Global Phase Diagram Research Articles

Weyl-Kondo semimetals in nonsymmorphic systems

There is considerable current interest to explore electronic topology in strongly correlated metals, with heavy fermion systems providing a promising setting. Recently, a Weyl-Kondo semimetal phase has been concurrently discovered in theoretical and experimental studies. The theoretical work was carried out in a Kondo lattice model that is time-reversal invariant but inversion-symmetry breaking. In this paper, we show in some detail how nonsymmorphic space-group symmetry and strong correlations cooperate to form Weyl nodal excitations with highly reduced velocity and pin the resulting Weyl nodes to the Fermi energy. A tilted variation of the Weyl-Kondo solution is further analyzed here, following the recent consideration of such effect in the context of understanding a large spontaneous Hall effect in Ce$_3$Bi$_4$Pd$_3$ (Dzsaber et al., arXiv:1811.02819). We discuss the implications of our results for the enrichment of the global phase diagram of heavy fermion metals, and for the space-group symmetry enforcement of topological semimetals in other strongly correlated settings.

Simulating bosonic Chern insulators in one-dimensional optical superlattices

We study the topological properties of an extended Bose-Hubbard model with cyclically modulated hopping and on-site potential parameters, which can be realized with ultracold bosonic atoms in a one-dimensional optical superlattice. We show that the interacting bosonic chain at half filling and in the deep Mott insulating regime can simulate bosonic Chern insulators with a topological phase diagram similar to that of the Haldane model of noninteracting fermions. Furthermore, we explore the topological properties of the ground state by calculating the many-body Chern number, the quasiparticle energy spectrum with gapless edge modes, the topological pumping of the interacting bosons, and the topological phase transition from normal (trivial) to topological Mott insulators. We also present the global phase diagram of the many-body ground state, which contains a superfluid phase and two Mott insulating phases with trivial (a zero Chern number) and nontrivial topologies (a nonzero Chern number), respectively.

Measurement-induced phase transition: A case study in the nonintegrable model by density-matrix renormalization group calculations

We study the effect of local projective measurements on the quantum quench dynamics. As a concrete example, a one-dimensional Bose-Hubbard model is simulated by the matrix product state and time-evolving block decimation. We map out a global phase diagram in terms of the measurement rate in spatial space and time domain, which demonstrates a volume-to-area law entanglement phase transition. When the measurement rate reaches the critical value, we observe a logarithmic growth of entanglement entropy as the subsystem size or evolved time increases. Moreover, we find that the probability distribution of the single-site entanglement entropy distinguishes the volume and area law phases, similar to the case of disorder-induced many-body localization. We also investigate the scaling behavior of entanglement entropy and mutual information between two separated sites, which is indicative of a single universality class and thus suggests a possible unified description of this transition.

Global phase diagram of the one-dimensional Sachdev-Ye-Kitaev model at finite N

Many key features of the higher-dimensional Sachdev-Ye-Kitaev (SYK) model at {\it finite} $N$ remain unknown. Here we study the SYK chain consisting of $N$ ($N$$\ge$$2$) fermions per site with random interactions and hoppings between neighboring sites. In the limit of vanishing SYK interactions, from both supersymmetric field theory analysis and numerical calculations we find that the random hopping model exhibits Anderson localization at finite $N$, irrespective of the parity of $N$. Moreover, the localization length scales linearly with N, implying no Anderson localization \textit{only} at $N\!=\!\infty$. For finite SYK interaction $J$ , from the exact diagonalization we show that there is a dynamic phase transition between many-body localization and thermal diffusion as $J$ exceeds a critical value $J_c$. In addition, we find that the critical value $J_c$ decreases with the increase of $N$, qualitatively consistent with the analytical result of $J_c/t \!\propto\! \frac{1}{N^{5/2}\log N}$ derived from the weakly interacting limit.

Symmetry-breaking morphological transitions at chemically nanopatterned walls.

