arXiv subjects

Muneto Nitta

Publications and source records attributed to Muneto Nitta.

At least 127 records · Page 7Linked to original sources

arXiv2020

Critical endpoint and universality class of neutron $^3P_2$ superfluids in neutron stars

We study the thermodynamics and critical behavior of neutron $^3P_2$ superfluids in the inner cores of neutron stars. $^3P_2$ superfluids offer a rich phase diagram including uniaxial/biaxial nematic phases, the ferromagnetic phase, and the cyclic phase. Using the Bogoliubov-de Gennes (BdG) equation as superfluid Fermi liquid theory, we show that a strong (weak) magnetic field drives the first (second) order transition from the dihedral-two biaxial nematic phase to dihedral-four biaxial nematic phase in low (high) temperatures, and their phase boundaries are divided by the critical endpoint (CEP). We demonstrate that the set of critical exponents at the CEP satisfies the Rushbrooke, Griffiths, and Widom equalities, indicating a new universality class. At the CEP, the $^3P_2$ superfluid exhibits critical behavior with nontrivial critical exponents, indicating a new universality class. Furthermore, we find that the Ginzburg-Landau (GL) equation up to the 8th-order expansion satisfies three equalities and properly captures the physics of the CEP. This implies that the GL theory can provide a tractable way for understanding critical phenomena which may be realized in the dense core of realistic magnetars.

nucl-th↗

arXiv2020

Emergent discrete 3-form symmetry and domain walls

We show that axion models with the domain wall number $k$ in $(3+1)$ dimensions, i.e., periodic scalar field theories admitting $k$ axion domain walls, exhibit an emergent ${\mathbb Z}_k$ 3-form symmetry for $k >1$ in addition to a conventional ${\mathbb Z}_k$ 0-form symmetry. The emergent 3-form symmetry is explicitly shown by establishing a low-energy dual transformation between the scalar field theory and a 3-form gauge theory. We further argue that the emergent 3-form symmetry is spontaneously broken, and the breaking pattern is so-called the type-B spontaneous symmetry breaking. We discuss similar and different points between the phase admitting the domain walls and topologically ordered phases.

hep-th↗

arXiv2020

Vortex confinement transitions in the modified Goldstone model

The modified XY model is a variation of the XY model extended by a half periodic term, exhibiting a rich phase structure. As the Goldstone model, also known as the linear O(2) model, can be obtained as a continuum and regular model for the XY model, we define the modified Goldstone model as that of the modified XY model. We construct a vortex, a soliton (domain wall), and a molecule of two half-quantized vortices connected by a soliton as regular solutions of this model. Then we investigate its phase structure in two Euclidean dimensions via the functional renormalization group formalism and full numerical simulations. We argue that the field dependence of the wave function renormalization factor plays a crucial role in the existence of the line of fixed points describing the Berezinskii-Kosterlitz-Thouless (BKT) transition, which can ultimately terminate not only at one but at two end points in the modified model. This structure confirms that a two-step phase transition of the BKT and Ising types can occur in the system. We compare our renormalization group results with full numerical simulations, which also reveal that the phase transitions show a richer scenario than expected.

cond-mat.stat-mech↗

arXiv2020

Domain walls in neutron $^{3}P_{2}$ superfluids in neutron stars

We work out domain walls in neutron $^{3}P_{2}$ superfluids realized in the core of neutron stars. Adopting the Ginzburg-Landau (GL) theory as a bosonic low-energy effective theory, we consider configurations of domain walls interpolating ground states, i.e., the uniaxial nematic (UN), D$_{2}$-biaxial nematic (D$_{2}$-BN), and D$_{4}$-biaxial nematic (D$_{4}$-BN) phases in the presence of zero, small and large magnetic fields, respectively. We solve the Euler-Lagrange equation from the GL free energy density, and calculate surface energy densities of the domain walls. We find that one extra Nambu-Goldstone mode is localized in the vicinity of a domain wall in the UN phase while a U(1) symmetry restores in the vicinity of one type of domain wall in the D$_{2}$-BN phase and all domain walls in the D$_{4}$-BN phase. Considering a pile of domain walls in the neutron stars, we find that the most stable configurations are domain walls perpendicular to the magnetic fields piled up in the direction along the magnetic fields in the D$_{2}$-BN and D$_{4}$-BN phases. We estimate the energy released from the deconstruction of the domain walls in the edge of a neutron star, and show that it can reach an astrophysical scale such as glitches in neutron stars.

