Holographic superuidity in imbalanced mixtures

It is widely accepted that a new phase structure will emerge in nuclear matter at high temperature and density. In this article the QCD (quantum chromodynamic) phase transitions are briefly reviewed from both theoretical and experimental aspects. Basing on the general principle of QCD and modern phase transition theory, we analyze potential phases in the strong interacting nuclear matter. The phase structure could be understood intuitively through the breaking and restoration of fundamental symmetries of QCD. In the space spanned by the temperature, baryon and isospin chemical potential there are different phases corresponding to three important symmetries, i.e. the color, chiral and isospin. At low temperature and density, the color and isospin symmetries are preserved, while the chiral one is spontaneously broken. At high temperature or density, the color or isospin or both of them would be broken as the chiral restoration. In order to explore the detailed structure of the phase diagram various theoretical approaches of studying the transitions are introduced, such as lattice QCD, mean field calculation basing on effective models, functional renormalization group and Dyson-Schwinger equation. In experiments there are two kinds of physics systems to realize conditions of QCD phase transitions: the relativistic heavy ion collisions and compact stars. Nuclear collision is the only way to approach hot QCD in laboratories on the earth. We focus on some robust probes to the quark gluon plasma formed in the early stage of the collisions. There are generally two types of the traditional signals which are focusing on the profile of the fire ball and the internal interaction of it respectively. For the first case we introduce collective flows as observables for the shape of fire ball. While for the second we review the jet quenching and the heavy flavor suppression. In the hot fire ball the classical transport theory should be modified by including quantum effects induced by the chiral restoration. This novel transport phenomenon of QCD at high temperature is named by the chiral anomalous transport. On the phase transitions at high density, we review the recent progress on color superconductivity and pion superfluidity. Color superconductivity is formed at high baryon chemical potential when quarks pair with each other into diquarks and condense. While pion superfluidity would emerge at high isospin chemical potential with pion condensate. Model studies suggest these states are able to exist in the core of compact star. By modifying the structure of them, such as the mass-radius relation, these states are expected to be identified by astronomical observation at higher precision. Currently dense systems are difficult to produce at main facilities of the world, such as RHIC (relativistic heavy ion collider) and LHC (large hadron collider) because of the designed high energy scale of the accelerators. Therefore it is a critical need for the facilities which could cover the low and medium energy region where the potential critical point and various phase structures would locate. Considering the running and constructing heavy ion facilities, the CSR (cooler-storage-ring) in Lanzhou and the high intensity HIAF (heavy-ion accelerator facility) in Huizhou, the properties of the new QCD phases and their realizations in nuclear collisions will be the new frontier of nuclear physics in China.

The phase transition in the polarization switching (PS) of vertical-cavity surface-emitting lasers (VCSELs) was recently reported to be a second-order phase transition (SOPT). However, some features of this phase transition indicate that the VCSEL’s PS (VPS) is different from the traditional SOPTs. Most of the phase transition investigations of the laser employ the laser’s intensity as the order parameter. In Landau’s paradigm, that parameter evolutes from zero to non-zero values, or vice versa, during SOPTs, corresponding to a transition between a disordered phase and an ordered phase. Nevertheless, in the VPS, the laser’s intensity remains constant before and after the PS, revealing an order-to-order transition. Furthermore, the laser’s transverse modes cannot transfer to each other through continuous deformations in geometry. That feature attributes a topological characteristic to the laser’s transverse modes. The spatial coherence of the laser also implements a globally geometric characteristic to the laser’s output. Accordingly, there are two similarities between the VPS and quantum phase transitions (QPTs) with topological order. First, both of them belong to the orderto- order phase transitions. Second, in both transitions, two ground states are orthogonal, and are degenerate at the critical point. This paper investigated the analogy between the QPT with topological order and the VPS, exploring that the VPS has a potential to simulate the QPTs of other physical systems.

The general issue of large ${N}_{c}$ QCD at nonzero chemical potential is considered with a focus on understanding the difference between large ${N}_{c}$ QCD with an isospin chemical potential and large ${N}_{c}$ QCD with a baryon chemical potential. A simple diagrammatic analysis analogous to 't Hooft's analysis at $\ensuremath{\mu}=0$ implies that the free energy with a given baryon chemical potential is equal to the free energy with an isospin chemical potential of the same value plus $1/{N}_{c}$ corrections. Phenomenologically, these two systems behave quite differently. A scenario to explain this difference in light of the diagrammatic analysis is explored. This scenario is based on a phase transition associated with pion condensation when the isospin chemical potential exceeds ${m}_{\ensuremath{\pi}}/2$; associated with this transition there is breakdown of the $1/{N}_{c}$ expansion---in the pion condensed phase there is a distinct $1/{N}_{c}$ expansion including a larger set of diagrams. While this scenario is natural, there are a number of theoretical issues which at least superficially challenge it. Most of these can be accommodated. However, the behavior of quenched QCD which raises a number of apparently analogous issues cannot be easily understood completely in terms of an analogous scenario. Thus, the overall issue remains open.

