Finite Chemical Potential Research Articles

Holographic Einstein ring of a charged AdS black hole

Taking into account that the real quantum materials are engineered generically at a finite chemical potential, we investigate the Einstein ring structure for the lensed response of the complex scalar field as a probe wave on the charged AdS black hole in the context of AdS/CFT. On the one hand, we find that the resulting Einstein ring radius has no variation with the chemical potential, which is similar to the behavior for the weakly interacting quantum system. On the other hand, not only can such a ring exist well within the screen, but also the temperature dependence of its radius exhibits a distinct feature in the sense that it displays an appreciable increase at low temperatures while the ring keeps unchanged right at the edge of the screen for the weakly interacting system. Note that such a Einstein ring emerges in the large frequencies and can be well captured by the photon sphere away from the black hole horizon in the geometric optics approximation, thus such a distinct feature may be regarded as a universal behavior associated with the high energy modes of the strongly coupled system which has a gravity dual.

Three-quark potential at finite temperature and chemical potential* *Supported by the NSFC (12175100, 11975132), the Research Foundation of Education Bureau of Hunan Province, China (21B0402, 20C1594) and the Natural Science Foundation of Hunan Province of China (2022JJ40344)

Using gauge/gravity duality, we study the potential energy and the melting of triply heavy baryon at finite temperature and chemical potential in this paper. First, we calculate the three-quark potential and compare the results with quark-antiquark potential. With the increase of temperature and chemical potential, the potential energy will decrease at large distances. It is found that the three-quark potential will have an endpoint at high temperature and/or large chemical potential, which means triply heavy baryons will melt at enough high temperature and/or large chemical potential. We also discuss screening distance which can be extracted from the three-quark potential. At last, we draw the melting diagram of triply heavy baryons in the plane.

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.

Magnonic spin Joule heating and rectification effects

Nonlinear devices, such as transistors, enable contemporary computing technologies. We theoretically investigate nonlinear effects, bearing a high fundamental scientific and technical relevance, in magnonics with emphasis on superconductor-ferromagnet hybrids. Accounting for finite magnon chemical potential, we theoretically demonstrate magnonic spin-Joule heating, the spin analogue of conventional electronic Joule heating. Besides suggesting a key contribution to magnonic heat transport in a broad range of devices, it provides insights into the thermal physics of non-conserved bosonic excitations. Considering a spin-split superconductor self-consistently, we demonstrate its interface with a ferromagnetic insulator to harbor large tunability of spin and thermal conductances. We further demonstrate hysteretic rectification I-V characteristics in this hybrid, where the hysteresis results from the superconducting state bistability.

Dual QCD thermodynamics at finite temperature and chemical potential

A Dual QCD formulation for [Formula: see text] color gauge has been developed in terms of dual gauge potentials, building on our previously published study for the [Formula: see text] case with zero bario-chemical potential [H. C. Chandola, G. Punetha and H. Dehnen, Nucl. Phys. A 945, 226 (2016).] and taking into account the local as well as topological structure of the color gauge group into its dynamics. For the purpose of examining the nonperturbative characteristics of QCD, the dynamical configuration of the resulting dual QCD vacuum and its flux tube configuration have been examined. The thermal behavior of the nonperturbative QCD vacuum has been investigated for exploring the dynamics of quark-hadron phase transition at finite chemical potential. Related thermodynamic quantities and equation of state (EoS) to characterize quark matter have also been discussed within the framework of dual QCD-based hadronic bag which guarantees the critical parameters and the associated critical points for quark-hadron phase transition. These thermodynamic quantities are expected to play important roles in understanding the order of quark-hadron phase transition and are likely to predict the features of a first-order quark-hadron phase transition for finite chemical potential. Moreover, we have investigated the bulk properties of quark matter by constructing the free energy change and the associated surface tension for quark-hadron phase transition. For consistency and compatibility check, we have also compared our results with state-of-the-art three-loop Hard Thermal Loop perturbative results and available lattice QCD results and in the process found reasonable agreements.

