Search

A coherent XY machine (CXYM) is a physical spin simulator that can simulate the XY model by mapping XY spins onto the continuous phases of non-degenerate optical parametric oscillators (NOPOs). Here, we demonstrated a large-scale CXYM with >47,000 spins by generating 10-GHz-clock time-multiplexed NOPO pulses via four-wave mixing in a highly nonlinear fiber inside a fiber ring cavity. By implementing a unidirectional coupling from the i-th pulse to the (i+1)-th pulse with a variable 1-pulse delay planar lightwave circuit interferometer, we successfully controlled the effective temperature of a one-dimensional XY spin network within two orders of magnitude., Comment: 5 pages, 4 figures

Partial synchronization is characteristic phase dynamics of coupled oscillators on various natural and artificial networks, which can remain undetected due to the complexity of the systems. With an analogy between pairwise asynchrony of oscillators and topological defects, i.e., vortices, in the two-dimensional XY spin model, we propose a robust and data-driven method to identify the partial synchronization on complex networks. The proposed method is based on an integer matrix whose element is pseudo-vorticity that discretely quantifies asynchronous phase dynamics in every two oscillators, which results in graphical and entropic representations of partial synchrony. As a first trial, we apply our method to 200 FitzHugh-Nagumo neurons on a complex small-world network. Partially synchronized chimera states are revealed by discriminating synchronized states even with phase lags. Such phase lags also appear in partial synchronization in chimera states. Our topological, graphical, and entropic method is implemented solely with measurable phase dynamics data, which will lead to a straightforward application to general oscillatory networks including neural networks in the brain., Comment: 9 pages, 5 figures

Noisy mean field annealing (NMFA) is an algorithm that mimics a coherent Ising machine (CIM), which is an optical system for solving Ising problems. The NMFA has reproduced the solver performance of the CIM for systems of limited size even though it simplifies the interaction between spins with a mean-field approximation. However, recent experiments observing various thermodynamic quantities have revealed that the CIM can capture the phase transitions of the two-dimensional Ising models that the mean field cannot capture. This situation leads to a fundamental question as to how well the NMFA can capture the features of the thermodynamic quantities around the phase transition. This paper answers that the NMFA reproduces the thermodynamic features of the mean field, but cannot reproduce the CIM results. This suggests that, in terms of sampling, the level of performance of the CIM is beyond that of the NMFA., Comment: 6 pages, 6 figures

A coherent Ising machine (CIM) is known to deliver the low-energy states of the Ising model. Here, we investigate how well the CIM simulates the thermodynamic properties of a two-dimensional square-lattice Ising model. Assuming that the spin sets sampled by the CIM can be regarded as a canonical ensemble, we estimate the effective temperature of the spins represented by degenerate optical parametric oscillator pulses by using maximum likelihood estimation. With the obtained temperature, we confirmed that the thermodynamic quantities obtained with the CIM exhibited a phase-transition-like behavior that better matches the analytical and numerical results than the mean field one., Comment: 6 pages, 3 figures

Non-orthogonal multiple access (NOMA) technique is important for achieving a high data rate in next-generation wireless communications. A key challenge to fully utilizing the effectiveness of the NOMA technique is the optimization of the resource allocation (RA), e.g., channel and power. However, this RA optimization problem is NP-hard, and obtaining a good approximation of a solution with a low computational complexity algorithm is not easy. To overcome this problem, we propose the coherent Ising machine (CIM) based optimization method for channel allocation in NOMA systems. The CIM is an Ising system that can deliver fair approximate solutions to combinatorial optimization problems at high speed (millisecond order) by operating optimization algorithms based on mutually connected photonic neural networks. The performance of our proposed method was evaluated using a simulation model of the CIM. We compared the performance of our proposed method to simulated annealing, a conventional-NOMA pairing scheme, deep Q learning based scheme, and an exhaustive search scheme. Simulation results indicate that our proposed method is superior in terms of speed and the attained optimal solutions., Comment: 16 pages, 10 figures. This work has been submitted to the IEEE for possible publication

We experimentally demonstrate that networks of identical photonic spiking neurons based on coupled degenerate parametric oscillators can show various chimera states, in which, depending on their local synchronization and desynchronization, different kinds of spiking dynamics can develop in a self-organized manner. Even when only a static interaction is implemented, through synchronized inputs from connected neurons, the spiking mode of photonic neurons can be spontaneously and adaptively changed between the Class-I and Class-II modes classified by A. L. Hodgkin. This spontaneous spiking-mode shift induces a significant change in the spiking frequency despite the all neurons having the same natural spiking frequency, which encourages the generation of chimera states. Controllability and self-organized flexibility of the spiking modes in the present system allow us to create an experimental platform to explore the nature of chimera states in neuromorphic spiking neural networks., Comment: 26 pages, 12 figures