We study the structure and morphological changes of fluids that are in contact with solid composites formed by alternating and microscopically wide stripes of two different materials. One type of the stripes interacts with the fluid via long-ranged Lennard-Jones-like potential and tends to be completely wet, while the other type is purely repulsive and thus tends to be completely dry. We consider closed systems with a fixed number of particles that allows for stabilization of fluid configurations breaking the lateral symmetry of the wall potential. These include liquid morphologies corresponding to a sessile drop that is formed by a sequence of bridging transitions that connect neighboring wet regions adsorbed at the attractive stripes. We study the character of the transitions depending on the wall composition, stripes width, and system size. Using a (classical) nonlocal density functional theory (DFT), we show that the transitions between different liquid morphologies are typically weakly first-order but become rounded if the wavelength of the system is lower than a certain critical value L_{c}. We also argue that in the thermodynamic limit, i.e., for macroscopically large systems, the wall becomes wet via an infinite sequence of first-order bridging transitions that are, however, getting rapidly weaker and weaker and eventually become indistinguishable from a continuous process as the size of the bridging drop increases. Finally, we construct the global phase diagram and study the density dependence of the contact angle of the bridging drops using DFT density profiles and a simple macroscopic theory.

Valence transition in topological Kondo insulator

We investigate the valence transition in three-dimensional topological Kondo insulator through slave-boson analysis of periodic Anderson model. By including the effect of intra-atomic Coulomb correlation between conduction and local electrons, we find a first-order valence transition from Kondo region to mixed valence state upon ascending of local f- level above a critical , and this valence transition usually occurs very close to or simultaneously with a topological transition. Near the parameter region of zero-temperature valence transition, rise of temperature can generate a thermal valence transition from mixed valence to Kondo region, accompanied by a first-order topological transition. Remarkably, above a critical which is considerably smaller than that generating paramagnetic valence transition, the original continuous antiferromagnetic transition is shifted to first order one, at which a discontinuous valence shift takes place. Upon increasing , the paramagnetic valence transition approaches then converges with the first-order antiferromagnetic transition, leaving a significant valence shift on the magnetic boundary. The continuous antiferromagnetic transition, first-order antiferromagnetic transition, paramagnetic valence transition and topological transitions are all summarized in a global phase diagram. Our proposed exotic transition processes can help to understand the thermal valence variation as well as the valence shift around the pressure-induced magnetic transition in topological Kondo insulator candidates and in other heavy-fermion systems.

Construction of global phase diagrams for binary mixtures with equal and unequal size of molecules by using the modified van der Waals model

The global phase diagram or master diagram is constructed for binary mixtures consist of the equal and unequal size of molecules by using the modified van der Waals model. The Griffiths shield region is also presented on the master diagram. The influence of various size differences ratio of molecules on the master diagram is investigated and discussed. It is observed that the GPD are symmetrical around ζ=0 for the equal-size of molecules and the deterioration in the symmetric behavior of GPD increases as differences of size of molecules increase. From the master diagram, all possible main types of phase behavior for every given interaction energy parameters and various size differences ratio of molecules can be seen directly without long and difficult calculations.

Heavy fermion quantum criticality at dilute carrier limit in CeNi2\u2212\u03b4(As1\u2212xPx)2

We study the quantum phase transitions in the nickel pnctides, CeNi2−δ(As1−xPx)2 (δ ≈ 0.07–0.22) polycrystalline samples. This series displays the distinct heavy fermion behavior in the rarely studied parameter regime of dilute carrier limit. We systematically investigate the magnetization, specific heat and electrical transport down to low temperatures. Upon increasing the P-content, the antiferromagnetic order of the Ce-4f moment is suppressed continuously and vanishes at xc ~ 0.55. At this doping, the temperature dependences of the specific heat and longitudinal resistivity display non-Fermi liquid behavior. Both the residual resistivity ρ0 and the Sommerfeld coefficient γ0 are sharply peaked around xc. When the P-content reaches close to 100%, we observe a clear low-temperature crossover into the Fermi liquid regime. In contrast to what happens in the parent compound x = 0.0 as a function of pressure, we find a surprising result that the non-Fermi liquid behavior persists over a nonzero range of doping concentration, xc < x < 0.9. In this doping range, at the lowest measured temperatures, the temperature dependence of the specific-heat coefficient is logarithmically divergent and that of the electrical resistivity is linear. We discuss the properties of CeNi2−δ(As1−xPx)2 in comparison with those of its 1111 counterpart, CeNi(As1−xPx)O. Our results indicate a non-Fermi liquid phase in the global phase diagram of heavy fermion metals.