Charmonium dissociation at high baryon chemical potential

We study the charmonium dissociation in the hot medium with finite baryon chemical potential $\mu_B$. Charmonium bound states are dissociated in the medium by the color screening effect and the random scatterings with thermal partons, which are included in the real and imaginary parts of the potential respectively. $J/\psi$ fraction in the $c\bar c$ pair defined to be the quantum overlap between the wave package and the wave function of $J/\psi$ eigenstate decreases with time due to the complex potentials. When $\mu_B$ is large compared with the medium temperature, the Deybe mass is increased evidently. We consider $\mu_B$-dependent Deybe mass in both real and imaginary parts of the potential to calculate the $J/\psi$ survival probability in the static medium and the Bjorken medium. $J/\psi$ survival probability is reduced evidently by the $\mu_B$ effect at low temperatures available in the medium produced in Beam Energy Scan experiments, while this effect becomes not apparent at high temperatures.

Integrating out beyond tree level and relativistic superfluids

We revisit certain subtleties of renormalization that arise when one derives a low-energy effective action by integrating out the heavy fields of a more complete theory. Usually these subtleties are circumvented by matching some physical observables, such as scattering amplitudes, but a more involved procedure is required if one is interested in deriving the effective theory to all orders in the light fields (but still to fixed order in the derivative expansion). As a concrete example, we study the U(1) Goldstone low-energy effective theory that describes the spontaneously broken phase of a ϕ4 theory for a complex scalar. Working to lowest order in the derivative expansion, but to all orders in the Goldstones, we integrate out the radial mode at one loop and express the low-energy effective action in terms of the renormalized couplings of the UV completion. This yields the one-loop equation of state for the superfluid phase of (complex) ϕ4. We perform the same analysis for a renormalizable scalar SO(N) theory at finite chemical potential, integrating out the gapped Goldstones as well, and confirm that the effective theory for the gapless Goldstone exhibits no obvious sign of the original SO(N) symmetry.

Momentum transport properties of a hot and dense QCD matter in a weak magnetic field

We have studied the momentum transport properties of a hot and dense QCD matter in the presence of weak magnetic field by determining the shear (eta ) and bulk (zeta ) viscosities in the relaxation time approximation of kinetic theory. The dependence of eta and zeta on the temperature has been explored in the presence of weak magnetic field (B-field) and finite chemical potential (mu ). It is observed that both shear and bulk viscosities get decreased in the presence of a weak magnetic field, whereas the finite chemical potential increases these viscosities, specifically at low temperatures. This study is important to understand the sound attenuation through the Prandtl number (Pr), the nature of the flow through the Reynolds number (Re), the fluidity and location of transition point of the matter through the ratios eta /s and zeta /s (s is the entropy density), respectively. The Prandtl number is observed to increase in the weak magnetic field, whereas the presence of a finite chemical potential reduces its magnitude as compared to the scenario of absence of B-field and mu . However, Pr still remains larger than unity, indicating that the energy dissipation due to the sound attenuation is mostly governed by the momentum diffusion. It is noticed that the weak magnetic field makes the Reynolds number larger, whereas the chemical potential makes it smaller than that in the absence of B-field and mu . We have observed that the ratio eta /s decreases in the weak magnetic field regime, whereas the finite chemical potential increases its value, but the ratio zeta /s is found to decrease in the presence of weak magnetic field as well as finite chemical potential.

Chiral gravitational waves from thermalized neutrinos in the early Universe

We investigate polarized gravitational waves generated by chiral fermions in the early Universe. In particular, we focus on the contribution from left-handed neutrinos in thermal equilibrium with finite temperature and chemical potential in the radiation dominated era. We compute the correlation functions of gravitational fields pertinent to the Stokes parameter V characterizing the circular polarization of gravitational waves in the Minkowski and expanding spacetime backgrounds. In the expanding universe, we find that the thermalized neutrinos induce a non-vanishing V linear to the neutrino degeneracy parameter and wavenumber of gravitational waves in the long wavelength region. While the magnitude of the gravitational waves generated by thermal neutrinos is too small to be detectable by current and planned third generation gravitational wave detectors, their observations by future generation detectors for ultra-high frequency regimes could provide information on the neutrino degeneracy parameter in the early Universe.

