Cluster Mean-field Approximation Research Articles

Synchronization of persistent oscillations in spin systems with nonlocal dissipation

We explore the synchronization phenomenon in the quantum few-body system of spins with the nonlocal dissipation. Without the external driving, we find that the system can exhibit stable oscillatory behaviors in the long-time dynamics accompanied by the appearance of the purely imaginary eigenvalues of the Liouvillian. Moreover, the oscillations of the next-nearest-neighboring spins are completely synchronized, which is revealed by the quantum trajectory analysis within the stochastic Schr\"odinger equation. The possibility of the appearance of the long-time oscillations in an infinite-size lattice by means of cluster mean-field approximation is also discussed.

The role of extended range of interactions in the dynamics of interacting molecular motors

Motor proteins, also known as biological molecular motors, play important roles in various intracellular processes. Experimental investigations suggest that molecular motors interact with each other during the cellular transport, but the nature of such interactions remains not well understood. Stimulated by these observations, we present a theoretical study aimed to understand the effect of the range of interactions on dynamics of interacting molecular motors. For this purpose, we develop a new version of the totally asymmetric simple exclusion processes in which nearest-neighbor as well as the next nearest-neighbor interactions are taken into account in a thermodynamically consistent way. A theoretical framework based on a cluster mean-field approximation, which partially takes correlations into account, is developed to evaluate the stationary properties of the system. It is found that fundamental current–density relations in the system strongly depend on the strength and the sign of interactions, as well as on the range of interactions. For repulsive interactions stronger than some critical value, a mean-field theoretical approach predicts that increasing the range of interactions might lead to a change from unimodal to trimodal dependence in the flux-density fundamental diagram. However, it is not fully supported by extensive Monte Carlo computer simulations that test theoretical predictions. Although in most ranges of parameters a reasonable agreement between theoretical calculations and computer simulations is observed, there are situations when the cluster mean-field approach fails to describe properly the dynamics in the system. Theoretical arguments to explain these observations are presented. Our theoretical analysis clarifies the microscopic picture of how the range of interactions influences the dynamics of interacting molecular motors.

The effect of local reversible dissociation of particles in interactive driven diffusive system

Motor proteins or biological molecular motors belong to a class of active enzymatic molecules that are responsible for transport and force generation in living cells. They typically operate in large teams and individual protein molecules interact with each other while moving along linear cytoskeleton filaments. Moreover, during their transportation the motors can reversibly dissociate from their tracks. Motivated by these observations, we propose a one dimensional totally asymmetric simple exclusion model for interacting particles that are allowed to reversibly dissociate/associate from a particular site far away from the system boundaries. A theoretical analysis of the model is based on cluster mean-field approximation that allows for a comprehensive description of the stationary properties in the system. It is found that the topology and nature of stationary phase diagrams for varying association/dissociation rates strongly depend on the sign and strength of interactions. Extensive Monte Carlo simulations are implemented to test our theoretical predictions.

Steady-state phases of the dissipative spin- 1/2 XYZ model with frustrated interactions

We investigate the steady-state phases of the dissipative spin-1/2 ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ XYZ model on a two-dimensional square lattice. We show the next-nearest-neighboring interaction plays a crucial role in determining the steady-state properties. By means of the Gutzwiller mean-field (MF) factorization, we find the emergence of antiferromagnetic (AFM) steady-state phases. The existence of such AFM steady-state phases in thermodynamic limit is confirmed by cluster mean-field (CMF) analysis. Moreover, we find evidence of the limit cycle phase through the largest quantum Lyapunov exponent in small cluster and check the stability of the oscillation by calculating the averaged oscillation amplitude up to $4\ifmmode\times\else\texttimes\fi{}4$ CMF approximation.

Field-induced phase transitions of tetramer-singlet states in synthetic SU(4) magnets

Phase transitions of quantum dimer magnets can be explained in terms of Bose-Einstein condensation of magnons. Here we consider a natural extension of the dimer magnets to SU(4)-symmetric tetramer systems, which could be created with four nuclear-spin components (named “u,” “d,” “c,” and “s”) of 173Yb atoms in optical superlattices. We apply the cluster mean-field approximation to the SU(4) Heisenberg model on a tetramerized square lattice, and study the phase transition phenomena in the presence of the field that creates a population imbalance between the two components u,d and the other two c,s. When the population of the four components is balanced, the ground state is approximately given by the direct product of local SU(4)-singlet states. When the field is applied, the population ratio of the components u and d is increased and the system eventually reaches a “saturated” state, which is a SU(2) system with only u and d. We show that in the saturation process, the system exhibits two successive step-like transitions, in contrast to the standard dimer magnets with continuous transition process associated with Bose-Einstein condensation of magnons. The intermediate phase in between the two step-like transitions is a nontrivial solid phase with alternating arrangement of the SU(4)-singlet and four-site resonating-valence-bond states.