Manipulation of cholesteric liquid crystal phase behavior and molecular assembly by molecular chirality.

Molecular simulation is used to study the effect of molecular chirality on liquid crystalline phase transition and molecular assembly behavior. Based on a flexible chain (FCh) model with helical arrangement of side beads, the phase behavior of FCh models with various molecular chiralities are studied as functions of pressure (or density). By modifying the molecular chirality of FCh, we can manipulate the relative stability of the nematic and cholesteric phases continuously; and we found that increasing molecular chirality may destabilize cholesteric order due to the effective reduction of chiral interactions. A semismectic phase is identified in the high-density region, in which the two-dimensional fluid layers overlap due to shift alignment formed by FCh particles. The global phase diagram of the FCh model is constructed and the potential energy surface is calculated to elucidate the formation of cholesteric phase in terms of two-body interactions.

Disorder-induced Chern insulator in the Harper-Hofstadter-Hatsugai model

We study the effects of disorder on the topological Chern insulating phase in the Harper--Hofstadter--Hatsugai (HHH) model. The model with half flux has a bulk band gap and thus exhibits a nontrivial topological phase. We consider two typical types of disorder: on-site random disorder and the Aubry--Andre type quasi-periodic potential. Using the coupling matrix method, we clarify the global topological phase diagram in terms of the Chern number. The disorder modifies the gap closing behavior of the system. This modification induces the Chern insulating phase even in the trivial phase parameter regime of the system in the clean limit. Moreover, we consider an interacting Rice--Mele model with disorder, which can be obtained by dimensional reduction of the HHH model. Moderately strong disorder leads to an increase in revival events of the Chern insulator at a specific parameter point.

Thermodynamic properties of a long-range interacting Bose system in staggered magnetic field

This paper provides a brief introduction to the thermodynamic properties of long-range interaction Bose systems in the staggered magnetic field by using the microcanonical approach. The entropy, temperature, heat capacity, phase translation are analyzed separately, and we constructed global phase diagram of the system. First-order phase transition, second-order phase transition, and negative specific heat can be observed in such system.

Excitonic pairing of two-dimensional Dirac fermions near the antiferromagnetic quantum critical point

Two-dimensional Dirac fermions are subjected to two types of interactions, namely the long-range Coulomb interaction and the short-range on-site interaction. The former induces excitonic pairing if its strength $\alpha$ is larger than some critical value $\alpha_c$, whereas the latter drives an antiferromagnetic Mott transition when its strength $U$ exceeds a threshold $U_c$. Here, we study the impacts of the interplay of these two interactions on excitonic pairing with the Dyson-Schwinger equation approach. We find that the critical value $\alpha_c$ is increased by weak short-range interaction. As $U$ increases to approach $U_c$, the quantum fluctuation of antiferromagnetic order parameter becomes important and interacts with the Dirac fermions via the Yukawa coupling. After treating the Coulomb interaction and Yukawa coupling interaction on an equal footing, we show that $\alpha_c$ is substantially increased as $U \rightarrow U_c$. Thus, the excitonic pairing is strongly suppressed near the antiferromagnetic quantum critical point. We obtain a global phase diagram on the $U$-$\alpha$ plane, and illustrate that the excitonic insulating and antiferromagnetic phases are separated by an intermediate semimetal phase. These results provide a possible explanation of the discrepancy between recent theoretical progress on excitonic gap generation and existing experiments in suspended graphene.