Persistent Homology Analysis for Dense QCD Effective Model with Heavy Quarks

The isospin chemical potential region is known as the sign-problem-free region of quantum chromodynamics (QCD). In this paper, we introduce the isospin chemical potential to the three-dimensional three-state Potts model to mimic dense QCD; e.g., the QCD effective model with heavy quarks at finite density. We call it the QCD-like Potts model. The QCD-like Potts model does not have a sign problem, but we expect it to share some properties with QCD. Since we can obtain the non-approximated Potts spin configuration at finite isospin chemical potential, where the simple Metropolis algorithm can work, we perform the persistent homology analysis toward exploring the dense spatial structure of QCD. We show that the averaged birth-death ratio has the same information with the Polyakov loop, but the maximum birth-death ratio has additional information near the phase transition where the birth-death ratio means the ratio of the creation time of a hole and its vanishing time based on the persistent homology.

Higgs/amplitude mode dynamics from holography

Second order phase transitions are universally driven by an order parameter which becomes trivial at the critical point. At the same time, collective excitations which involve the amplitude of the order parameter develop a gap which smoothly closes to zero at criticality. We develop analytical techniques to study this “Higgs” mode in holographic systems which undergo a continuous phase transition at finite temperature and chemical potential. This allows us to study the linear response of the system at energy scales of the order of the gap. We express the Green’s functions of scalar operators in terms of thermodynamic quantities and a single transport coefficient which we fix in terms of black hole horizon data.

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.

Inverse catalysis effect of the quark anomalous magnetic moment to chiral restoration and deconfinement phase transitions at finite baryon chemical potential

The effect of quark anomalous magnetic moment (AMM) to chiral restoration and deconfinement phase transitions in baryon chemical potential-temperature $(\mu_B-T)$ plane under magnetic fields is investigated in frame of a Pauli-Villars regularized PNJL model. It's found that the quark AMM plays the role of inverse catalysis to the phase transitions, and large quark AMM will change the magnetic catalysis phenomena of phase transitions to inverse magnetic catalysis in the whole $\mu_B-T$ plane. For a fixed magnetic field, the critical temperature $T_c$ and critical baryon chemical potential $\mu_B^c$ decreases with quark AMM. The stronger the magnetic field is, the inverse catalysis effect of AMM becomes more important. For a small AMM $\kappa=\kappa_1$, it shows the magnetic catalysis effect for critical temperature $T_c$ at vanishing $\mu_B$ with increasing magnetic field, and (inverse) magnetic catalysis effect for critical baryon chemical potential $\mu_B^c$ at vanishing $T$ under (weak) strong magnetic field. At finite $T$ and $\mu_B$, there exist some crossings of the phase transition lines with different magnetic field. For a large AMM $\kappa=\kappa_2$, we obtain the inverse magnetic catalysis effect in the whole $\mu_B-T$ plane, and no crossings of phase transition lines happen.

New way to resum the lattice QCD Taylor series equation of state at finite chemical potential

Taylor expansion of the thermodynamic potential in powers of the (baryo)chemical potential ${\ensuremath{\mu}}_{B}$ is a well-known method to bypass the sign problem of lattice QCD. Due to the difficulty in calculating the higher order Taylor coefficients, various alternative expansion schemes as well as resummation techniques have been suggested to extend the Taylor series to larger values of ${\ensuremath{\mu}}_{B}$. Recently, a way to resum the contribution of the first $N$ charge density correlation functions ${D}_{1},\dots{},{D}_{N}$ to the Taylor series to all orders in ${\ensuremath{\mu}}_{B}$ was proposed in [Phys. Rev. Lett. 128, 022001 (2022)]. The resummation takes the form of an exponential factor. Since the correlation functions are calculated stochastically, the exponential factor contains a bias which can be significant for large $N$ and ${\ensuremath{\mu}}_{B}$. In this paper, we present a new method to calculate the QCD equation of state based on the well-known cumulant expansion from statistics. By truncating the expansion at a maximum order $M$, we end up with only finite products of the correlation functions which can be evaluated in an unbiased manner. Although our formalism is also applicable for ${\ensuremath{\mu}}_{B}\ensuremath{\ne}0$, here we present it for the simpler case of a finite isospin chemical potential ${\ensuremath{\mu}}_{I}$ for which there is no sign problem. We present and compare results for the pressure and the isospin density obtained using Taylor expansion, exponential resummation and cumulant expansion, and provide evidence that the absence of bias in the latter actually improves the convergence.