Nonlinear dynamics of spiking neural networks has recently attracted much interest as an approach to understand possible information processing in the brain and apply it to artificial intelligence. Since information can be processed by collective spiking dynamics of neurons, the fine control of spiking dynamics is desirable for neuromorphic devices. Here we show that photonic spiking neurons implemented with paired nonlinear optical oscillators can be controlled to generate two modes of bio-realistic spiking dynamics by changing the optical pump amplitude. When they are coupled in a network, we found that the interaction between the photonic neurons induces an effective change in the pump amplitude depending on the order parameter that characterizes synchronization. The experimental results show that the effective change causes spontaneous modification of the spiking modes and firing rates of clustered neurons, and such collective dynamics can be utilized to realize efficient heuristics for solving NP-hard combinatorial optimization problems., Comment: 43 pages, 9 figures

We present the first experimental measurement of the ensemble averages of both the kinetic and interaction energies of the three-dimensional Bose--Hubbard model at finite temperature and various optical lattice depths across weakly to strongly interacting regimes, for an almost unit filling factor. The kinetic energy is obtained through Fourier transformation of a time-of-flight signal, and the interaction energy is measured using a newly developed atom-number-projection spectroscopy technique, by exploiting an ultra-narrow optical transition of two-electron atoms. The obtained experimental results can be used as benchmarks for state-of-the-art numerical methods of quantum many-body theory. As an illustrative example, we compare the measured energies with numerical calculations involving the Gutzwiller and cluster-Gutzwiller approximations, assuming realistic trap potentials and particle numbers at nonzero entropy (finite temperature); we obtain good agreement without fitting parameters. We also discuss the possible application of this method to temperature estimations for atoms in optical lattices using the thermodynamic relation. This study offers a unique advantage of cold atom system for `quantum simulators', because, to the best of our knowledge, it is the first experimental determination of both the kinetic and interaction energies of quantum many-body system., Comment: 22 pages, 20 figures

Physical annealing systems provide heuristic approaches to solving NP-hard Ising optimization problems. Here, we study the performance of two types of annealing machines--a commercially available quantum annealer built by D-Wave Systems, and measurement-feedback coherent Ising machines (CIMs) based on optical parametric oscillator networks--on two classes of problems, the Sherrington-Kirkpatrick (SK) model and MAX-CUT. The D-Wave quantum annealer outperforms the CIMs on MAX-CUT on regular graphs of degree 3. On denser problems, however, we observe an exponential penalty for the quantum annealer ($\exp(-\alpha_\textrm{DW} N^2)$) relative to CIMs ($\exp(-\alpha_\textrm{CIM} N)$) for fixed anneal times, on both the SK model and on 50%-edge-density MAX-CUT, where the coefficients $\alpha_\textrm{CIM}$ and $\alpha_\textrm{DW}$ are problem-class-dependent. On instances with over $50$ vertices, a several-orders-of-magnitude time-to-solution difference exists between CIMs and the D-Wave annealer. An optimal-annealing-time analysis is also consistent with a significant projected performance difference. The difference in performance between the sparsely connected D-Wave machine and the measurement-feedback facilitated all-to-all connectivity of the CIMs provides strong experimental support for efforts to increase the connectivity of quantum annealers., Comment: 12 pages, 5 figures, 1 table (main text); 14 pages, 12 figures, 2 tables (supplementary)

A network of optical parametric oscillators is used to simulate classical Ising and XY spin chains. The collective nonlinear dynamics of this network, driven by quantum noise rather than thermal fluctuations, seeks out the Ising / XY ground state as the system transitions from below to above the lasing threshold. We study the behavior of this "Ising machine" for three canonical problems: a 1D ferromagnetic spin chain, a 2D square lattice, and problems where next-nearest-neighbor couplings give rise to frustration. If the pump turn-on time is finite, topological defects form (domain walls for the Ising model, winding number and vortices for XY) and their density can be predicted from a numerical model involving a linear "growth stage" and a nonlinear "saturation stage". These predictions are compared against recent data for a 10,000-spin 1D Ising machine., Comment: 34 pages, 15 figures. Preprint of an article submitted for consideration in International Journal of Modern Physics B. [Copyright 2016 World Scientific Publishing Company] [www.worldscientific.com/worldscinet/ijmpb]