Global phase diagram of a spin–orbit-coupled Kondo lattice model on the honeycomb lattice**Project supported by the Ministry of Science and Technology of China, the National Key R&D Program of China (Grant No. 2016YFA0300504), the National Natural Science Foundation of China (Grant No. 11674392), and the Research Funds of Remnin University of China (Grant No. 18XNLG24). Work at Rice was in

Motivated by the growing interest in the novel quantum phases in materials with strong electron correlations and spin–orbit coupling, we study the interplay among the spin–orbit coupling, Kondo interaction, and magnetic frustration of a Kondo lattice model on a two-dimensional honeycomb lattice. We calculate the renormalized electronic structure and correlation functions at the saddle point based on a fermionic representation of the spin operators. We find a global phase diagram of the model at half-filling, which contains a variety of phases due to the competing interactions. In addition to a Kondo insulator, there is a topological insulator with valence bond solid correlations in the spin sector, and two antiferromagnetic phases. Due to the competition between the spin–orbit coupling and Kondo interaction, the direction of the magnetic moments in the antiferromagnetic phases can be either within or perpendicular to the lattice plane. The latter antiferromagnetic state is topologically nontrivial for moderate and strong spin–orbit couplings.

Global phase diagrams of run-and-tumble dynamics: equidistribution, waves, and blowup

For spatially one-dimensional run-and-tumble dynamics with mass conservation we develop a coarse phase diagram, that discriminates between global decay to equidistributed constant states, existence of spatially non-trivial waves, and finite time blowup of solutions. Motivated by counter-migrating ripples of high and low population density and fruiting body formation in myxobacteria, we identify phase boundaries as particular critical tumbling dynamics that allow for switching between these spatio-temporal phases upon slight changes in mass densities or parameter values.

Two-dimensional ground-state mapping of a Mott-Hubbard system in a flexible field-effect device.

A Mott insulator sometimes induces unconventional superconductivity in its neighbors when doped and/or pressurized. Because the phase diagram should be strongly related to the microscopic mechanism of the superconductivity, it is important to obtain the global phase diagram surrounding the Mott insulating state. However, the parameter available for controlling the ground state of most Mott insulating materials is one-dimensional owing to technical limitations. Here, we present a two-dimensional ground-state mapping for a Mott insulator using an organic field-effect device by simultaneously tuning the bandwidth and bandfilling. The observed phase diagram showed many unexpected features such as an abrupt first-order superconducting transition under electron doping, a recurrent insulating phase in the heavily electron-doped region, and a nearly constant superconducting transition temperature in a wide parameter range. These results are expected to contribute toward elucidating one of the standard solutions for the Mott-Hubbard model.

Thermodynamic analysis of a long-range interacting spin system

A long-range interacting Fermi chain placed in the uniform and the staggered magnetic field is studied via the micro-canonical approach. The relation between the entropy and the energy of the system is obtained by counting the number of microscopic states. We find that this system is non-ergodic and can exhibit first-order phase transition, second-order phase transition, or both. The microcanonical ensemble predicts negative specific heat regions and temperature jumps. Moreover, the global phase diagram of the system is constructed.

Kitaev-like honeycomb magnets: Global phase behavior and emergent effective models

Compounds of transition metal ions with strong spin-orbit coupling recently attracted attention due to the possibility to host frustrated bond-dependent anisotropic magnetic interactions. In general, such interactions lead to complex phase diagrams that may include exotic phases, e.g. the Kitaev spin liquid. Here we report on our comprehensive analysis of the global phase diagram of the extended Kitaev-Heisenberg model relevant to honeycomb lattice compounds Na2IrO3 and alpha-RuCl3. We have utilized recently developed method based on spin coherent states that enabled us to resolve arbitrary spin patterns in the cluster ground states obtained by exact diagonalization. Global trends in the phase diagram are understood in combination with the analytical mappings of the Hamiltonian that uncover peculiar links to known models - Heisenberg, Ising, Kitaev, or compass models on the honeycomb lattice - or reveal entire manifolds of exact fluctuation-free ground states. Finally, our study can serve as a methodological example that can be applied to other spin models with complex bond-dependent non-Heisenberg interactions.