nucl-th↗

arXiv2020

Topological Nambu monopole in two Higgs doublet models

We show that a topological Nambu monopole exists as a regular solution for a large range of parameters in two Higgs doublet models, contrary to the standard model admitting only non-topological Nambu monopoles. We analyze a Higgs potential with a global $U(1)$ symmetry and a discrete symmetry $\mathbb{Z}_2$. The monopole is attached by two topological $Z$ strings ($Z$ flux tubes) from both sides. Despite of a trivial second homotopy group, the discrete symmetry $\mathbb{Z}_2$ together with a non-trivial first homotopy group for $Z$ strings topologically ensures the topological stability. After analytically constructing an asymptotic form of such a configuration, we explicitly construct a solution of the equation of motion based on a 3D numerical simulation, in which magnetic fluxes spherically emanating from the monopole at large distances are deformed in the vicinity of the monopole. Since the monopoles are expected to be abundant in the present universe, they might be observed in the current monopole searches.

hep-ph↗

arXiv2019

Topological order in a color-flavor locked phase of $(3+1)$-dimensional $U(N)$ gauge-Higgs system

We study a $(3+1)$-dimensional $U(N)$ gauge theory with $N$-flavor fundamental scalar fields, whose color-flavor locked (CFL) phase has topologically stable non-Abelian vortices. The $U(1)$ charge of the scalar fields must be $Nk+1$ for some integer $k$ in order for them to be in the representation of $U(N)$ gauge group. This theory has a $\mathbb{Z}_{Nk+1}$ one-form symmetry, and it is spontaneously broken in the CFL phase, i.e., the CFL phase is topologically ordered if $k\not=0$. We also find that the world sheet of topologically stable vortices in CFL phase can generate this one-form symmetry.

hep-th↗

arXiv2019

$\mathbb{Z}_n$ modified XY and Goldstone models and vortex confinement transition

The modified XY model is a modification of the XY model by addition of a half-periodic term. The modified Goldstone model is a regular and continuum version of the modified XY model. The former admits a vortex molecule, that is, two half-quantized vortices connected by a domain wall, as a regular topological soliton solution to the equation of motion while the latter admits it as a singular configuration. Here we define the ${\mathbb Z}_n$ modified XY and Goldstone models as the $n=2$ case to be the modified XY and Goldstone models, respectively. We exhaust all stable and metastalble vortex solutions for $n=2,3$ and find a vortex confinement transition from an integer vortex to a vortex molecule of $n$ $1/n$-quantized vortices, depending on the ratio between the term of the XY model and the modified term. We find for the case of $n=3$, a rod-shaped molecule is the most stable while a Y-shaped molecule is metastable. We also construct some solutions for the case of $n=4$.The vortex confinement transition can be understood in terms of the ${\mathbb C}/{\mathbb Z}_n$ orbifold geometry.

hep-th↗

arXiv2019

Collision dynamics and reactions of fractional vortex molecules in coherently coupled Bose-Einstein condensates

Coherently coupled two-component Bose-Einstein condensates (BEC) exhibit vortex confinement resembling quark confinement in Quantum Chromo Dynamics (QCD). Fractionally quantized vortices winding only in one of two components are attached by solitons, and they cannot stably exist alone. Possible stable states are "hadrons" either of mesonic type, i.e., molecules made of a vortex and anti-vortex in the same component connected by a soliton, or of baryonic type, i.e., molecules made of two vortices winding in two different components connected by a soliton. Mesonic molecules move straight with a constant velocity while baryonic molecules rotate. We numerically simulate collision dynamics of mesonic and baryonic molecules and find that the molecules swap a partner in collisions in general like chemical and nuclear reactions, summarize all collisions as vortex reactions, and describe those by Feynman diagrams. We find a selection rule for final states after collisions of vortex molecules, analogous to that for collisions of hadrons in QCD.

cond-mat.quant-gas↗

arXiv2019

Topologically nontrivial Andreev bound states

Andreev bound states are low energy excitations appearing below the particle-hole gap of superconductors, and are expected to be topologically trivial. Here, we report the theoretical prediction of topologically $nontrivial$ Andreev bound states in one-dimensional superconductors. These states correspond to another topological invariant defined in a synthetic two-dimensional space, the particle-hole Chern number, which we construct in analogy to the spin Chern number in quantum spin Hall systems. Nontrivial Andreev bound states have distinct features and are topologically nonequivalent to Majorana bound states. Yet, they can coexist in the same system, have similar spectral signatures, and materialize with the concomitant opening of the particle-hole gap. The coexistence of Majorana and nontrivial Andreev bound state is the direct consequence of "double dimensionality", i.e., the dimensional embedding of the one-dimensional system in a synthetic two-dimensional space, which allows the definition of two distinct topological invariants ($\mathbb{Z}_2$ and $\mathbb{Z}$) in different dimensionalities.

