, expansion techniques are used in order to update the single components before their coupling. But the expansion can be affected adversely if the measurements are not properly correlated with the updated model or if they have significant errors. Therefore, a frequency domain expansion method called System Equivalent Model Mixing (SEMM) is used to expand a limited set of measurements to a larger set of numerical DoF. Different measured models — termed the overlay models — are taken from an impact testing campaign of a blade and a disk and coupled to the numerical model according to the SEMM. The expanded models — termed the hybrid models — are then correlated with the validation channels in a round-robin way by means of Frequency Response Assurance Criteria (FRAC). The global correlations depict whether or not a measurement and the respective expansion is properly correlated. By this approach, the least correlated channels can be done away with from the measurements to have a better updated hybrid model. The method is tested on both the structures (the blade and the disk) and it is successfully shown that removing the uncorrelated channels does improve the quality of the hybrid models.

Slow Light Effect of Photonic Crystal Waveguides by Adjusting Parameters of Crescent Scatterers

2014 ◽  
Vol 926-930 ◽  
pp. 415-418
Author(s):  
Yong Wan ◽  
Yue Guo ◽  
Jing Gao ◽  
Ming Hui Jia
Keyword(s):  
Photonic Crystal ◽  
Degrees Of Freedom ◽  
Slow Light ◽  
Expansion Method ◽  
Photonic Crystal Waveguides ◽  
Light Effect ◽  
Plane Wave Expansion Method ◽  
Multiple Degrees Of Freedom ◽  
Low Dispersion ◽  
Center Distance

Crescent scatterers possess the properties of anisotropy and multiple degrees of freedom. With plane-wave expansion method (PWE), the slow light effect with high ngand low dispersion can be achieved by optimizing the structure parameters of photonic crystal waveguide with line defect, such as changing the radius of two circles and center distance. Slow light with low dispersion can be obtained by these methods, which implies that choosing suitable scatterers and adjusting their parameters can efficiently achieve slow light with high ng and low dispersion.

scholarly journals Thermodynamics of Gas–Liquid Colloidal Equilibrium States: Hetero-Phase Fluctuations

Entropy ◽  
2019 ◽  
Vol 21 (12) ◽  
pp. 1189 ◽  
Author(s):  
Leslie V. Woodcock
Keyword(s):  
Thermodynamic Properties ◽  
Degrees Of Freedom ◽  
Chemical Potential ◽  
Thermodynamic Description ◽  
Colloidal Dispersion ◽  
Equilibrium States ◽  
Phase Volume ◽  
Phase Fluctuations ◽  
Constant Change ◽  
Liquid States

Following on from two previous JETC (Joint European Thermodynamics Conference) presentations, we present a preliminary report of further advances towards the thermodynamic description of critical behavior and a supercritical gas-liquid coexistence with a supercritical fluid mesophase defined by percolation loci. The experimental data along supercritical constant temperature isotherms (T ≥ Tc) are consistent with the existence of a two-state mesophase, with constant change in pressure with density, rigidity, (dp/dρ) T, and linear thermodynamic state-functions of density. The supercritical mesophase is bounded by 3rd-order phase transitions at percolation thresholds. Here we present the evidence that these percolation transitions of both gaseous and liquid states along any isotherm are preceded by pre-percolation hetero-phase fluctuations that can explain the thermodynamic properties in the mesophase and its vicinity. Hetero-phase fluctuations give rise to one-component colloidal-dispersion states; a single Gibbs phase retaining 2 degrees of freedom in which both gas and liquid states with different densities percolate the phase volume. In order to describe the thermodynamic properties of two-state critical and supercritical coexistence, we introduce the concept of a hypothetical homo-phase of both gas and liquid, defined as extrapolated equilibrium states in the pre-percolation vicinity, with the hetero-phase fractions subtracted. We observe that there can be no difference in chemical potential between homo-phase liquid and gaseous states along the critical isotherm in mid-critical isochoric experiments when the meniscus disappears at T = Tc. For T > Tc, thermodynamic states comprise equal mole fractions of the homo-phase gas and liquid, both percolating the total phase volume, at the same temperature, pressure, and with a uniform chemical potential, stabilised by a positive finite interfacial surface tension.

scholarly journals Worldlines and worldsheets for non-abelian lattice field theories: Abelian color fluxes and Abelian color cycles

2018 ◽  
Vol 175 ◽  
pp. 11007 ◽  
Author(s):  
Christof Gattringer ◽  
Daniel Göschl ◽  
Carlotta Marchis
Keyword(s):  
Degrees Of Freedom ◽  
Chemical Potential ◽  
Space Time ◽  
Field Theories ◽  
Gauge Fields ◽  
Chiral Model ◽  
Staggered Fermions ◽  
Lattice Field ◽  
Principal Chiral Model ◽  
Matter Fields

We discuss recent developments for exact reformulations of lattice field theories in terms of worldlines and worldsheets. In particular we focus on a strategy which is applicable also to non-abelian theories: traces and matrix/vector products are written as explicit sums over color indices and a dual variable is introduced for each individual term. These dual variables correspond to fluxes in both, space-time and color for matter fields (Abelian color fluxes), or to fluxes in color space around space-time plaquettes for gauge fields (Abelian color cycles). Subsequently all original degrees of freedom, i.e., matter fields and gauge links, can be integrated out. Integrating over complex phases of matter fields gives rise to constraints that enforce conservation of matter flux on all sites. Integrating out phases of gauge fields enforces vanishing combined flux of matter-and gauge degrees of freedom. The constraints give rise to a system of worldlines and worldsheets. Integrating over the factors that are not phases (e.g., radial degrees of freedom or contributions from the Haar measure) generates additional weight factors that together with the constraints implement the full symmetry of the conventional formulation, now in the language of worldlines and worldsheets. We discuss the Abelian color flux and Abelian color cycle strategies for three examples: the SU(2) principal chiral model with chemical potential coupled to two of the Noether charges, SU(2) lattice gauge theory coupled to staggered fermions, as well as full lattice QCD with staggered fermions. For the principal chiral model we present some simulation results that illustrate properties of the worldline dynamics at finite chemical potentials.

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