Topological states of matter are characterized by global topological invariants which change their value across a topological quantum phase transition. It is commonly assumed that the transition between topologically distinct noninteracting gapped phases of fermions is necessarily accompanied by the closing of the band gap as long as the symmetries of the system are maintained. We show that such a quantum phase transition is possible without closing the gap in the case of a three-dimensional topological band insulator. We demonstrate this by calculating the free energy of the minimal model for a topological insulator, the Bernevig-Hughes-Zhang model, and show that as the band curvature continuously varies, a jump between the band gap minima corresponding to the topologically trivial and nontrivial insulators occurs. Therefore, this first order phase transition is a generic feature of three-dimensional topological band insulators. For a certain parameter range we predict a re-entrant topological phase transition. We discuss our findings in connection with the recent experimental observation of a discontinuous topological phase transition in a family of topological crystalline insulators.

Chapter 13 - Applications of Thermodynamics to Phase Equilibria Studies of Pure Substances

We revisit two-color, two-flavor chiral perturbation theory at finite isospin and baryon density. We investigate the phase diagram obtained varying the isospin and the baryon chemical potentials, focusing on the phase transition occurring when the two chemical potentials are equal and exceed the pion mass (which is degenerate with the diquark mass). In this case, there is a change in the order parameter of the theory that does not lend itself to the standard picture of first order transitions. We explore this phase transition both within a Ginzburg-Landau framework valid in a limited parameter space and then by inspecting the full chiral Lagrangian in all the accessible parameter space. Across the phase transition between the two broken phases the order parameter becomes an SU(2) doublet, with the ground state fixing the expectation value of the sum of the magnitude squared of the pion and the diquark fields. Furthermore, we find that the Lagrangian at equal chemical potentials is invariant under global SU(2) transformations and construct the effective Lagrangian of the three Goldstone degrees of freedom by integrating out the radial fluctuations.

This chapter is devoted to a discussion of quantum phase transitions in regularly alternating spin-1/2 Ising chain in a transverse field. After recalling some generally-known topics of the classical (temperature-driven) phase transition theory and some basic concepts of the quantum phase transition theory I pass to the statistical mechanics calculations for a one-dimensional spin-1/2 Ising model in a transverse field, which is the simplest possible system exhibiting the continuous quantum phase transition. The essential tool for these calculations is the Jordan-Wigner fermionization. The latter technique being completed by the continued fraction approach permits to obtain analytically the thermodynamic quantities for a `slightly complicated' model in which the intersite exchange interactions and on-site fields vary regularly along a chain. Rigorous analytical results for the ground-state and thermodynamic quantities, as well as exact numerical data for the spin correlations computed for long chains (up to a few thousand sites) demonstrate how the regularly alternating bonds/fields effect the quantum phase transition. I discuss in detail the case of period 2, swiftly sketch the case of period 3 and finally summarize emphasizing the effects of periodically modulated Hamiltonian parameters on quantum phase transitions in the transverse Ising chain and in some related models.

Dicke model describes a collective interaction between the two-level atoms and the light cavity and has been predicted to show a peculiar quantum phase transition, which is a second-order phase transition from a normal phase (in a weak-coupling strength) to a superradiant phase (in a strong-coupling strength). The model plays an important role in illustrating the quantum ground-state properties of many-body macroscopic quantum states. In the experiment, Dicke quantum phase transition in an open system could be formed by a Bose-Einstein condensate coupled to a high-finesse optical cavity. This experiment on the Bose-Einstein condensate trapped in the optical cavity have opened new frontiers, which could combine the cold atoms with quantum optics and makes it possible to enter into the strongly coupled regime of cavity quantum electrodynamics. In strong coupled regime, the atoms exchange the photons many times before spontaneous emission and cavity losses set in. It has become a hot research topic in recent years and plays an important role in many fields of modern physics, such as condensed matter physics, nuclear physics, etc. It can be applied to the manipulation of the geometric phase and entanglement in quantum information and computing. Quantum phase transition has been widely studied for the Dicke model as a typical example. Many different research methods about the mean-field approximation have been used to analyze the ground state properties of the Dicke model. In this paper, we study the ground state properties of two-component Bose-Einstein condensate in a single-mode cavity. Meanwhile, the associated quantum phase transition is described by the spin-coherent-state variational method, whose advantage is that the ground state energy and wave function can be obtained without the thermodynamic limit. By taking the average in the boson coherent state, we obtain an equivalent effective pesudospin Hamiltonian, which will be diagonalized by using the spin coherent state. Finally, we can obtain the energy functional, which is the basics of the variation to obtain the numerical solution of photon number and the expression of the atomic number and the ground state energy. This paper presents a rich phase diagram, which can be manipulated by changing the atom-field coupling imbalance between two components and the atom-field frequency detuning. While in the single-mode Dicke model there exist only the normal phase and the superradiation phase. When the frequency of one component atom is zero or the frequency of the two component atoms are equal in optical cavity, the system returns to the standard Dicke model, in which there occurs the second-order phase transition from the normal phase to the superradiant phase by adjusting the atom-field coupling. In conclusion, we discover that the stimulated radiation comes from the collective state of atomic population inversion, which does not exist in the single-mode Dicke model. Meanwhile, the new stimulated-radiation state S and S, which can only be produced by one component of the atom, are observed in the two-component Bose-Einstein condensates in the single-mode optical cavity. By adjusting the atom-field coupling imbalance and the atom-field frequency detuning (the blue or red detuning), the order of the superradiation state and the stimulated-radiation states can be exchanged between the two components of the atom.