Higher-derivative holography with a chemical potential

We carry out an extensive study of the holographic aspects of any-dimensional higher-derivative Einstein-Maxwell theories in a fully analytic and non-perturbative fashion. We achieve this by introducing the d-dimensional version of Electromagnetic Quasitopological gravities: higher-derivative theories of gravity and electromagnetism that propagate no additional degrees of freedom and that allow one to study charged black hole solutions analytically. These theories contain non-minimal couplings, that in the holographic context give rise to a modified 〈JJ〉 correlator as well as to a general 〈TJJ〉 structure whose coefficients we compute. We constrain the couplings of the theory by imposing CFT unitarity and positivity of energy (which we show to be equivalent to causality in the bulk) as well as positive-entropy bounds from the weak gravity conjecture. The thermodynamic properties of the dual plasma at finite chemical potential are studied in detail, and we find that exotic zeroth-order phase transitions may appear, but that many of them are ruled out by the physical constraints. We further compute the shear viscosity to entropy density ratio, and we show that it can be taken to zero while respecting all the constraints, providing that the chemical potential is large enough. We also obtain the charged Rényi entropies and we observe that the chemical potential always increases the amount of entanglement and that the usual properties of Rényi entropies are preserved if the physical constraints are met. Finally, we compute the scaling dimension and magnetic response of twist operators and we provide a holographic derivation of the universal relations between the expansion of these quantities and the coefficients of 〈JJ〉 and 〈TJJ〉.

Chirality dependence in charge and heat transport in thermal QCD

As the strength of the magnetic field ($B$) becomes weak, novel phenomena, similar to the Hall effect in condensed matter physics, emerges both in charge and heat transport in a thermal QCD medium with a finite quark chemical potential ($\ensuremath{\mu}$). So we have calculated the transport coefficients in a kinetic theory within a quasiparticle framework, wherein we compute the effective mass of quarks for the aforesaid medium in a weak magnetic field (B) limit ($|eB|\ensuremath{\ll}{T}^{2}$; $T$ is temperature) by the perturbative thermal QCD up to one loop, which depends on $T$ and $B$ differently to left-handed (L) and right-handed (R) chiral modes of quarks, lifting the prevalent degeneracy in L and R modes in strong magnetic field limit ($|eB|\ensuremath{\gg}{T}^{2}$). Another implication of weak $B$ is that the transport coefficients assume a tensorial structure: The diagonal elements represent the usual (electrical and thermal) conductivities (${\ensuremath{\sigma}}_{\text{Ohmic}}$ and ${\ensuremath{\kappa}}_{0}$ as the coefficients of charge and heat transport, respectively) and the off-diagonal elements denote their Hall counterparts (${\ensuremath{\sigma}}_{\text{Hall}}$ and ${\ensuremath{\kappa}}_{1}$, respectively). It is found in charge transport that the magnetic field acts on L and R modes of the Ohmic part of electrical conductivity in an opposite manner, viz. ${\ensuremath{\sigma}}_{\text{Ohmic}}$ for L mode decreases and for R mode, increases with $B$ whereas the Hall-part ${\ensuremath{\sigma}}_{\text{Hall}}$ for both L and R modes always increases with $B$. In heat transport too, the effect of the magnetic field on the usual thermal conductivity (${\ensuremath{\kappa}}_{0}$) and Hall-type coefficient (${\ensuremath{\kappa}}_{1}$) in both modes is identical to the above-mentioned effect of $B$ on charge transport coefficients. We have then derived some coefficients from the above transport coefficients, namely Knudsen number ($\mathrm{\ensuremath{\Omega}}$ is the ratio of the mean-free path to the length scale of the system) and Lorenz number in Wiedemann-Franz law. The effect of $B$ on $\mathrm{\ensuremath{\Omega}}$ either with ${\ensuremath{\kappa}}_{0}$ or with ${\ensuremath{\kappa}}_{1}$ for both modes is identical to the behavior of ${\ensuremath{\kappa}}_{0}$ and ${\ensuremath{\kappa}}_{1}$ with $B$. The value of $\mathrm{\ensuremath{\Omega}}$ is always less than unity for the entire temperature range, validating our calculations. Lorenz number (${\ensuremath{\kappa}}_{0}/{\ensuremath{\sigma}}_{\text{Ohmic}}T$) and Hall-Lorenz number (${\ensuremath{\kappa}}_{1}/{\ensuremath{\sigma}}_{\text{Hall}}T$) for L mode increases and for R mode decreases with magnetic field. It also does not remain constant with temperature hence violating the Wiedemann-Franz law.

