Global Phase Diagram Research Articles

Revealing the phase diagram of Kitaev materials by machine learning: Cooperation and competition between spin liquids

Kitaev materials are promising materials for hosting quantum spin liquids and investigating the interplay of topological and symmetry-breaking phases. We use an unsupervised and interpretable machine-learning method, the tensorial-kernel support vector machine, to study the honeycomb Kitaev-$\Gamma$ model in a magnetic field. Our machine learns the global classical phase diagram and the associated analytical order parameters, including several distinct spin liquids, two exotic $S_3$ magnets, and two modulated $S_3 \times Z_3$ magnets. We find that the extension of Kitaev spin liquids and a field-induced suppression of magnetic order already occur in the large-$S$ limit, implying that critical parts of the physics of Kitaev materials can be understood at the classical level. Moreover, the two $S_3 \times Z_3$ orders are induced by competition between Kitaev and $\Gamma$ spin liquids and feature a different type of spin-lattice entangled modulation, which requires a matrix description instead of scalar phase factors. Our work provides a direct instance of a machine detecting new phases and paves the way towards the development of automated tools to explore unsolved problems in many-body physics.

Anisotropy-independent packing of confined hard ellipses

We have examined the close-packed structure and ordering properties of hard ellipses between two parallel hard walls by using geometrical conjectures and Monte Carlo simulations. Starting from closely packed hard disk structures, we discover two competing densest packings of ellipses with the stretching of hard disks into different directions. We find that parallel and tilted close-packed structures alternate with widening pore width up to the two-dimensional bulk limit, where both structures produce the same close packing value (η=π/12). Our results highlight that the densest packing does not depend on the aspect ratio of the ellipse. This universal behavior is confirmed for three different aspect ratios (κ=2, 3, and 4) using replica exchange Monte Carlo simulation. Our simulation results show that even the global phase diagram is universal, where layering transitions between parallel structures and tilted-parallel structural changes are present.

Comprehensive study of the global phase diagram of the J−K−Γ model on a triangular lattice

The celebrated Kitaev honeycomb model provides an analytically tractable example with an exact quantum spin liquid ground state. While in real materials, other types of interactions besides the Kitaev coupling ($K$) are present, such as the Heisenberg ($J$) and symmetric off-diagonal ($\Gamma$) terms, and these interactions can also be generalized to a triangular lattice. Here, we carry out a comprehensive study of the $J$-$K$-$\Gamma$ model on the triangular lattice covering the full parameters region, using the combination of the exact diagonalization, classical Monte Carlo and analytic methods. In the HK limit ($\Gamma=0$), we find five quantum phases which are quite similar to their classical counterparts. Among them, the stripe-A and dual N\'{e}el phase are robust against the $\Gamma$ term, in particular the stripe-A extends to the region connecting the $K=-1$ and $K=1$ for $\Gamma<0$. Though the 120$^\circ$ N\'{e}el phase also extends to a finite $\Gamma$, its region has been largely reduced compared to the previous classical result. Interestingly, the ferromagnetic (dubbed as FM-A) phase and the stripe-B phase are unstable in response to an infinitesimal $\Gamma$ interaction. Moreover, we find five new phases for $\Gamma\ne 0$ which are elaborated by both the quantum and classical numerical methods. Part of the space previously identified as 120$^\circ$ N\'{e}el phase in the classical study is found to give way to the modulated stripe phase. Depending on the sign of the $\Gamma$, the FM-A phase transits into the FM-B ($\Gamma>0$) and FM-C ($\Gamma<0$) phase with different spin orientations, and the stripe-B phase transits into the stripe-C ($\Gamma>0$) and stripe-A ($\Gamma<0$). Around the positive $\Gamma$ point, due to the interplay of the Heisenberg, Kiatev and $\Gamma$ interactions, we find a possible quantum spin liquid with a continuum in spin excitations.

Zeroth order phase transition induced by ergodicity breaking in a mean-field system

A spin chain model with mean-field interactions is studied within the microcanonical ensemble. Under local microcanonical dynamics, gaps in the space of extensive variables can be open up leading to the ergodicity breaking of this system. As a consequence, our mean-field system can exhibit the zero-order phase transition accompanied with an entropy jump at the transition point. Moreover, the global phase diagram of the system is constructed.

On the liquid demixing of water + elastin-like polypeptide mixtures: bimodal re-entrant phase behaviour.

