Mean-field Phase Diagram Research Articles

Excitonic and nematic instabilities on the surface of topological Kondo insulators

We study the effects of strong electron-electron interactions on the surface of cubic topological Kondo insulators (such as samarium hexaboride, SmB$_6$). Cubic topological Kondo insulators generally support three copies of massless Dirac nodes on the surface, but only two of them are energetically degenerate and exhibit an energy offset relative to the third one. With a tunable chemical potential, when the surface states host electron and hole pockets of comparable size, strong interactions may drive this system into rotational symmetry breaking nematic and translational symmetric breaking excitonic spin- or charge-density-wave phases, depending on the relative chirality of the Dirac cones. Taking a realistic surface band structure into account we analyze the associated Ginzburg-Landau theory and compute the mean field phase diagram for interacting surface states. Beyond mean field theory, this system can be described by a two-component isotropic Ashkin-Teller model at finite temperature, and we outline the phase diagram of this model. Our theory provides a possible explanation of recent measurements which detect a two-fold symmetric magnetoresistance and an upturn in surface resistivity with tunable gate voltage in SmB$_6$. Our discussion can also be germane to other cubic topological insulators, such as ytterbium hexaboride (YbB$_6$), plutonium hexaboride (PuB$_6$).

Extended Bose-Hubbard model in a shaken optical lattice

We study an extended Bose-Hubbard model with next-nearest-neighbor (NNN) hopping in a shaken optical lattice. We show how mean-field phase diagram evolves with the change of NNN hopping amplitude $t_{2}$, which can be easily tuned via shaking amplitude. As $t_{2}$ increases, a $Z_{2}$-symmetry-breaking superfluid ($Z_{2}$SF) phase emerges at the bottom of the Mott lobs. The tricritical points between normal superfluid, $Z_{2}$SF, and Mott insulator (MI) phases are identified. We further demonstrate the tricritical point can be tuned to the tip of the Mott lobe, in which case a new critical behavior has been predicted. Within random-phase approximation, excitation spectra in the three phases are obtained, which indicate how the phase transitions occur.

Reexamination of the mean-field phase diagram of biaxial nematic liquid crystals: Insights from Monte Carlo studies.

Investigations of the phase diagram of biaxial liquid-crystal systems through analyses of general Hamiltonian models within the simplifications of mean-field theory (MFT), as well as by computer simulations based on microscopic models, are directed toward an appreciation of the role of the underlying molecular-level interactions to facilitate its spontaneous condensation into a nematic phase with biaxial symmetry. Continuing experimental challenges in realizing such a system unambiguously, despite encouraging predictions from MFT, for example, are requiring more versatile simulational methodologies capable of providing insights into possible hindering barriers within the system, typically gleaned through its free-energy dependences on relevant observables as the system is driven through the transitions. The recent paper from this group [Kamala Latha et al., Phys. Rev. E 89, 050501(R) (2014)], summarizing the outcome of detailed Monte Carlo simulations carried out employing an entropic sampling technique, suggested a qualitative modification of the MFT phase diagram as the Hamiltonian is asymptotically driven toward the so-called partly repulsive regions. It was argued that the degree of (cross) coupling between the uniaxial and biaxial tensor components of neighboring molecules plays a crucial role in facilitating a ready condensation of the biaxial phase, suggesting that this could be a plausible factor in explaining the experimental difficulties. In this paper, we elaborate this point further, providing additional evidence from curious variations of free-energy profiles with respect to the relevant orientational order parameters, at different temperatures bracketing the phase transitions.