Asymptotic critical behavior of holographic superconductor phase transition — the spectrum of excited states becomes continuous at T = 0

Within the framework of AdS/CFT duality, excited states of the conformal field living at the global AdS boundary of a four-dimensional spacetime Einstein gravity are investigated analytically in the probe limit where the field equations are linearized. At asymptotically large values, the threshold chemical potential for the appearance of excited condensate states are discrete, equal spacing, with the gap approaches zero logarithmically in the limit T → 0. Remarkably, numerical results show that, this behavior applies even for states as low as for the first or the second excited state of the condensate. This is especially significant on the liquid side of the black hole van der Waals-like phase transition (small or zero topological charge) where there seems to be no gap between the ground state and the first excited state at zero temperature. We postulate that, at the exact limit T = 0 where the gap is zero, the spectrum of threshold chemical potentials becomes continuous, all excited states of the condensate are activated above a finite chemical potential, suggesting a new quantum phase transition as a function of the chemical potential. Previous studies have largely missed this continuous spectrum of excited states in the T → 0 limit. This fact should be taken into account carefully in AdS/CFT duality studies.

Running coupling constant at finite chemical potential and magnetic field from holography * *X.C. is supported by the Research Foundation of Education Bureau of Hunan Province, China (21B0402). L.Z. is supported in part by the Fundamental Research Funds for the Central Universities. D.H. is in part supported by the National Natural Science Foundation of China (11735007, 11890711)

According to gauge/gravity duality, we use an Einstein-Maxwell-dilaton (EMD) model to study the running coupling constant at finite chemical potential and magnetic field. First, we calculate the effect of temperature on the running coupling constant and find the results are qualitatively consistent with lattice guage theory. Subsequently, we calculate the effect of chemical potential and magnetic field on running coupling. It is found that the chemical potential and magnetic field both suppress the running coupling constant. However, the effect of the magnetic field is slightly larger than that of chemical potential for a fixed temperature. Compared with the confinement phase, the magnetic field has a large influence on the running coupling in the deconfinement phase.

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.

Tensor renormalization group study of (3+1)-dimensional ℤ2 gauge-Higgs model at finite density

We investigate the critical endpoints of the (3+1)-dimensional ℤ2 gauge-Higgs model at finite density together with the (2+1)-dimensional one at zero density as a benchmark using the tensor renormalization group method. We focus on the phase transition between the Higgs phase and the confinement phase at finite chemical potential along the critical end line. In the (2+1)-dimensional model, the resulting endpoint is consistent with a recent numerical estimate by the Monte Carlo simulation. In the (3+1)-dimensional case, however, the location of the critical endpoint shows disagreement with the known estimates by the mean-field approximation and the Monte Carlo studies. This is the first application of the tensor renormalization group method to a four-dimensional lattice gauge theory and a key stepping stone toward the future investigation of the phase structure of the finite density QCD.