Nonuniform phases in the geometrically frustrated dissipative XYZ model

We investigate the steady-state phase diagram of the dissipative spin-1/2 XYZ model on a two-dimensional triangular lattice, in which each site is coupled to a local environment. By means of cluster mean-field approximation, we find that the steady-state phases of the system are rather rich, in particular there exist various types of nonuniform antiferromagnetic phases due to the geometrical frustration. As the short-range correlations included in the analysis, the numerical results show that the oscillatory phase disappears while the triantiferromagnetic and biantiferromagnetic phases remain to exist in the thermodynamic limit. Moreover, the existence of the spin-density-wave phase, which is missed by the single-site mean-field analysis, is also revealed by the spin-structure factor.

The Ising model on the layered J1-J2 square lattice

We investigate the phase transitions in the Ising model on a layered square lattice with first-(J1) and second-(J2) neighbor intralayer interactions and interlayer couplings (J). The thermodynamics of the system is evaluated within a cluster mean-field approximation, which allows us to identify the nature of the thermally driven phase transitions hosted by the model. As a result, we find that interlayer couplings reduce the region of first-order phase transitions between paramagnetic and superantiferromagnetic states. We also find that the interlayer couplings reduce the frustration effects by reducing the entropy content of the low-temperature phases. Our results suggest that tricriticality is present in the special case J=J1, which is in qualitative agreement with recent Monte Carlo simulations for the model.

Magnetocaloric effect in the [formula omitted] transverse Ising model

The magnetocaloric properties of the J1–J2 transverse Ising model are studied by the Correlated Cluster Mean Field approximation. We focus on the particular case J1=1 and J2=-1. The model exhibits a complex phase diagram where three phases were identified: superantiferromagnetic, mixed and paramagnetic. The change in entropy, the cooling ratio and the adiabatic temperature were calculated; we distinguish two types of magnetocaloric effect: normal and inverse. The magnetocaloric properties of the model are discussed as a function of temperature, transverse and longitudinal fields.

The role of dynamic defects in transport of interacting molecular motors

Motor proteins or biological molecular motors are special enzyme molecules that drive biological transport in living cells by moving cellular cargoes along linear protein filaments. The experimental evidences suggest that while performing their mechanical work biological molecular motors interact with each other, and there are other biological molecules on their tracks that influence their progression. Stimulated by these observations, we propose a one-dimensional totally asymmetric simple exclusion process with nearest-neighbor interactions and a dynamic defect that is allowed to reversibly bind and unbind at a specific site far away from the boundaries. A theoretical framework based on cluster mean-field approximation is adopted to determine the stationary properties of the system. The role of interactions and the effect the reversible defect associations on the dynamics of the system is discussed. It is found that three or less stationary phases can exist in the system, depending on the interaction strength, and only one of them is strongly affected by the defect association/dissociation dynamics. The theoretical results are validated through extensive Monte Carlo simulations.

Multistability in an unusual phase diagram induced by the competition between antiferromagnetic-like short-range and ferromagnetic-like long-range interactions

The interplay between competing short-range (SR) and long-range (LR) interactions can cause nontrivial structures in phase diagrams. Recently, horn-shaped unusual structures were found by Monte Carlo simulations in the phase diagram of the Ising antiferromagnet (IA) with infinite-range ferromagnetic-like (F) interactions [Phys. Rev. B {\bf 93}, 064109 (2016); {\bf 96}, 174428 (2017)], and also in an IA with LR interactions of elastic origin modeling spin-crossover materials [Phys. Rev. B {\bf 96}, 144425 (2017)]. To clarify the nature of the phases associated with the horn structures, we study the phase diagram of the IA model with infinite-range F interactions by applying a variational free energy in a cluster mean-field (CMF) approximation. While the simple Bragg-Williams mean-field theory for each sublattice does not produce a horn structure, we find such structures with the CMF method. This confirms that the local thermal fluctuations enabled by the multisite clusters are essential for this phenomenon. We investigate in detail the structure of metastable phases in the phase diagram. In contrast to the phase diagram obtained by the Monte Carlo studies, we find a triple point, at which ferromagnetic-like, antiferromagnetic-like, and disordered phases coexist, and also six tristable regions accompanying the horn structure. We also point out that several characteristic endpoints of first-order transitions appear in the phase diagram. We propose three possible scenarios for the transitions related to the tristable regions. Finally, we discuss the relation between the triple point in this phase diagram and that of a possible lattice-gas model, in which solid, liquid, and gas phases can coexist.