Simulating a network of Ising spins with physical systems is now emerging as a promising approach for solving mathematically intractable problems. Here we report a large-scale network of artificial spins based on degenerate optical parametric oscillators (DOPO), paving the way towards a photonic Ising machine capable of solving difficult combinatorial optimization problems. We generated >10,000 time-division-multiplexed DOPOs using dual-pump four-wave mixing (FWM) in a highly nonlinear fibre (HNLF) placed in a fibre cavity. Using those DOPOs, a one-dimensional (1D) Ising model was simulated by introducing nearest-neighbour optical coupling. We observed the formation of spin domains and found that the domain size diverged near the DOPO threshold, which suggests that the DOPO network can simulate the behavior of low-temperature Ising spins., Comment: 6 pages, 3 figures. First draft in Nature Photonics (2016)

We develop a general description of the superconductivity of lattice fermions based on the BCS theory. We propose a modeling of the density of states (DOS) of lattice fermions, where divergent and semi-metallic structures are described by asymptotic expansions around the Fermi energy. This modeling leads to a unified representation of the transition temperature $T_c$ at half filling, which reproduces asymptotic forms of $T_c$ derived in several lattices, such as the square, honeycomb, and Lieb lattices, for the weakly interacting limit. The derived asymptotic forms of $T_c$ are categorized into four types, which is attributed to the different responses of the degenerate fermions depending on the DOS structures. The DOS with a delta-functional singularity induces the highest $T_c$ in the weakly interacting region, where $T_c$ is linearly proportional to the pairing interaction $U$. Three kinds of universal ratios defined in the BCS theory no longer reduce to constants independent of the system parameters but can be parameterized with a certain variable that characterizes the singular structures of the DOS. We find universal relationship among thermodynamic quantities that holds for all parameter regions. Further, we numerically demonstrate that in multi-band systems the correlation effects can induce an effective delta-functional singularity. This phenomenon generally appears in multi-energy (or multi-gap) systems and may provide a plausible guideline for material designs of high-$T_c$ superconductor., Comment: 17 pages (main text:12 pages; appendix:3.5 pages), 5 figures

We provide a numerical method to calculate comprehensively the microwave and the laser spectra of ultracold bosonic atoms in optical lattices at finite temperatures. Our formulation is built up with the sum rules, up to the second order, derived from the general principle of spectroscopy. The sum rule approach allows us to discuss the physical origins of a spectral peak shift and also a peak broadening. We find that a spectral broadening of superfluid atoms can be determined from number fluctuations of atoms, while that of normal-state atoms is mainly attributed to quantum fluctuations resulting from hopping of atoms. To calculate spectra at finite temperatures, based on the sum rule approach, we provide a two-mode approximation assuming that spectra of the superfluid and normal state atoms can be calculated separately. Our method can properly deal with multi-peak structures of spectra resulting from thermal fluctuations and also coexisting of the superfluid and the normal states. By combining the two-mode approximation with a finite temperature Gutzwiller approximation, we calculate spectra at finite temperatures by considering realistic systems, and the calculated spectra show nice agreements with those in experiments., Comment: 12 pages, 4 figures

We describe the enhanced magnetic transition temperatures $T_c$ of two-component fermions in three-dimensional layered Lieb lattices, which are created in cold atom experiments. We determine the phase diagram at half-filling using the dynamical mean-field theory. The dominant mechanism of enhanced $T_c$ gradually changes from the (delta-functional) flat-band to the (logarithmic) Van Hove singularity as the interlayer hopping increases. We elucidate that the interaction induces an effective flat-band singularity from a dispersive flat (or narrow) band. We offer a general analytical framework for investigating the singularity effects, where a singularity is treated as one parameter in the density of states. This framework provides a unified description of the singularity-induced phase transitions, such as magnetism and superconductivity, where the weight of the singularity characterizes physical quantities. This treatment of the flat-band provides the transition temperature and magnetization as a universal form (i.e., including the Lambert function). We also elucidate a specific feature of the magnetic crossover in magnetization at finite temperatures., Comment: 7 pages, 4 figures, to appear in PRA