Water + elastin-like polypeptides (ELPs) exhibit a transition temperature below which the chains transform from collapsed to expanded states, reminiscent of the cold denaturation of proteins. This conformational change coincides with liquid-liquid phase separation. A statistical-thermodynamics theory is used to model the fluid-phase behavior of ELPs in aqueous solution and to extrapolate the behavior at ambient conditions over a range of pressures. At low pressures, closed-loop liquid-liquid equilibrium phase behavior is found, which is consistent with that of other hydrogen-bonding solvent + polymer mixtures. At pressures evocative of deep-sea conditions, liquid-liquid immiscibility bounded by two lower critical solution temperatures (LCSTs) is predicted. As pressure is increased further, the system exhibits two separate regions of closed-loop of liquid-liquid equilibrium (LLE). The observation of bimodal LCSTs and two re-entrant LLE regions herald a new type of binary global phase diagram: Type XII. At high-ELP concentrations the predicted phase diagram resembles a protein pressure denaturation diagram; possible "molten-globule"-like states are observed at low concentration.

Emergent chiral symmetry in a three-dimensional interacting Dirac liquid

We compute the effects of strong Hubbardlike local electronic interactions on three-dimensional four-component massless Dirac fermions, which in a noninteracting system possess a microscopic global U(1) ⊗ SU(2) chiral symmetry. A concrete lattice realization of such chiral Dirac excitations is presented, and the role of electron-electron interactions is studied by performing a field theoretic renormalization group (RG) analysis, controlled by a small parameter ϵ with ϵ = d−1, about the lower-critical one spatial dimension. Besides the noninteracting Gaussian fixed point, the system supports four quantum critical and four bicritical points at nonvanishing interaction couplings ∼ ϵ. Even though the chiral symmetry is absent in the interacting model, it gets restored (either partially or fully) at various RG fixed points as emergent phenomena. A representative cut of the global phase diagram displays a confluence of scalar and pseudoscalar excitonic and superconducting (such as the s-wave and p-wave) mass ordered phases, manifesting restoration of (a) chiral U(1) symmetry between two excitonic masses for repulsive interactions and (b) pseudospin SU(2) symmetry between scalar or pseudoscalar excitonic and superconducting masses for attractive interactions. Finally, we perturbatively study the effects of weak rotational symmetry breaking on the stability of various RG fixed points.

Screening Masses Towards Chiral Limit

A possible effective restoration of the anomalous $U_A(1)$ symmetry would have a non-trivial effect on the global phase diagram of QCD. In this work we investigate the effective restoration of the $U_A(1)$ through the calculation of scalar and pseudo-scalar screening masses and corresponding susceptibilities, for physical and lower than physical pion masses. Calculations have been performed in (2+1)-flavor HISQ discretization scheme with a physical value of the strange quark mass. Preliminary calculations of the continuum extrapolated scalar and pseudo-scalar masses are presented, based on lattices with three different temporal extent. Non-trivial structure of the difference between scalar and pseudo-scalar susceptibilites are discussed for $N_\tau=8$ lattices.

Fermi Surface Reconstruction without Symmetry Breaking

We present a sign-problem free quantum Monte Carlo study of a model that exhibits quantum phase transitions without symmetry breaking and associated changes in the size of the Fermi surface. The model is an Ising gauge theory on the square lattice coupled to an Ising matter field and spinful `orthogonal' fermions at half-filling, both carrying Ising gauge charges. In contrast to previous studies, our model hosts an electron-like, gauge-neutral fermion excitation providing access to Fermi liquid phases. One of the phases of the model is a previously studied orthogonal semi-metal, which has $\mathbb{Z}_2$ topological order, and Luttinger-volume violating Fermi points with gapless orthogonal fermion excitations. We elucidate the global phase diagram of the model: along with a conventional Fermi liquid phase with a large Luttinger-volume Fermi surface, we also find a `deconfined' Fermi liquid in which the large Fermi surface co-exists with fractionalized excitations. We present results for the electron spectral function, showing its evolution from the orthogonal semi-metal with a spectral weight near momenta $\{\pm \pi/2, \pm \pi/2\}$, to a large Fermi surface.

Non-Hermitian effects of the intrinsic signs in topologically ordered wavefunctions

Negative signs in many-body wavefunctions play an important role in quantum mechanics because interference relies on cancellation between amplitudes of opposite signs. The ground-state wavefunction of double semion model contains negative signs that cannot be removed by any local transformation. Here we study the quantum effects of these intrinsic negative signs. By proposing a generic double semion wavefunction in tensor network representation, we show that its norm can be mapped to the partition function of a triangular lattice Ashkin-Teller model with imaginary interactions. We use numerical tensor-network methods to solve this non-Hermitian model with parity-time symmetry and determine a global phase diagram. In particular, we find a dense loop phase described by non-unitary conformal field theory and a parity-time-symmetry breaking phase characterized by the zeros of the partition function. Therefore, our work establishes a connection between the intrinsic signs in the topological wavefunction and non-unitary phases in the parity-time-symmetric non-Hermitian statistical model.

Intrinsic Bulk Quantum Oscillations in a Bulk Unconventional Insulator SmB6.

