Chiral Phase Transition Research Articles

Conformal and chiral phase transitions in Rydberg chains

Using density matrix renormalization group simulations on open chains, we map out the wave-vector in the incommensurate disordered phase of a realistic model of Rydberg chains with $1/r^6$ interactions, and we locate and characterize the points along the commensurate lines where the transition out of the period 3 and 4 phases is conformal. We confirm that it is 3-state Potts for the period-3 phase, and we show that it is Ashkin-Teller with $\nu\simeq 0.80$ for the period-4 phase. We further show that close to these points the transition is still continuous, but with a completely different scaling of the wave-vector, in agreement with a chiral transition. Finally, we propose to use the conformal points as benchmarks for Kibble-Zurek experiments, defining a roadmap towards a conclusive identification of the chiral universality class.

Regulator scheme dependence of the chiral phase transition at high densities

A common feature of recent functional renormalization group investigations of effective low-energy QCD is the appearance of a back-bending behavior of the chiral phase transition line at low temperatures together with a negative entropy density in the symmetric regime. The regulator scheme dependence of this phenomenon and the necessary modifications at finite densities are analyzed within a two-flavor quark-meson model. The flows at finite densities for three different regulators of three- or four-dimensional momenta are confronted to each other. It is found that the back-bending behavior and the negative entropy density can be traced back to the explicit momentum dependence of the regulator shape function. While it persists for the often-used three-dimensional flat regulator, it vanishes for Callan-Symanzik type regulators. This points to truncation artifacts in the lowest order of the derivative expansion. A careful theoretical as well as numerical exploration is given.

Fate of the first-order chiral phase transition in QCD: Implications for dark QCD studied via a Nambu–Jona-Lasinio model

The first-order nature of the chiral phase transition in QCD-like theories can play crucial roles to address a dark side of the Universe, where the created out-of equilibrium is essential to serve as cosmological and astrophysical probes such as gravitational wave productions, which have extensively been explored. This interdisciplinary physics is built based on a widely-accepted conjecture that the thermal chiral phase transition in QCD-like theories with massless (light) three flavors is of first order. We find that such a first order feature may not hold, when ordinary or dark quarks are externally coupled to a weak enough background field of photon or dark photon (which we collectively call a ``magnetic" field). We assume that a weak ``magnetic" background field could be originated from some ``magnetogenesis" in the early Universe. We work on a Nambu-Jona-Lasinio model which can describe the chiral phase transition in a wide class of QCD-like theories. We show that in the case with massless (light) three flavors, the first-order feature goes away when $2 f_\pi^2 \lesssim eB ( \ll (4 \pi f_\pi)^2)$, where $eB$ is the ``magnetic" field strength and $f_\pi$ the pion decay constant at the vacuum. This disappearance is the generic consequence of the presence of the ``magnetically" induced scale anomaly and the ``magnetic" catalysis for the chiral symmetry breaking, and would impact or constrain modeling dark QCD coupled to an external ``magnetic" field.

Enhanced pion-to-proton ratio at the onset of the QCD phase transition

The pion-to-proton ratio is identified as a potential signal for a non-equilibrium first-order chiral phase transition in heavy-ion collisions, as the pion multiplicity is directly related to entropy production. To showcase this effect, a non-equilibrium Bjorken expansion starting from realistic initial conditions along a Taub adiabat is used to simulate the entropy production. Different dynamical criteria to determine the final entropy-per-baryon number are investigated and matched to a hadron resonance gas model along the chemical freeze out curve to obtain the final pion and proton numbers. We detect a strong enhancement of their multiplicity ratio at the energies where the system experiences a strong phase transition as compared to a smooth crossover which shows almost no enhancement.