We theoretically study magnetic properties of two-component cold fermions in half-filled multilayer Lieb optical lattices, i.e., two, three, and several layers, using the dynamical mean-field theory. We clarify that the magnetic properties of this system become quite different depending on whether the number of layers is odd or even. In odd-number-th layers in an odd-number-layer system, finite magnetization emerges even with an infinitesimal interaction. This is a striking feature of the flatband ferromagnetic state in multilayer systems as a consequence of the Lieb theorem. In contrast, in even-number layers, magnetization develops from zero on a finite interaction. These different magnetic behaviours are triggered by the flat bands in the local density of states and become identical in the limit of the infinite-layer (i.e., three-dimensional) system. We also address how interlayer hopping affects the magnetization process. Further, we point out that layer magnetization, which is a population imbalance between up and down atoms on a layer, can be employed to detect the emergence of the flat-band ferromagnetic state without addressing sublattice magnetization., Comment: 11 pages, 9 figures

We investigate the effects of a repulsive three-body interaction on the Mott transition of the repulsively interacting three-component fermionic atoms in optical lattices by means of the self-energy functional approach. We find that the three-body repulsion hardly affects the qualitative features of the Mott transition, because the three-body repulsion does not compete with the two-body repulsions. When the three-body repulsion is extremely strong, the triple occupancy vanishes in the Fermi liquid state. This situation is equivalent to that caused by strong three-body losses. Our results imply that three-body losses have little influence on the Mott transitions in the repulsively interacting three-component fermionic atoms in optical lattices., Comment: 6 pages, 3 figures, Proceedings of MBT17

We review our theoretical analysis of repulsively interacting three-component fermionic atoms in optical lattices. We discuss quantum phase transitions at around half filling with a balanced population by focusing on Mott transitions, staggered ordering, and superfluidity. At half filling (with 3/2 atoms per site), characteristic Mott transitions are induced by the anisotropic interactions, where two-particle repulsions between any two of the three colors have different strengths. At half filling, two types of staggered ordered states appear at low temperatures depending on the anisotropy of the interactions. As the temperature increases, phase transitions occur from the staggered ordered states to the unordered Mott states. Deviating from half filling, an exotic superfluid state appears close to a regime in which the Mott transition occurs. We explain the origin of these phase transitions and present the finite-temperature phase diagrams., Comment: 24 pages, 16 figures

We investigate the superfluid state of repulsively interacting three-component (color) fermionic atoms in optical lattices. When the anisotropy of the three repulsive interactions is strong, atoms of two of the three colors form Cooper pairs and atoms of the third color remain a Fermi liquid. An effective attractive interaction is induced by density fluctuations of the third-color atoms. This superfluid state is stable against changes in filling close to half filling. We determine the phase diagrams in terms of temperature, filling, and the anisotropy of the repulsive interactions., Comment: 5 pages, 6 figures

We study the ground state properties of spin-1 bosons in a two-dimensional optical lattice, by applying a variational Monte Carlo method to the S=1 Bose-Hubbard model on a square lattice at unit filling. A doublon-holon binding factor introduced in the trial state provides a noticeable improvement in the variational energy over the conventional Gutzwiller wave function and allows us to deal effectively with the inter-site correlations of particle densities and spins. We systematically show how spin-dependent interactions modify the superfluid-Mott insulator transitions in the S=1 Bose-Hubbard model due to the interplay between the density and spin fluctuations of bosons. Furthermore, regarding the magnetic phases in the Mott region, the calculated spin structure factor elucidates the emergence of nematic and ferromagnetic spin orders for antiferromagnetic ($U_2>0$) and ferromagnetic ($U_2<0$) couplings, respectively., Comment: 5 pages, 5 figures, to appear in Journal of the Physical Society of Japan

We propose a method for generating high-fidelity multipartite spin-entanglement of ultracold atoms in an optical lattice in a short operation time with a scalable manner, which is suitable for measurement-based quantum computation. To perform the desired operations based on the perturbative spin-spin interactions, we propose to actively utilize the extra degrees of freedom (DOFs) usually neglected in the perturbative treatment but included in the Hubbard Hamiltonian of atoms, such as, (pseudo-)charge and orbital DOFs. Our method simultaneously achieves high fidelity, short operation time, and scalability by overcoming the following fundamental problem: enhancing the interaction strength for shortening operation time breaks the perturbative condition of the interaction and inevitably induces unwanted correlations among the spin and extra DOFs., Comment: 9 pages, 11 figures