cond-mat.supr-con↗

arXiv2019

Lattice study on the twisted ${\mathbb C}P^{N-1}$ models on ${\mathbb R}\times S^{1}$

We report the results of the lattice simulation of the ${\mathbb C} P^{N-1}$ sigma model on $S_{s}^{1}$(large) $\times$ $S_τ^{1}$(small). We take a sufficiently large ratio of the circumferences to approximate the model on ${\mathbb R} \times S^1$. For periodic boundary condition imposed in the $S_τ^{1}$ direction, we show that the expectation value of the Polyakov loop undergoes a deconfinement crossover as the compactified circumference is decreased, where the peak of the associated susceptibility gets sharper for larger $N$. For ${\mathbb Z}_{N}$ twisted boundary condition, we find that, even at relatively high $β$ (small circumference), the regular $N$-sided polygon-shaped distributions of Polyakov loop leads to small expectation values of Polyakov loop, which implies unbroken ${\mathbb Z}_{N}$ symmetry if sufficient statistics and large volumes are adopted. We also argue the existence of fractional instantons and bions by investigating the dependence of the Polyakov loop on $S_{s}^{1}$ direction, which causes transition between ${\mathbb Z}_{N}$ vacua.

hep-lat↗

arXiv2019

Ground state modulations in the ${\mathbb C}P^{N-1}$ model

In this work we examine a system consisting of a confined one-dimensional arrangement of atoms that we describe by using the 2-dimensional ${\mathbb C}P^{N-1}$ model, restricted to an interval and at finite temperature. We develop a method to obtain the bulk and boundary parts of the one-loop effective action as a function of the effective mass of the fluctuations. The formalism has the advantage of allowing for a systematic analysis of a large class of boundary conditions and to model the (adiabatic) response of the ground state to changes in the boundary conditions. In the case of periodic boundary conditions, we find that inhomogeneous phases are disfavored for intervals of large size. Away from periodic boundary conditions, our numerical results show that the ground state has a generic crystal-like structure that can be modulated by variations of the boundary conditions. The results presented here could be relevant for experimental implementations of nonlinear sigma models and could be tested by lattice numerical simulations.

hep-th↗

arXiv2019

Casimir Force for the ${\mathbb C}P^{N-1}$ Model

In this work, we derive exact self-consistent solutions to the gap equations of the $\mathbb{C}P^{N-1}$ model on a finite interval with Dirichlet boundary conditions in the large-$N$ approximation. The solution reproduce the confining phase in the infinite system by taking the appropriate limit. We compute the vacuum energy and the Casimir force and observe that the sign of the force is always attractive.

hep-th↗

arXiv2019

Berezinskii-Kosterlitz-Thouless transition of two-component Bose mixtures with inter-component Josephson coupling

We study the Berezinskii-Kosterlitz-Thouless (BKT) transition of two-component Bose mixtures in two spatial dimensions. When phases of both components are decoupled, half-quantized vortex-antivortex pairs of each component induce two-step BKT transitions. On the other hand, when phases of the both components are synchronized through the inter-component Josephson coupling, two species of vortices of each component are bind to form a molecule, and in this case, we find that there is only one BKT transition by molecule-antimolecule pairs. Our results can be tested by two weakly-connected Bose systems such as two-component ultracold dilute Bose mixtures with the Rabi oscillation, and multiband superconductors.

cond-mat.stat-mech↗

arXiv2019

Reexamining Ginzburg-Landau theory for neutron $^3P_2$ superfluidity in neutron stars

The Ginzburg-Landau (GL) effective theory is a useful tool to study a superconductivity or superfluidity near the critical temperature, and usually the expansion up to the 4th order in terms of order parameters is sufficient for the description of the second-order phase transition. In this paper, we discuss the GL equation for the neutron $^{3}P_{2}$ superfluidity relevant for interior of neutron stars. We derive the GL expansion up to the 8th order in the condensates and find that this order is necessary for the system to have the unique ground state, unlike the ordinary cases. Starting from the $LS$ potential, which provides the dominant attraction between two neutrons at the high density, we derive the GL equation in the path-integral formalism, where the auxiliary field method and the Nambu-Gor'kov representation are used. We present the detailed description for the trace calculation necessary in the derivation of the GL equation. As numerical results, we show the phase diagram of the neutron $^{3}P_{2}$ superfluidity on the plane spanned by the temperature and magnetic field, and find that the 8th order terms lead to a first-order phase transition, whose existence was predicted in the Bogoliubov-de Gennes equation but has not been found thus far within the framework of the GL expansion up to the 6th order.The first-order phase transition will affect the interior structures inside the neutron stars.