Magnetic and topological transitions in three-dimensional topological Kondo insulator☆☆Supported by the National Natural Science Foundation of China under Grant Nos 11764010, 11504061, 11564008, 11704084, and 11704166, the Natural Science Foundation of Guangxi Province under Grant Nos 2017GXNSFAA198169 and 2017GXNSFBA198115, and the SPC-Lab Research Fund under Grant No XKFZ201605.

Using an extended slave-boson method, we draw a global phase diagram summarizing both magnetic phases and paramagnetic (PM) topological insulators (TIs) in a three-dimensional topological Kondo insulator (TKI). By including electron hopping (EH) up to the third neighbors, we identify four strong TI (STI) phases and two weak TI (WTI) phases. Then, the PM phase diagrams characterizing topological transitions between these TIs are depicted as functions of EH, f-electron energy level, and hybridization constant. We also find an insulator–metal transition from an STI phase that has surface Fermi rings and spin textures in qualitative agreement with the TKI candidate SmB6. In the weak hybridization regime, antiferromagnetic (AF) order naturally arises in the phase diagrams. Depending on how the magnetic boundary crosses the PM topological transition lines, AF phases are classified into the AF topological insulator (AFTI) and the non-topological AF insulator, according to their indices. In two small regions of parameter space, two distinct topological transition processes between AF phases occur, leading to two types of AFTIs showing distinguishable surface dispersions around their Dirac points.

Lower lower-critical spin-glass dimension from quenched mixed-spatial-dimensional spin glasses

By quenched-randomly mixing local units of different spatial dimensionalities, we have studied Ising spin-glass systems on hierarchical lattices continuously in dimensionalities 1 =< d =< 3. The global phase diagram in temperature, antiferromagnetic bond concentration, and spatial dimensionality is calculated. We find that, as dimension is lowered, the spin-glass phase disappears to zero temperature at the lower-critical dimension d_c=2.431. Our system being a physically realizable system, this sets an upper limit to the lower-critical dimension in general for the Ising spin-glass phase. As dimension is lowered towards d_c, the spin-glass critical temperature continuously goes to zero, but the spin-glass chaos fully sustains to the brink of the disappearance of the spin-glass phase. The Lyapunov exponent, measuring the strength of chaos, is thus largely unaffected by the approach to d_c and shows a discontinuity to zero at d_c.

Global Phase Diagram of a Dirty Weyl Liquid and Emergent Superuniversality

Pursuing complementary field-theoretic and numerical methods, we here paint the global phase diagram of a three-dimensional dirty Weyl system. The generalized Harris criterion, augmented by a perturbative renormalization-group (RG) analysis shows that weak disorder is an irrelevant perturbation at the Weyl semimetal(WSM)-insulator quantum critical point (QCP). But, a metallic phase sets in through a quantum phase transition (QPT) at strong disorder across a multicritical point (MCP). The field theoretic predictions for the correlation length exponent $\nu=2$ and dynamic scaling exponent $z=5/4$ at this MCP are in good agreement with the ones extracted numerically, yielding $\nu=1.98 \pm 0.10$ and $z=1.26 \pm 0.05$, from the scaling of the average density of states (DOS). Deep inside the WSM phase, generic disorder is also an irrelevant perturbation, while a metallic phase appears at strong disorder through a QPT. We here demonstrate that in the presence of generic, but strong disorder the WSM-metal QPT is ultimately always characterized by the exponents $\nu=1$ and $z=3/2$ (to one-loop order), originating from intra-node or chiral symmetric (e.g., regular and axial potential) disorder. We here anchor such emergent \emph{chiral superuniversality} through complementary RG calculations, controlled via $\epsilon$-expansions, and numerical analysis of average DOS across WSM-metal QPT. In addition, we also discuss a subsequent QPT (at even stronger disorder) of a Weyl metal into an Anderson insulator by numerically computing the typical DOS at zero energy. The scaling behavior of various physical observables, such as residue of quasiparticle pole, dynamic conductivity, specific heat, Gr$\ddot{\mbox{u}}$neisen ratio, inside various phases as well as across various QPTs in the global phase diagram of a dirty Weyl liquid are discussed.