Strange quark matter from a baryonic approach

We construct a model for dense matter based on low-density nuclear matter properties that exhibits a chiral phase transition and that includes strangeness through hyperonic degrees of freedom. Empirical constraints from nuclear matter alone allow for various scenarios, from a strong first-order chiral transition at relatively low densities through a weaker transition at higher densities, even up to a smooth crossover not far beyond the edge of the allowed range. The model parameters can be chosen such that at asymptotically large densities the chirally restored phase contains strangeness and the speed of sound approaches the conformal limit, resulting in a high-density phase that resembles deconfined quark matter. Additionally, if the model is required to reproduce sufficiently massive compact stars, the allowed parameter range is significantly narrowed down, resulting for instance in a very narrow range for the poorly known slope parameter of the symmetry energy, $L\ensuremath{\simeq}(88--92)\text{ }\text{ }\mathrm{MeV}$. We also find that for the allowed parameter range strangeness does not appear in the form of hyperons in the chirally broken phase and the chiral transition is of first order. Due to its unified approach and relative simplicity---here we restrict ourselves to zero temperature and the mean-field approximation---the model can be used in the future to study dense matter under compact star conditions in the vicinity of the chiral phase transition, for instance to compute the surface tension or to investigate spatially inhomogeneous phases.

Properties of strange quark matter under strong rotation

We investigate the rotating quark matter in the three-flavor Nambu--Jona-Lasinio (NJL) model. The chiral condensation, spin polarization, and number susceptibility of the light and strange quarks are carefully studied at finite temperatures without or with finite chemical potential in this model. We find that the rotation suppresses the chiral condensation and enhances the first-order quark spin polarization, however for the second-order quark spin polarization and quark number susceptibility the effect is complicated and interesting. When extending to the situation with finite chemical potential, we find the angular velocity also plays a crucial role, at small angular velocity the chemical potential enhances the susceptibility, however in the middle region of angular velocity the effect of the chemical potential is suppressed by the angular velocity and susceptibility can be changed considerably, it can be observed that at very low temperature in the presence of quark chemical potential the quark number susceptibility has two maxima with increasing angular velocity. Furthermore, it is found that at sufficiently large angular velocity the contributions played by the light quark and the strange quark to these phenomena are almost equal. We also discuss the chiral phase transition of rotating quark matter in the three-flavor NJL model. We expect these studies to be used to understand the chiral symmetry breaking and restoration as well as probe the QCD phase transition.

Replica symmetry breaking for the integrable two-site Sachdev–Ye–Kitaev model

We analyze a two-body non-Hermitian two-site Sachdev–Ye–Kitaev (SYK) model with the couplings of one site complex conjugated to the other site. This model, with no explicit coupling between the sites, shows an infinite number of second-order phase transitions, which is a consequence of the factorization of the partition function into a product over Matsubara frequencies. We calculate the quenched free energy in two different ways: first in terms of the single-particle energies and second by solving the Schwinger–Dyson equations of the two-site model. The first calculation can be done entirely in terms of a one-site model. The conjugate replica enters due to non-analyticities when Matsubara frequencies enter the spectral support of the coupling matrix. The second calculation is based on the replica trick of the two-site partition function. Both methods give the same result. The free-fermion partition function can also be rephrased as a matrix model for the coupling matrix. Up to minor details, this model is the random matrix model that describes the chiral phase transition of QCD, and the order parameter of the two-body model corresponds to the chiral condensate of QCD. Comparing to the corresponding four-body model, we are able to determine which features of the free energy are due to the chaotic nature of the four-body model. The high-temperature phase of both models is entropy dominated, and in both cases, the free energy is determined by the spectral density. The chaotic four-body SYK model has a low-temperature phase whose free energy is almost temperature-independent, signaling an effective gap of the theory even though the actual spectrum does not exhibit a gap. On the other hand, the low-temperature free energy of the two-body SYK model is not flat; in fact, it oscillates to arbitrarily low temperature. This indicates a less desirable feature that the entropy of the two-body model is not always positive in the low-temperature phase, which most likely is a consequence of the non-hermiticity.