SummaryThe finding of bulk quantum oscillations in the Kondo insulator SmB6 proved a considerable surprise. Subsequent measurements of bulk quantum oscillations in other correlated insulators including YbB12 lent support to our discovery of a class of bulk unconventional insulators that host bulk quantum oscillations. Here we perform a series of experiments to examine evidence for the intrinsic character of bulk quantum oscillations in floating zone-grown single crystals of SmB6 that have been the subject of our quantum oscillation studies. We present results of thermodynamic, transport, and composition analysis experiments on pristine floating zone-grown single crystals of SmB6 and compare quantum oscillations with metallic LaB6 and elemental aluminum. These results establish the intrinsic origin of quantum oscillations from the insulating bulk of floating zone-grown SmB6. The similarity of the Fermi surface in insulating SmB6 with the conduction-electron Fermi surface in metallic hexaborides is at the heart of a theoretical mystery.

Quantum criticality of magnetic catalysis in two-dimensional correlated Dirac fermions

We study quantum criticality of the magnetic field induced charge density wave (CDW) order in correlated spinless Dirac fermions on the $\pi$-flux square lattice at zero temperature as a prototypical example of the magnetic catalysis, by using the infinite density matrix renormalization group. It is found that the CDW order parameter $M(B)$ exhibits an anomalous magnetic field $(B)$ scaling behavior characteristic of the $(2+1)$-dimensional chiral Ising universality class near the quantum critical point, which leads to a strong enhancement of $M(B)$ compared with a mean field result. We also establish a global phase diagram in the interaction-magnetic field plane for the fermionic quantum criticality.

Geometric investigation of the three-coefficient Redlich-Kister expansion global phase diagram for binary mixtures

The Redlich-Kister (RK) three-coefficient expansion for gE is investigated geometrically and its global phase diagram is presented. The azeotropy and stability conditions yield surfaces (envelopes) in the three-dimensional azeotropy space and stability space respectively, whose axes represent variables determined from Henry's constants, pure substance vapor pressures and the highest-order RK coefficient. Zeotropy, single, double, triple, and tangent azeotropy (or saddle-point azeotropy), as well as stability, are identified in regions of the azeotropy and stability spaces. The connection between the two spaces is established. Envelopes for gE = 0 and dgE/dx=0 are also constructed in the azeotropy or stability spaces, to indicate the gE shape. Some results regarding the shape of gE are transferable to hE and vE when these are described independently by three-coefficient Redlich-Kister expansions. The analysis is applied to eleven actual mixtures, whose state is represented in the azeotropy and stability space. Fitting temperature-dependent RK coefficients allows to estimate the continuous path the mixture follows in both spaces at varying temperature, revealing possible intermediate states and the mixture tendency at the extreme temperatures.

Spin-1 pyrochlore antiferromagnets: Theory, model, and materials’ survey

Pyrochlore magnets can be a unique platform to demonstrate numerous important concepts and applications of frustrated magnetic physics in modern condensed matter physics. Most works on pyrochlore magnets deal with the interacting spin-1/2 local moments, while much less works have studied the spin-1 systems. We here review the physics with interacting spin-1 local moments on the pyrochlore lattice to illustrate the potentially interesting physics associated with spin-1 magnets. The generic pyrochlore spin-1 model includes the antiferromagnetic Heisenberg interaction, the Dzyaloshinskii-Moriya interaction and the single-ion spin anisotropy. The global phase diagram of this generic spin model is reviewed, and the relation between different quantum phases in the phase diagram is clarified. The critical properties of the transition from the parent quantum paramagnet to the proximate orders are discussed. The presence of quantum order by disorder in the parts of the ordered phases is analyzed. The elementary excitations with respect to the ground states are further reviewed, and the topological natures of these excitations are carefully addressed. The materials’ relevance of the spin-1 pyrochlore magnets are finally reviewed. This review may provide insights about the interesting spin-1 local moments on frustrated systems.

Dynamical vortex phase diagram of two-dimensional superconductivity in gated MoS2

Recent discoveries of two-dimensional (2D) superconductors have uncovered various new aspects of physical properties including vortex matter. In this paper, we report transport properties and a dynamical phase diagram at zero magnetic field in ion-gated MoS2. In addition to the universal jump in the current-voltage characteristic showing unambiguous evidence of the Berezinskii-Kosterlitz-Thouless (BKT) transition, we observed multiple peaks in the temperature- and current-derivative of the electrical resistance, based on which a dynamical phase diagram in the current-temperature plane was constructed. We found current-induced dynamical states of vortex-antivortex pairs, containing that with the phase slip line. Also, we present a global phase diagram of vortices in gated MoS2 which captures the nature of vortex matter of clean 2D superconductors.