Electronic nematic phase transition in the presence of anisotropy

We study the phase diagram of electronic nematic instability in the presence of xy anisotropy. While a second order transition cannot occur in this case, mean-field theory predicts that a first order transition occurs near van Hove filling and its phase boundary forms a wing structure, which we term a Griffiths wing, referring to his original work of He3-He4 mixtures. When crossing the wing, the anisotropy of the electronic system exhibits a discontinuous change, leading to a meta-nematic transition, i.e., the analog to a meta-magnetic transition in a magnetic system. The upper edge of the wing corresponds to a critical end line, which shows a non-monotonic temperature dependence as a function of the external anisotropy and vanishes at a quantum critical end point for a strong anisotropy. The mean-field phase diagram is, however, very sensitive to fluctuations of the nematic order parameter, yielding a topologically different phase diagram. The Griffiths wing is broken into two pieces. A tiny wing appears close to zero anisotropy and the other is realized for a strong anisotropy. Consequently three quantum critical end points are realized. We discuss that these results can be related to various materials including a cold atom system.

Hard-Core Bosons on a Two-Dimensional Square Optical Superlattice* *Supported by the National Natural Science Foundation of China under Grant Nos. 10904096, 10604024, 11474025, and the Natural Science Foundation of Beijing under Grant No. 1092009

In this work, we theoretically study hard-core bosons on a two-dimensional square optical superlattice at T = 0. First of all, we present the mean field phase diagram of this model in terms of the chemical potential μ and the alternating potential strength Δ. Besides a superfluid (SF) phase at Δ = 0 and a charge density wave (CDW) phase in the large Δ at half filling, we demonstrate that a supersolid (SS) phase emerges in the moderate Δ. Then, we focus on the μ = 0, e.g., half filling case, using large-S semiclassical spin-wave approximation to study the SS to CDW quantum phase transition. In particular, we calculate the ground-state energy and the superfluid density at the level of 1/S correction. We then compare the spin-wave results with the large scale quantum Monte Carlo (QMC) simulations using the cluster stochastic series expansion (CSSE) algorithm, and find that while the spin wave method is intuitive with clear physical pictures, the quantum critical point is quite different from that of numerical results which is believed to be accurate. We suggest that as simple as it is, this model still exhibits strong quantum fluctuations near the quantum critical point beyond the power of semiclassical spin-wave approach.

Striped ferronematic ground states in a spin-orbit-coupledS=1Bose gas

We theoretically establish the mean-field phase diagram of a homogeneous spin-$1$, spin-orbit coupled Bose gas as a function of the spin-dependent interaction parameter, the Raman coupling strength and the quadratic Zeeman shift. We find that the interplay between spin-orbit coupling and spin-dependent interactions leads to the occurrence of ferromagnetic or ferronematic phases which also break translational symmetry. For weak Raman coupling, increasing attractive spin-dependent interactions (as in $^{87}$Rb or $^7$Li) induces a transition from a uniform to a stripe XY ferromagnet (with no nematic order). For repulsive spin-dependent interactions however (as in $^{23}$Na), we find a transition from an $XY$ spin spiral phase ($<S_{z} >= 0$ and uniform total density) with uniaxial nematic order, to a biaxial ferronematic, where the total density, spin vector and nematic director oscillate in real space. We investigate the stability of these phases against the quadratic Zeeman effect, which generally tends to favor uniform phases with either ferromagnetic or nematic order but not both. We discuss the relevance of our results to ongoing experiments on spin-orbit coupled, spinor Bose gases.

Magnetic phase diagram of the Hubbard model in the Lieb lattice

We study the mean-field phase diagram of the repulsive Hubbard model in the Lieb lattice. Far from half-filling, the most stable phases are paramagnetism for low on-site interaction U/t and ferromagnetism for high U/t, as in the case of the mean-field phase diagram of the square lattice Hubbard model obtained by Dzierzawa (1991) [1]. At half-filling, the ground state was found to be ferrimagnetic [a (π,π) spiral phase], in agreement with a theorem by Lieb (1989) [2]. The total magnetization approaches Lieb's prediction as U/t becomes large. As we move away from half-filling, this ferrimagnetic phase becomes a (q1,q1) spiral phase with q1≈π and then undergoes a series of first-order phase transitions, (q1,q1)→(q1,q2)→(q1,0), with q2≈π/2, before becoming ferromagnetic at large U/t or paramagnetic at low U/t.