Phase diagram and spin correlations of the Kitaev-Heisenberg model: Importance of quantum effects

We explore the phase diagram of the Kitaev-Heisenberg model with nearest neighbor interactions on the honeycomb lattice using the exact diagonalization of finite systems combined with the cluster mean field approximation, and supplemented by the insights from the linear spin-wave and second--order perturbation theories. This study confirms that by varying the balance between the Heisenberg and Kitaev term, frustrated exchange interactions stabilize in this model four phases with magnetic long range order: N\'eel phase, ferromagnetic phase, and two other phases with coexisting antiferromagnetic and ferromagnetic bonds, zigzag and stripy phases. They are separated by two disordered quantum spin-liquid phases, and the one with ferromagnetic Kitaev interactions has a substantially broader range of stability as the neighboring competing ordered phases, ferromagnetic and stripy, have very weak quantum fluctuations. Focusing on the quantum spin-liquid phases, we study spatial spin correlations and dynamic spin structure factor of the model by the exact diagonalization technique, and discuss the evolution of gapped low-energy spin response across the quantum phase transitions between the disordered spin liquid and magnetic phases with long range order.

Weak randomness in geometrically frustrated systems: spin-glasses

We study the competition between the spin-glass (SG) phase and antiferromagnetic (AF), superantiferromagnetic or ferromagnetic (FE) order in geometrically frustrated systems. We consider a model with two types of frustration: one coming from disordered interactions (J) and another coming from the square-lattice Ising spin system with first-(J1) and second-(J2) neighbor interactions (intrinsic frustration). The disordered interactions are between clusters and they follow the van Hemmen model, which represents a limit of weak frustration. The cluster mean-field approximation is used to treat the short-range intercluster interactions. Results are exhibited in phase diagrams of the temperature T versus J for several values of . When the intrinsic frustration increases, the Néel and Curie temperatures decrease at the same time so that the SG phase appears at a lower J. Moreover, the FE correlations enhance the SG behavior, while AF correlations reduce the SG region at the same level of intrinsic frustration. These results indicate that a weak disorder in geometrically frustrated systems is able to stabilize the SG phase.

Quasiparticle light elements and quantum condensates in nuclear matter

Nuclei in dense matter are influenced by the medium. In the cluster mean field approximation, an effective Schrodinger equation for the A-particle cluster is obtained accounting for the effects of the surrounding medium, such as self-energy and Pauli blocking. Similar to the single-baryon states (free neutrons and protons), the light elements (2 ≤ A ≤ 4, internal quantum state ν) are treated as quasiparticles with energies EA,ν(P; T, nn, np) that depend on the center of mass momentum P⃗, the temperature T, and the total densities nn, np of neutrons and protons, respectively. We consider the composition and thermodynamic properties of nuclear matter at low densities. At low temperatures, quartetting is expected to occur. Consequences for different physical properties of nuclear matter and finite nuclei are discussed.

Stability of superflow in supersolid phases of lattice bosons with dipole-dipole interaction

We investigate the stability of superflow of bosons with isotropic dipole-dipole interactions in a two-dimensional optical lattice. We perform linear stability analyses for the dipolar Bose-Hubbard model in the hardcore boson limit, and show that the superflow can exist in a supersolid phase unless the velocity exceeds a certain critical value and that the critical value is remarkably smaller than that in the standard superfluid phase. Additionally, it is found that there exists a parameter range in which the SS phases are stabilized by a finite superflow. We also discuss the influence of quantum fluctuations on these results within the cluster mean-field approximation.

LIGHT CLUSTERS IN NUCLEAR MATTER

Nuclei in dense matter are influenced by the medium. In the cluster mean-field approximation, an effective Schrodinger equation for the A-nucleon cluster is obtained accounting for the effects of the surrounding medium, such as self-energy and Pauli blocking. Similar to the single-baryon states (free protons and neutrons), the light elements (A ≤ 4) are treated as quasiparticles. Fit formulae are given for the quasiparticle shifts as function of temperature, density, asymmetry, and momentum. Composition, quantum condensates and thermodynamic functions are considered. The relevance for nuclear structure, heavy ion collisions and supernova astrophysics is shown.

Z2-slave-spin theory for strongly correlated fermions

We review a representation of Hubbard-like models that is based on auxiliary pseudospin variables. These pseudospins refer to the local charge modulo two in the original model and display a local ${\mathsf{Z}}_{2}$ gauge freedom. We discuss the associated mean-field theory in a variety of different contexts which are related to the problem of the interaction-driven metal-insulator transition at half-filling including Fermi surface deformation and spectral features beyond the local approximation. Notably, on the mean-field level, the Hubbard bands are derived from the excitations of an Ising model in a transverse field and the quantum critical point of this model is identified with the Brinkman-Rice criticality of the almost localized Fermi liquid state. Nonlocal correlations are included using a cluster mean-field approximation and the Schwinger boson theory for the auxiliary quantum Ising model.