nucl-th↗

arXiv2019

Confinement-Deconfinement Crossover in the Lattice $\mathbb{C}P^{N-1}$ Model

The $\mathbb{C}P^{N-1}$ sigma model at finite temperature is studied using lattice Monte Carlo simulations on $S_{s}^{1} \times S_τ^{1}$ with radii $L_{s}$ and $L_τ$, respectively, where the ratio of the circumferences is taken to be sufficiently large ($L_{s}/L_τ \gg 1$) to simulate the model on $\mathbb{R} \times S^1$. We show that the expectation value of the Polyakov loop undergoes a deconfinement crossover as $L_τ$ is decreased, where the peak of the associated susceptibility gets sharper for larger $N$. We find that the global PSU($N$)=SU($N$)$/{\mathbb Z}_{N}$ symmetry remains unbroken at "quantum" and "classical" levels for the small and large $L_τ$, respectively: in the small $L_τ$ region for finite $N$, the order parameter fluctuates extensively with its expectation value consistent with zero after taking an ensemble average, while in the large $L_τ$ region the order parameter remains small with little fluctuations. We also calculate the thermal entropy and find that the degrees of freedom in the small $L_τ$ regime are consistent with $N-1$ free complex scalar fields, thereby indicating a good agreement with the prediction from the large-$N$ study for small $L_τ$.

hep-th↗

arXiv2019

Instantons in Chiral Magnets

We exhaustively construct instanton solutions and elucidate their properties in one-dimensional anti-ferromagnetic chiral magnets based on the $O(3)$ nonlinear sigma model description of spin chains with the Dzyaloshinskii-Moriya (DM) interaction. By introducing an easy-axis potential and a staggered magnetic field, we obtain a phase diagram consisting of ground-state phases with two points (or one point) in the easy-axis dominant cases, a helical modulation at a fixed latitude of the sphere, and a tricritical point allowing helical modulations at an arbitrary latitude. We find that instantons (or skyrmions in two-dimensional Euclidean space) appear as composite solitons in different fashions in these phases: temporal domain walls or wall-antiwall pairs (bions) in the easy-axis dominant cases, dislocations (or phase slips) with fractional instanton numbers in the helical state, and isolated instantons and calorons living on the top of the helical modulation at the tricritical point. We also show that the models with DM interaction and an easy-plane potential can be mapped into those without them, providing a useful tool to investigate the model with the DM interaction.

cond-mat.mes-hall↗

arXiv2019

Topological couplings in higher derivative extensions of supersymmetric three-form gauge theories

We consider a topological coupling between a pseudo-scalar field and a 3-form gauge field in ${\cal N}=1$ supersymmetric higher derivative 3-form gauge theories in four spacetime dimensions. We show that ghost/tachyon-free higher derivative Lagrangians with the topological coupling can generate various potentials for the pseudo-scalar field by solving the equation of motion for the 3-form gauge field. We give two examples of higher derivative Lagrangians and the corresponding potentials: one is a quartic order term of the field strength and the other is the term which can generate a cosine-type potential of the pseudo-scalar field.

hep-th↗

arXiv2019

Aharonov-Bohm defects

We discuss what happens when a field receiving an Aharonov-Bohm (AB) phase develops a vacuum expectation value (VEV), with an example of an Alice string in a $U(1) \times SU(2)$ gauge theory coupled with complex triplet scalar fields. We introduce scalar fields belonging to the doublet representation of $SU(2)$, charged or chargeless under the $U(1)$ gauge symmetry, that receives an AB phase around the Alice string. When the doublet develops a VEV, the Alice string turns to a global string in the absence of the interaction depending on the relative phase between the doublet and triplet, while, in the presence of such an interaction, the Alice string is confined by a soliton or domain wall and therefore the spontaneous breaking of a spatial rotation around the string is accompanied. We call such an object induced by an AB phase as an ``AB defect'', and argue that such a phenomenon is ubiquitously appearing in various systems.

hep-th↗