Phase Diagram of the Kitaev-type Model on a Decorated Honeycomb Lattice in the Isolated Dimer Limit

An effective model in the isolated dimer limit of the Kitaev-type model on a decorated honeycomb lattice is investigated at finite temperature. The ground state of this model is exactly shown to be a chiral spin liquid with spontaneous breaking of time reversal symmetry. We elab- orate the finite-temperature phase diagram by using the mean-field approximation and Monte Carlo simulation. We find that the phase transition between the high-temperature paramagnetic phase and the low-temperature chiral spin liquid phase is always of second order in the Monte Carlo results, although a tricritical point appears in the mean-field phase diagram. The finite-size scaling analysis of the Monte Carlo data suggests that the phase transition belongs to the two-dimensional Ising universality class.

Superfluid-insulator transition of two-dimensional disordered Bose gases

We study the two-dimensional weakly repulsive Bose gas at zero temperature in the presence of correlated disorder. Using large-scale simulations, we show that the low-energy Bogoliubov cumulative density of states remains quadratic up to a critical disorder strength, beyond which a power law with disorder-dependent exponent $\beta<2$ sets in. We associate this threshold behavior with the transition from superfluid to Bose glass, and compare the resulting mean-field phase diagram with scaling laws and the Thomas-Fermi percolation threshold of the mean-field density profile.

Emergent dome of nematic order around a quantum anomalous Hall critical point

We consider a model of spinful fermions on the triangular lattice which exhibits a C=2 Chern insulator (CI) phase with a quantized anomalous Hall effect, sandwiched between two normal insulator (NI) phases. The first NI-CI quantum phase transition is driven by simultaneous mass inversion of a pair of Dirac fermions, with short range interactions being perturbatively irrelevant. The second CI-NI transition is driven by a single quadratic band touching point protected by momentum space topology and C_6 lattice symmetry. A one-loop renormalization group analysis shows that short range interactions lead to a single marginally relevant perturbation at this transition. We obtain the mean field phase diagram of this model incorporating weak repulsive Hubbard interactions, finding an emergent nematic dome around this CI-NI topological phase transition. We discuss the crossovers in the anomalous Hall conductivity at nonzero temperature, and the Landau theory of the quantum and thermal transitions out of the nematic phase. Our results may be relevant to ferromagnetic double perovskite films with spin-orbit coupling which have been proposed to host such a NI-CI transition. Our work provides perhaps the simplest example of an emergent phase near a quantum phase transition.

Effective three-body interactions via photon-assisted tunneling in an optical lattice

We present a simple, experimentally realizable method to make coherent three-body interactions dominate the physics of an ultracold lattice gas. Our scheme employs either lattice modulation or laser-induced tunneling to reduce or turn off two-body interactions in a rotating frame, promoting three-body interactions arising from multi-orbital physics to leading-order processes. This approach provides a route to strongly-correlated phases of lattice gases that are beyond the reach of previously proposed dissipative three-body interactions. In particular, we study the mean-field phase diagram for spinless bosons with three- and two- body interactions, and provide a roadmap to dimer states of varying character in 1D. This new toolset should be immediately applicable in state-of-the-art cold atom experiments.

Macroscopic Phase Separation, Modulated Phases, and Microemulsions: A Unified Picture of Rafts

We simulate a simple phenomenological model describing phase behavior in a multicomponent membrane, a model capable of producing macroscopic phase separation, modulated phases, and microemulsions, all of which have been discussed in terms of raft phenomena. We show that one effect of thermal fluctuations on the mean-field phase diagram is that it permits a direct transition between either one of the coexisting liquid phases to a microemulsion. This implies that one system exhibiting phase separation can be related to a similar system exhibiting the heterogeneities characteristic of a microemulsion. The two systems could differ in their average membrane composition or in the relative compositions of their exoplasmic and cytoplasmic leaves. The model provides a unified description of these raft-associated phenomena.