We study the ground states of low-density hadronic matter and high-density color-flavor locked color superconducting phase in three-flavor QCD at finite baryon chemical potential under rotation. We find that, in both cases under sufficiently fast rotation, the combination of the rotation-induced topological term for the η′ meson and the QCD anomaly leads to an inhomogeneous condensate of the η′ meson, known as the chiral soliton lattice (CSL). We find that, when baryon chemical potential is much larger than isospin chemical potential, the critical angular velocity for the realization of the η′ CSL is much smaller than that for the π0 CSL found previously. We also argue that the η′ CSL states in flavor-symmetric QCD at low density and high density should be continuously connected, extending the quark-hadron continuity conjecture in the presence of the rotation.

We investigate the interplay of the Polyakov loop and the quark–antiquark condensates in scalar and pseudoscalar channels in the extended-Polyakov–NJL (PNJL) model at finite temperature and isospin chemical potential without baryon chemical potential. We discuss the effect of the dynamical parameter ϕ and thermodynamical parameter μI on the chiral property especially. The meson's collective excitation modes are calculated and compared with the NJL model's results. The T–μI phase diagram is obtained. It contains four regions, including the meson gas, two-flavor quark gas, the BEC superfluidity and BCS superfluidity.

The color superconductivity was studied with an adaptation of the Nambu and Jona-Lasinio model (NJL). This one was coupled to a Polyakov loop, to form the PNJL model. A $\mu$-dependent Polyakov loop potential was considered. An objective of the presented works was to describe the analytical calculations required to establish the equations to be solved, in all of the treated cases. They concerned the normal quark phase, the 2-flavor color-superconducting and the color-flavor-locked phases, in an SU(3)f X SU(3)c description. The calculations were performed according to the temperature T, the chemical potentials $\mu_{f}$ or according to the densities $\rho_{f}$, with or without the isospin symmetry. Among the obtained results, it was found that at low T, the restoration of the chiral symmetry, the deconfinement transition and the transition between the normal quark and 2-flavor color-superconducting phases occur via first order phase transitions at the same chemical potential. Moreover, an sSC phase was identified in the $\rho_{q}$, $\rho_{s}$ plane.

Superconductivity from gauge/gravity duality with flavor

Critical scattering at a marginally first order phase transition in two dimensions: the order-disorder transition of O/Ni(111)-p(2 × 2)

Hybrid hadron-quark equations of state that give rise a third family of stable compact stars have been shown to be compatible with the LIGO-Virgo event GW170817. Stable configurations in the third family are called hybrid hadron-quark stars. The equilibrium stable hybrid hadron-quark star branch is separated by the stable neutron star branch with a branch of unstable hybrid hadron-quark stars. The end-state of these unstable configurations has not been studied, yet, and it could have implications for the formation and existence of twin stars -- hybrid stars with the same mass as neutron stars but different radii. We modify existing hybrid hadron-quark equations of state with a first-order phase transition in order to guarantee a well-posed initial value problem of the equations of general relativistic hydrodynamics, and study the dynamics of non-rotating or rotating unstable twin stars via 3-dimensional simulations in full general relativity. We find that unstable twin stars naturally migrate toward the hadronic branch. Before settling into the hadronic regime, these stars undergo (quasi)radial oscillations on a dynamical timescale while the core bounces between the two phases. Our study suggests that it may be difficult to form stable twin stars if the phase transition is sustained over a large jump in energy density, and hence it may be more likely that astrophysical hybrid hadron-quark stars have masses above the twin star regime. We also study the minimum-mass instability for hybrid stars, and find that these configurations do not explode, unlike the minimum-mass instability for neutron stars. Additionally, our results suggest that oscillations between the two Quantum Chromodynamic phases could provide gravitational wave signals associated with such phase transitions in core-collapse supernovae and white dwarf-neutron star mergers.

We consider the phase diagram of twisted mass Wilson fermions of two-flavor\nQCD in the parameter space of the quark mass, the isospin chemical potential,\nthe twist angle and the lattice spacing. This work extends earlier studies in\nthe continuum and those at zero chemical potential. We evaluate the phase\ndiagram as well as the spectrum of the (pseudo-)Goldstone bosons using the\nchiral Lagrangian for twisted mass Wilson fermions at non-zero isospin chemical\npotential. The phases are obtained from a mean field analysis. At zero twist\nangle we find that already an infinitesimal isospin chemical potential destroys\nthe Aoki phase. The reason is that in this phase we have massless Goldstone\nbosons with a non-zero isospin charge. At finite twist angle only two different\nphases are present, one phase which is continuously connected to the Bose\ncondensed phase at non-zero chemical potential and another phase which is\ncontinuously connected to the normal phase. For either zero or maximal twist\nthe phase diagram is more complicated as the saddle point equations allow for\nmore solutions.\n