Slave spins away from half filling: Cluster mean-field theory of the Hubbard and extended Hubbard models

A slave-spin representation of fermion operators has recently been proposed for the half-filled single and multiband Hubbard model. We show that with the addition of a gauge variable, the formalism can be extended to finite doping. We solve the resulting spin problem using the cluster mean-field approximation. This approximation takes short-range correlations into account by exact diagonalization on the cluster, whereas long-range correlations beyond the size of clusters are treated at the mean-field level. In the limit where the cluster has only one site and the interaction strength $U$ is infinite, this approach reduces to the Gutzwiller approximation. There are some qualitative differences when the size of the cluster is finite. We first compute the critical $U$ for the Mott transition as a function of a frustrating nearest-neighbor interaction on lattices relevant for various correlated systems, namely, the cobaltates, the layered organic superconductors and the high-temperature superconductors. For the triangular lattice, we also study the extended Hubbard model with nearest-neighbor repulsion. In addition to a uniform metallic state, we find a $\sqrt{(3)}\ifmmode\times\else\texttimes\fi{}\sqrt{(3)}$ charge density wave in a broad doping regime, including commensurate ones. We find that in the large $U$ limit, intersite Coulomb repulsion $V$ strongly suppresses the single-particle weight of the metallic state.

Light nuclei quasiparticle energy shifts in hot and dense nuclear matter

Nuclei in dense matter are influenced by the medium. In the cluster mean-field approximation, an effective Schr\odinger equation for the $A$-particle cluster is obtained accounting for the effects of the correlated medium such as self-energy, Pauli blocking, and Bose enhancement. Similar to the single-baryon states (free neutrons and protons), the light elements ($2\ensuremath{\leqslant}A\ensuremath{\leqslant}4$, internal quantum state \ensuremath{\nu}) are treated as quasiparticles with energies ${E}_{A,\ensuremath{\nu}}(\mathbf{P};T,{n}_{n},{n}_{p})$. These energies depend on the center-of-mass momentum $\mathbf{P}$, as well as temperature $T$ and the total densities ${n}_{n}$, ${n}_{p}$ of neutrons and protons, respectively. No $\ensuremath{\beta}$ equilibrium is considered so that ${n}_{n}$, ${n}_{p}$ (or the corresponding chemical potentials ${\ensuremath{\mu}}_{n}$, ${\ensuremath{\mu}}_{p}$) are fixed independently. For the single-nucleon quasiparticle energy shift, different approximate expressions such as Skyrme or relativistic mean-field approaches are well known. Treating the $A$-particle problem in appropriate approximations, results for the cluster quasiparticle shifts are given. Properties of dense nuclear matter at moderate temperatures in the subsaturation density region considered here are influenced by the composition. This in turn is determined by the cluster quasiparticle energies, in particular the formation of clusters at low densities when the temperature decreases and their dissolution due to Pauli blocking as the density increases. Our finite-temperature Green function approach covers different limiting cases: the low-density region where the model of nuclear statistical equilibrium and virial expansions can be applied and the saturation-density region where a mean-field approach is possible.

Magnetization and magnetic susceptibility of the Ising ferromagnetic/antiferromagnetic superlattice

A linear cluster mean-field approximation is used to study the magnetic properties of the Ising ferromagnetic/antiferromagnetic superlattice, which is composed of a spin-1/2 ferromagnetic monolayer and a spin-1 antiferromagnetic monolayer with a single-ion anisotropy alternatively. By using the transfer matrix method, we calculate the magnetization and the initial magnetic susceptibility as functions of temperature for different interlayer coupling, single-ion anisotropy. We summarize the changing behaviors of the spin structure in ferromagnetic and antiferromagnetic layers and the characteristics of the corresponding magnetic susceptibilities, give the transition temperature as a function of the interlayer exchange coupling for different single-ion anisotropy, and analyze the features of the magnetization and the magnetic susceptibility.

Cluster mean-field approximations with the coherent-anomaly-method analysis for the driven pair contact process with diffusion

The cluster mean-field approximations are performed, up to 13 cluster sizes, to study the critical behavior of the driven pair contact process with diffusion (DPCPD) and its precedent, the PCPD in one dimension. Critical points are estimated by extrapolating our data to the infinite cluster size limit, which are in good accordance with recent simulation results. Within the cluster mean-field approximation scheme, the PCPD and the DPCPD share the same mean-field critical behavior. The application of the coherent anomaly method, however, shows that the two models develop different coherent anomalies, which lead to different true critical scaling. The values of the critical exponents for the particle density, the pair density, the correlation length, and the relaxation time are fairly well estimated for the DPCPD. These results support and complement our recent simulation results for the DPCPD.