Phase Diagram of a $$^6Li$$ 6 L i – $$^{40}K$$ 40 K Mixture in a Square Lattice

We calculate the mean-field phase diagram for an attractive interacting Fermi mixture of Lithium-6 ( $$^6Li$$ ) and Potassium-40 ( $$^{40}K$$ ) atoms in a two-dimensional optical lattice at finite temperatures. The polarization versus temperature diagrams show that there are three phases: the Sarma phase (in which the condensed pairs have zero net momentum), the Fulde–Ferrell (FF) phase (in which the pairs have non-zero net momentum), and the normal phase (in which the Helmholtz free energy is minimized for gapless phase). The zero polarization line is the conventional Bardeen–Cooper–Schrieffer state. The phase diagram contains a Lifshitz point. When the interaction strength is increased, the Lifshitz point moves toward the higher temperatures and larger polarizations. Moreover, contrary to the phase diagram of population-imbalanced $$^6Li$$ Fermi gas, where the phase separation appears for low polarizations, we found the existence of a polarization window for the FF phase. This means that as soon as the system is polarized it goes into the FF phase if the temperature is low enough. This polarization window is larger for a majority of $$^{40}K$$ atoms compared to the majority of $$^6Li$$ atoms. We also find that the largest polarization that the system can support before it becomes a normal fluid is larger for majority of $$^6Li$$ atoms.

Periodic ordering of clusters and stripes in a two-dimensional lattice model. I. Ground state, mean-field phase diagram and structure of the disordered phases

The short-range attraction and long-range repulsion between nanoparticles or macromolecules can lead to spontaneous pattern formation on solid surfaces, fluid interfaces, or membranes. In order to study the self-assembly in such systems we consider a triangular lattice model with nearest-neighbor attraction and third-neighbor repulsion. At the ground state of the model (T = 0) the lattice is empty for small values of the chemical potential μ, and fully occupied for large μ. For intermediate values of μ periodically distributed clusters, bubbles, or stripes appear if the repulsion is sufficiently strong. At the phase coexistences between the vacuum and the ordered cluster phases and between the cluster and the lamellar (stripe) phases the entropy per site does not vanish. As a consequence of this ground state degeneracy, disordered fluid phases consisting of clusters or stripes are stable, and the surface tension vanishes. For T > 0 we construct the phase diagram in the mean-field approximation and calculate the correlation function in the self-consistent Brazovskii-type field theory.

Spiral ferrimagnetic phases in the two-dimensional Hubbard model

We address the possibility of spiral ferrimagnetic phases in the mean-field phase diagram of the two-dimensional (2D) Hubbard model. For intermediate values of the interaction U (6≲U/t≲11) and doping n, a spiral ferrimagnetic phase is the most stable phase in the (n,U) phase diagram. Higher values of U lead to a non-spiral ferrimagnetic phase. If phase separation is allowed and the chemical potential μ replaces the doping n as the independent variable, the (μ,U) phase diagram displays, in a considerable region, a spiral (for 6≲U/t≲11) and non-spiral (for higher values of U) ferrimagnetic phase with fixed particle density, n=0.5, reflecting the opening of an energy gap in the mean-field quasi-particle bands

Fulde-Ferrell states and Berezinskii-Kosterlitz-Thouless phase transition in two-dimensional imbalanced Fermi gases

We study the superfluid properties of two-dimensional spin-population-imbalanced Fermi gases to explore the interplay between the Berezinskii-Kosterlitz-Thouless (BKT) phase transition and the possible instability towards the Fulde-Ferrell (FF) state. By the mean-field approximation together with quantum fluctuations, we obtain phase diagrams as functions of temperature, chemical potential imbalance, and binding energy. We find that the fluctuations change the mean-field phase diagram significantly. We also address possible effects of the phase separation and/or the anisotropic FF phase to the BKT mechanism. The superfluid density tensor of the FF state is obtained, and its transverse component is found always vanishing. This causes divergent fluctuations and possibly precludes the existence of the FF state at any nonzero temperature.