Anisotropic pressure of magnetized quark matter with anomalous magnetic moment

We investigate magnetic field $(eB)$ dependence of constituent quark mass, the longitudinal and transverse pressure as well as the magnetization and magnetic susceptibility of strongly interacting quark matter. We employ the two-flavor Polyakov Nambu--Jona-Lasinio model with the inclusion of the anomalous magnetic moment (AMM) of the quarks at finite temperature ($T$) and finite quark chemical potential $({\ensuremath{\mu}}_{q})$ capturing different stages of chiral phase transition. We find that the transverse pressure, magnetization, and magnetic susceptibility become highly oscillatory for large values of $eB$ in the chiral symmetry broken phase. However, the oscillations cease to occur at higher values of $T$ and ${\ensuremath{\mu}}_{q}$ when chiral symmetry is (partially) restored and the anisotropic nature of the pressure becomes significant even at smaller values of $eB$. As the inclusion of AMM of the quarks leads to inverse magnetic catalysis of the transition temperature, we observe that the variations of transverse pressure, magnetization, and magnetic susceptibility are significantly modified in the vicinity of the chiral transition temperature. Furthermore, above the chiral transition temperature the magnetic susceptibility is found to remain positive for a wide range of $eB$, indicating a paramagnetic character of the strongly interacting quark matter. Finally, we have also examined the magnetism of strongly interacting matter in the quarkyonic phase. The obtained results could be useful for a magnetohydrodynamic evolution of hot and dense matter created in heavy-ion collisions.

Driving chiral phase transition with ring diagram

We study the dressing of four-quark interaction by the ring diagram, and its feeding back to the quark gap equation, in an effective chiral quark model. Implementing such an in-medium coupling naturally reduces the chiral transition temperature in a class of chiral models, and is capable of generating the inverse magnetic catalysis at finite temperatures. We also demonstrate the important role of confining forces, via the Polyakov loop, in a positive feedback mechanism which reinforces the inverse magnetic catalysis.

Effects of the quark anomalous magnetic moment in the thermodynamical properties of the magnetized two flavor Nambu–Jona-Lasinio model

The influence of the anomalous magnetic moment (AMM) of quarks in the chiral phase transition is studied in the context of the hot and magnetized two flavor Nambu–Jona-Lasinio model. Making use of the mean field approximation (MFA) and the vacuum magnetic regularization (VMR) scheme, we obtain the effective quark masses as a function of the magnetic field for the two usual different sets of AMM. Basic thermodynamical properties are explored and compared with the zero AMM-case, as the pressure, entropy, energy density, interaction measure and the specific heat. The main differences are present in the thermodynamical quantities when one consider a sizable value of AMM, in which an underestimation over the transition region is observed.

Intrinsically chiral ferronematic liquid crystals: An inversion of the helical twist sense at the chiral nematic – Chiral ferronematic phase transition

The ferroelectric nematic phase is a unique example of a polar phase without positional order of the constituent molecules. The properties of the ferronematic phase formed by intrinsically chiral molecules are discussed. Chirality makes the phase structure helical with the similar pitch length in the N* and N F * phases, but with opposite sense. The materials show strong non-linear optical properties. • Intrinsically chiral mesogens forming ferroelectric fluidic nematic, N F *, phase were obtained and studied. • In both, paraelectric and ferroelectric nematic phases, molecular chirality leads to helical structure. • Inversion of helix twist sense was observed at the N*-N F *phase transition. • Giant dielectric permittivity, above 10 4 , was determined in ferroelectric nematic phase. • Strong nonlinear optical properties were confirmed for ferronematic phase. Strongly dipolar mesogenic compounds with a chiral center located in a lateral alkyl chain were synthesized, and shown to form the ferroelectric nematic phase. The presence of molecular chirality induced a helical structure in both the N* and N F * phases, but with opposite helix sense in the two phases. The relaxation frequency of the polar fluctuations is only weakly affected by helical structure, it was found to be slightly lower for the chiral N F * phase than for its achiral, non-branched counterpart with the same lateral chain length.

Quantum simulation of chiral phase transitions

The Nambu–Jona-Lasinio (NJL) model has been widely studied for investigating the chiral phase structure of strongly interacting matter. The study of the thermodynamics of field theories within the framework of Lattice Field Theory is limited by the sign problem, which prevents Monte Carlo evaluation of the functional integral at a finite chemical potential. Using the quantum imaginary time evolution (QITE) algorithm, we construct a quantum simulation for the (1 + 1) dimensional NJL model at finite temperature and finite chemical potential. We observe consistency among digital quantum simulation, exact diagonalization and analytical solution, indicating further applications of quantum computing in simulating QCD thermodynamics.