We study the Kondo effect of a two-orbital vertical quantum dot (QD) coupled to two ferromagnetic leads by employing an equation of motion method. When the ferromagnetic leads are coupled with parallel spin polarization, we find three peaks in the single-particle excitation spectra. The middle one is the Kondo resonance caused by the orbital degrees of freedom. In magnetic fields, the Kondo effect vanishes. However, at a certain magnetic field new two-fold degenerate states arise and the Kondo effect emerges there. In contrast, when the ferromagnetic leads are coupled with antiparallel spin polarization, the Kondo effect caused by the spin (orbital) degrees of freedom survives (is suppressed) in magnetic fields. We investigate the field dependence of the conductance in the parallel and antiparallel spin polarizations of the leads and find that the conductance changes noticeably in magnetic fields., Comment: 10 pages, 8 figures

Many-body effects are at the very heart of diverse phenomena found in condensed-matter physics. One striking example is the Mott insulator phase where conductivity is suppressed as a result of a strong repulsive interaction. Advances in cold atom physics have led to the realization of the Mott insulating phases of atoms in an optical lattice, mimicking the corresponding condensed matter systems. Here, we explore an exotic strongly-correlated system of Interacting Dual Mott Insulators of bosons and fermions. We reveal that an inter-species interaction between bosons and fermions drastically modifies each Mott insulator, causing effects that include melting, generation of composite particles, an anti-correlated phase, and complete phase-separation. Comparisons between the experimental results and numerical simulations indicate intrinsic adiabatic heating and cooling for the attractively and repulsively interacting dual Mott Insulators, respectively.

We investigate the finite-temperature properties of attractive three-component (colors) fermionic atoms in optical lattices using a self-energy functional approach. As the strength of the attractive interaction increases in the low temperature region, a second-order transition occurs from a Fermi liquid to a color superfluid (CSF). In the strong attractive region, a first-order transition occurs from a CSF to a trionic state. In the high temperature region, a crossover between a Fermi liquid and a trionic state is observed with increasing the strength of the attractive interaction. The crossover region for fixed temperature is almost independent of filling., Comment: 8 pages, 5 figures, Final version, Mod. Phys. Lett. B 25, 987 (2011)

We investigate the Mott transitions of three-component (colors) repulsive fermionic atoms in optical lattices using the dynamical mean field theory. We find that for SU(3) symmetry breaking interactions the Mott transition occurs at incommensurate half filling. As a result, a characteristic Mott insulating state appears, where paired atoms with two different colors and atoms with the third color are localized at different sites. We also find another Mott state where atoms with two different colors are localized at different sites and atoms with the third color remain itinerant. We demonstrate that these exotic Mott phases can be detected by experimental double occupancy observations., Comment: 5 pages, 4 figures

We study the finite temperature properties of two-component fermionic atoms trapped in a two-dimensional optical lattice. We apply the self-energy functional approach to the two-dimensional Hubbard model with a harmonic trapping potential, and systematically investigate the thermodynamic properties of this system. We find that entropy and grand potential provide evidence of a crossover between the Mott insulating and metallic phases at certain temperatures. In addition, we find that entropy exhibits a cusp-like anomaly at lower temperatures, suggesting a second or higher order antiferromagnetic transition. We estimate the antiferromagnetic transition temperatures, and clarify how the trapping potential affects this magnetic transition., Comment: 9 pages, 13 figures

We propose a simple method to detect the antiferromagnetic (AF) state of fermionic atoms in an optical lattice by combining a time-of-flight (TOF) imaging method and a Feshbach resonance. In this scheme, the nontrivial dynamics of fermionic atoms during the imaging process works as a probe with respect to the breaking of the translational symmetry in the AF state. Precise numerical simulations demonstrate that the characteristic oscillatory dynamics induced by the scattering process that transfers an AF ordering vector appears in TOF images, which can be easily observed experimentally., Comment: 4 pages, 5 figures

We investigate three-component (colors) repulsive fermionic atoms in optical lattices using the dynamical mean field theory. Depending on the anisotropy of the repulsive interactions, either a color density-wave state or a color selective staggered state appears at half filling. In the former state, pairs of atoms with two of the three colors and atoms with the third color occupy different sites alternately. In the latter state, atoms with two of the three colors occupy different sites alternately and atoms with the third color are itinerant throughout the system. When the interactions are isotropic, both states are degenerate. We discuss the results using an effective model., Comment: 5 pages, 5 figures