Macroscopic Phase Separation, Modulated Phases, and Microemulsions: a Unified Picture of Rafts

We simulate a simple phenomenological model describing phase behavior in a multicomponent membrane, a model capable of producing macroscopic phase separation, modulated phases, and microemulsions, all of which have been discussed in terms of raft phenomena. We show that one effect of thermal fluctuations on the mean-field phase diagram is that it permits a direct transition between either one of the coexisting liquid phases to a microemulsion. This implies that one system exhibiting phase separation can be related to a similar system exhibiting the heterogeneities characteristic of a microemulsion. The two systems could differ in their average membrane composition or in the relative compositions of their exoplasmic and cytoplasmic leaves. The model provides a unified description of these raft-associated phenomena.

Attempts to form the 10-nm-order pitch of self-assembled nanodots using PS-PDMS block copolymer

Block copolymer (BCP) self-assembly exhibits its ability to form various nanostructures with a size down to 3 nm, which is particularly attractive for emerging technologies such as bit patterned media (BPM). Poly(styrene-b-dimethyl siloxane) (PS-PDMS) has been acknowledged as the most promising block copolymer for self-assembly fabrication due to its possibility to form nanopattern with a fine pitch, high etching selectivity, and its characteristic of robustness for pattern transfer. Here, we attempt to form PS-PDMS self-assembled nanodot array with a 10-nm-order pitch in order to satisfy the demand of low cost technique to form ultrahigh density nanodot array for BPM, which is regarded as the next-generation magnetic recording media, and for quantum devices such as the third-generation quantum dot photovoltaic cell and future battery cell. In this study, self-assembled nanodot array on a large area with pitches of 11 nm ( σ = 2.08 nm) and 10 nm ( σ = 1.61 nm) was formed using PS-PDMS with molecular weights of 5600–1300 g/mol (minority block volume fraction f PDMS = 19.8%) and 4700–1200 g/mol (f PDMS = 21.4%), respectively. In experiments, it was shown that some critical parameters, such as the thickness of PS-PDMS film, the treatment of the substrate surface, and annealing condition, played crucial roles in forming 10-nm-order size of self-assembled nanodot array using PS-PDMS. The relationships between pitches of PS-PDMS nanodot array and the product of the total number of segments and the Flory-Huggins segmental interaction parameter (χN) obtained by calculations and experiments will be discussed. Based on the position of PS-PDMS on mean-field phase diagram for BCP melts, the possibility to form nanodot array with a pitch of less than 10 nm is described. This study promises to open way toward the fabrication of more than 7.45 Tbit/in. 2 storage devices and the application of quantum devices.

Interaction-driven phases in the half-filled spinless honeycomb lattice from exact diagonalization

We investigate the fate of interaction driven phases in the half-filled honeycomb lattice for finite systems via exact diagonalization with nearest and next nearest neighbour interactions. We find evidence for a charge density wave phase, a Kekul\'e bond order and a sublattice charge modulated phase in agreement with previously reported mean-field phase diagrams. No clear sign of an interaction driven Chern insulator phase (Haldane phase) is found despite being predicted by the same mean-field analysis. We characterize these phases by their ground state degeneracy and by calculating charge order and bond order correlation functions.

Theory of Antiferromagnetic Order in High-Tc Oxides: An Approach Based on Ginzburg–Landau Expansion

The mean-field phase diagram of antiferromagnetic order in t-J model has been examined, using the free energy obtained by Ginzburg-Landau (GL) expansion. We extended the usual GL theory in two ways: First, we have included higher order terms with respect to the spatial derivative (or wave number) to incorporate the incommensurate antiferromagnetic order. Second, we have also included higher order terms with respect to the order parameter amplitude, in order to treat the first order phase transition between paramagnetic and antiferromagnetic phase, which appears at some doping rates. We found the possibility of tricritical point and critical endpoint in the magnetic phase diagram of the high-Tc oxides associated with the commensurate and incommensurate antiferromagnetic order. The possible effects of thermal fluctuations and randomness (spin glass) are also discussed qualitatively based on the GL free energy.