Light mesons and phase structures in μ B -T-eB and μ I -T-eB spaces * *Supported by the National Natural Science Foundation of China (11775165)

Light mesons are investigated in and spaces using a two-flavor NJL model and used to determine chiral symmetry restoration and the pion superfluid phase transition. In space, during the chiral symmetry restoration process, the mass of the pseudo-Goldstone mode increases, with sudden jumps. At the critical end point, the meson exhibits a sharp but continuous mass increase, with a sudden mass jump at the Mott transition. In the nearby first order chiral phase transition region, we observe two mass jumps, one induced by the Mott transition and the other by the quark mass jump. The mass of the Higgs mode σ first decreases and then increases with chiral symmetry restoration, only showing a jump at the first order chiral phase transition. We plot a chiral phase diagram in terms of the change in quark mass, the Mott transition of the pseudo-Goldstone mode , and the minimum mass of the Higgs mode σ. Owing to explicit breaking of chiral symmetry in the physical case, the chiral restoration phase boundaries on the plane from the order parameter side and meson side are different. The and σ mass jumps will be helpful to the experimental search for the chiral phase diagram and critical end point. On the plane, the competition between the pion superfluid phase transition and chiral symmetry restoration under magnetic fields is studied in terms of the Goldstone mode and pseudo-Goldstone mode . In contrast to the two mass jumps of in the first order chiral phase transition region, the meson displays several mass jumps in the chiral crossover region. At the critical end point, also has sharp but continuous mass change, with a mass jump at the Mott transition. The isospin symmetry is strict, and the pion superfluid phase transition is uniquely determined by the massless Goldstone mode . The separation of chiral restoration and the pion superfluid phase boundaries is enhanced by the external magnetic field.

Toward the chiral phase transition in the Roberge-Weiss plane

We discuss the interplay between chiral and center sector phase transitions that occur in QCD with an imaginary quark chemical potential $\ensuremath{\mu}=i(2n+1)\ensuremath{\pi}T/3$. Based on a finite size scaling analysis in ($2+1$)-flavor QCD using highly improved staggered quark fermions with a physical strange quark mass and a range of light quark masses, we show that the endpoint of the line of first-order Roberge-Weiss (RW) transitions between center sectors is second order for light quark masses ${m}_{l}\ensuremath{\ge}{m}_{s}/320$, and that it belongs to the 3-d, $Z(2)$ universality class. The operator for the chiral condensate behaves like an energylike operator in an effective spin model for the RW phase transition. As a consequence, for any nonzero value of the quark mass, the chiral condensate will have an infinite slope at the RW phase transition temperature, ${T}_{\mathrm{RW}}$. Its fluctuation, the disconnected chiral susceptibility, behaves like the specific heat in $Z(2)$ symmetric models and diverges in the infinite volume limit at the RW phase transition temperature ${T}_{\mathrm{RW}}$ for any nonzero value of the light quark masses. Our analysis suggests the critical temperatures for the RW phase transition and the chiral phase transition coincide in the RW plane. On lattices with temporal extent ${N}_{\ensuremath{\tau}}=4$, we find in the chiral limit ${T}_{\ensuremath{\chi}}={T}_{\mathrm{RW}}=195(1)\text{ }\text{ }\mathrm{MeV}$.

New interpretation of the chiral phase transition: Violation of the trilemma in QCD

We find that the chiral phase transition (chiral crossover) in QCD at physical point is triggered by big imbalance among three fundamental quantities essential for the QCD vacuum structure: susceptibility functions for the chiral symmetry, axial symmetry, and the topological charge. The balance, dobbed the QCD trilemma, is unavoidably violated when one of the magnitudes among them is highly dominated, or suppressed. Based on a three-flavor Nambu-Jona-Lasinio model, we explicitly evaluate the amount of violation of the QCD trilemma at physical point, and show that the violation takes place not only at vacuum, but even in a whole temperature regime including the chiral crossover epoch. This work confirms and extends the suggestion recently reported from lattice QCD with 2 flavors on dominance of the axial and topological susceptibilities left in the chiral susceptibility at high temperatures. It turns out that the imbalance is essentially due to the flavor symmetry violation of the lightest three flavors, and the flavor breaking specifically brings enhancement of the axial anomaly contribution in the chiral order parameter, while the the strength of the axial breaking and the transition rate of the topological charge are fairly insensitive to the flavor symmetry. The violation of QCD trilemma and its flavor dependence can be tested by lattice simulations with 2 + 1 flavors in the future, and would also give a new guiding principle to explore the flavor dependence of the chiral phase transition, such as the Columbia plot, including possible extension with external fields.