We investigate the finite-temperature properties of attractive three-component (colors) fermionic atoms in optical lattices using a self-energy functional approach. As the strength of the attractive interaction increases in the low-temperature region, we observe a second-order transition from a Fermi liquid to a color superfluid (CSF), where atoms from two of the three colors form Cooper pairs. In the strong attractive region, we observe a first-order transition from a CSF to a trionic state, where three atoms with different colors form singlet bound states. A crossover between a Fermi liquid and a trionic state is observed in the high-temperature region. We present a phase diagram covering zero to finite temperatures. We demonstrate that the CSF transition temperature is enhanced by the anisotropy of the attractive interaction., Comment: 4 pages, 4 figures

We study the two-band effects on ultracold fermionic atoms in optical lattices by means of dynamical mean-field theory. We find that at half-filling the atomic-density-wave (ADW) state emerges owing to the two-band effects in the attractive interaction region, while the antiferromagnetic state appears in the repulsive interaction region. As the orbital splitting is increased, the quantum phase transitions from the ADW state to the superfluid state and from the antiferromagnetic state to the metallic state occur in respective regions. Systematically changing the orbital splitting and the interaction, we obtain the phase diagram at half-filling. The results are discussed using the effective boson model derived for the strong attractive interaction., Comment: 7 pages, 7 figures

We study ultracold fermionic atoms trapped in an optical lattice with harmonic confinement by combining the real-space dynamical mean-field theory with a two-site impurity solver. By calculating the local particle density and the pair potential in the systems with different clusters, we discuss the stability of a supersolid state, where an s-wave superfluid coexists with a density-wave state of checkerboard pattern. It is clarified that a confining potential plays an essential role in stabilizing the supersolid state. The phase diagrams are obtained for several effective particle densities., Comment: 7 pages, 5 figures, Phys. Rev. A in press

We study ultracold fermionic atoms trapped in an optical lattice with harmonic confinement by means of the dynamical mean-field approximation. It is demonstrated that a supersolid state, where an s-wave superfluid coexists with a density-wave state with a checkerboard pattern, is stabilized by attractive onsite interactions on a square lattice. Our new finding here is that a confining potential plays an invaluable role in stabilizing the supersolid state. We establish a rich phase diagram at low temperatures, which clearly shows how the insulator, the density wave and the superfluid compete with each other to produce an intriguing domain structure. Our results shed light on the possibility of the supersolid state in fermionic optical lattice systems., Comment: 5 pages, 4 figures

The superfluid-insulator transitions of the fermionic atoms in optical lattices are investigated by the two-site dynamical mean-field theory. It is shown that the Mott transition occurs as a result of the multiband effects. The quasiparticle weight in the superfluid state decreases significantly, as the system approaches the Mott transition point. By changing the interaction and the orbital splitting, we obtain the phase diagram at half filling. The numerical results are discussed in comparison with the effective boson model., Comment: 4 pages, 3 figures, Phys. Rev. A 77, 043624 (2008)

We investigate the infinite-dimensional two-orbital Hubbard model at arbitrary band fillings. By means of the self-energy functional approach, we discuss the stability of the metallic state in the systems with same and different bandwidths. It is found that the Mott insulating phases are realized at commensurate band fillings. Furthermore, it is clarified that the orbital selective Mott phase with one orbital localized and the other itinerant is stabilized even at fractional band fillings in the system with different bandwidths., Comment: 7 pages, 10 figures

Mott transitions in the two-orbital Hubbard model with different bandwidths are investigated at finite temperatures. By means of the self-energy functional approach, we discuss the stability of the intermediate phase with one orbital localized and the other itinerant, which is caused by the orbital-selective Mott transition (OSMT). It is shown that the OSMT realizes two different coexistence regions at finite temperatures in accordance with the recent results of Liebsch. We further find that the particularly interesting behavior emerges around the special condition $U=U'$ and J=0, which includes a new type of the coexistence region with three distinct states. By systematically changing the Hund coupling, we establish the global phase diagram to elucidate the key role played by the Hund coupling on the Mott transitions., Comment: 4 pages, 6 figures

We investigate the Mott transitions in the multi-orbital Hubbard model at half-filling by means of the self-energy functional approach. The phase diagrams are obtained at finite temperatures for the Hubbard model with up to four-fold degenerate bands. We discuss how the first-order Mott transition points $U_{c1}$ and $U_{c2}$ as well as the critical temperature $T_c$ depend on the orbital degeneracy. It is elucidated that enhanced orbital fluctuations play a key role to control the Mott transitions in the multi-orbital Hubbard model., Comment: 8 pages, 7 figures