Melting of crystals of polarization vortices and chiral phase transitions in oxide superlattices

We study the equilibrium arrangements of polarization vortices in (PbTiO$_3$)$_n$/(SrTiO$_3$)$_n$ superlattices by means of second-principles simulations. We find that, at low temperatures, polarization vortices organize in a regular arrangement in which clockwise and counter-clockwise vortices alternate positions, leading to a crystal-like structure with well defined handedness. This chiral crystal melts at a critical temperature $T_\mathrm{M}$ into a chiral liquid, where long-range order is lost but handedness is preserved. At even higher temperatures, $T_\mathrm{C}$, a second phase transition occurs, at which the chiral liquid of polarization vortices loses its handedness. Both phase transitions can be readily identified by the adequate choices of order parameters.

Nonextensive effects on QCD chiral phase transition with a chiral chemical potential* *Supported by the National Natural Science Foundation of China (12005192) and the Project funded by China Postdoctoral Science Foundation (2020M672255, 2020TQ0287)

In this study, we investigate the QCD chiral phase diagram in the presence of a chiral chemical potential based on nonextensive statistical mechanics. A feature of this new statistic is a dimensionless nonextensivity parameter q, which summarizes all possible effects violating the assumptions of Boltzmann-Gibbs (BG) statistics (when , it returns to the BG case). Within the nonextensive Polyakov-Nambu-Jona-Lasinio model, we find that as increases, the critical end point (CEP) in the plane continues to in the plane, and nonextensive effects have a significant impact on the evolution from the CEP to . Generally, with an increase in q, both the CEP and move in the direction of a lower temperature T and larger chemical potential μ (). In addition, we find that chiral charge density generally increases with T, μ, , and q. Our study may provide useful hints about lattice QCD and relativistic heavy-ion collision experiments.

QCD phase diagram in a finite volume in the PNJL model

Abstract In this work, we study the quantum chromodynamics phase diagram at finite temperature and non-zero chemical potential in the framework of the SU(2) flavor of the Polyakov–Nambu – Jona–Lasinio model (PNJL). Applying multiple reflection expansion to cubic and spherical finite volumes of different sizes and boundary conditions, the chiral phase transition and deconfinement of strongly interacting matter are analyzed. We give special attention to find and locate the critical endpoint and locating the critical endpoint, if it exists, as a function of the volume size and its shape, and its dependence of chemical potential and temperature.

Second-order chiral phase transition in three-flavor quantum chromodynamics?

We calculate the renormalization group flows of all perturbatively renormalizable interactions in the three-dimensional Ginzburg-Landau potential for the chiral phase transition of three-flavor quantum chromodynamics. On the contrary to the common belief we find a fixed point in the system that is able to describe a second-order phase transition in the infrared. This shows that long-standing assumptions on the transition order might be false. If the transition is indeed of second order, our results may hint that the axial $U(1)$ symmetry restores at the transition temperature.

Effects of a Finite Volume in the Phase Structure of QCD

Working in the SU(2) flavor version of the NJL model, we study the effect of taking a finite system volume on a strongly interacting system of quarks, and, in particular, the location of the chiral phase transition and the CEP. We consider two shapes for the volume, spherical and cubic regions with different sizes and different boundary conditions. To analyze the QCD phase diagram, we use a novel criterion to study the crossover zone. A comparison between the results obtained from the two different shapes and several boundary conditions is carried out. We use the method of Multiple Reflection Expansion to determine the density of states and three kinds of boundary conditions over the cubic shape. These boundary conditions are: periodic, anti-periodic and stationary boundary conditions on the quark fields.