Field-free quantum-spin-1/2 XXZ model in three-dimensions:phases, phase transitions, and phase diagrams by renormalization group theory

The field-free quantum-spin-1/2 XXZ model is studied in three-dimensions using renormalization group theory. We obtain global phase diagrams and critical properties. We identify zero-temperature quantum phase transitions at isotropic points, as well as long-range order below critical temperatures at all anisotropies. We show that the excitation spectrum is gapless in XY-like, and gapped in Ising-like anisotropy regimes. Besides, internal energy density, specific heat, nearest-neighbor entanglement measures and spin-spin correlations are obtained globally at all temperatures. Our numerical results cover the global range of anisotropy parameter, for both ferromagnetic and antiferromagnetic cases.

Progress, Challenges, and Rewards in Probing Melt Dynamics, Configurational Entropy Change, and Topological Phases of Group V‐ and Group IV‐Based Multicomponent Sulfide Glasses

The observation of reversibility windows (RWs) in binary GexS100−x, AsxS100−x and ternary GexAsxS100−2x glass systems permits constructing a global topological phase diagram in the GeAsS composition triangle. The RW denotes glass compositions for which the enthalpy of relaxation at Tg vanishes, leading to thermally reversing glass transitions. The phase diagram permits delineating glass compositions that are in the flexible phase (FP), intermediate phase (IP), and the stressed rigid phase (SRP) for all ternary GexAsxS100−2x glass compositions. For the IP compositions examined, a general lowering of the molar volumes, Vm, is observed in relation to those for non‐IP compositions, giving rise to a volumetric window. Melt dynamics of IP compositions reveal a fragility index, m &lt; 20, lower than that for non‐IP melts for which m &gt; 20 displays a fragility window, underscoring in part the reason for the delayed homogenization of melts in these sulfide glasses. The observations of the three types of window characteristics of IP compositions are feasible only when the homogeneous bulk glasses are synthesized, in which the variance ⟨Δx⟩ in As and Ge concentrations, x, across batch compositions is less than 0.01%. This is established by Fourier transform–Raman profiling of each batch of composition that is synthesized.

Global phase diagrams in a polymer-solvent system under the positive and negative pressure at and near the mathematical double points

Global phase diagrams are one of the crucial tools to investigate the phase behavior of simple and complex mixtures both theoretically and experimentally. The critical lines and global phase behavior of polymer-solvent systems under the negative pressure at and near the mathematical double points (MDPs) are studied. We present the critical lines of polymer mixtures in three different planes for various values of interaction energy parameters, and change the factor (r) and the deviation coefficient (Δ) from the MDPs. We use the full Tompa model to obtain the equation for the critical line within the molecular-field approximation. We find that r and Δ values influence the critical lines and global phase behavior of the system. Moreover, as the r increases, the MDPs shift to the low-pressure region and it will be located in a negative pressure region forr≥9.

Global Phase Diagram of a Spin-Orbital Kondo Impurity Model and the Suppression of Fermi-Liquid Scale.

Many correlated metallic materials are described by Landau Fermi-liquid theory at low energies, but for Hund metals the Fermi-liquid coherence scale T_{FL} is found to be surprisingly small. In this Letter, we study the simplest impurity model relevant for Hund metals, the three-channel spin-orbital Kondo model, using the numerical renormalization group (NRG) method and compute its global phase diagram. In this framework, T_{FL} becomes arbitrarily small close to two new quantum critical points that we identify by tuning the spin or spin-orbital Kondo couplings into the ferromagnetic regimes. We find quantum phase transitions to a singular Fermi-liquid or a novel non-Fermi-liquid phase. The new non-Fermi-liquid phase shows frustrated behavior involving alternating overscreenings in spin and orbital sectors, with universal power laws in the spin (ω^{-1/5}), orbital (ω^{1/5}) and spin-orbital (ω^{1}) dynamical susceptibilities. These power laws, and the NRG eigenlevel spectra, can be fully understood using conformal field theory arguments, which also clarify the nature of the non-Fermi-liquid phase.

Role of the spin anisotropy of the interchain interaction in weakly coupled antiferromagnetic Heisenberg chains**Project supported by the National Natural Science Foundation of China (Grant No. 11674392), the Ministry of Science and Technology of China, National Program on Key Research Project (Grant No. 2016YFA0300504), and the Research Funds of Remnin University of China (Grant No. 18XNLG24). R.Y. acknowledges the hospitality

In quasi-one-dimensional (q1D) quantum antiferromagnets, the complicated interplay of intrachain and interchain exchange couplings may give rise to rich phenomena. Motivated by recent progress on field-induced phase transitions in the q1D antiferromagnetic (AFM) compound YbAlO3, we study the phase diagram of spin-1/2 Heisenberg chains with Ising anisotropic interchain couplings under a longitudinal magnetic field via large-scale quantum Monte Carlo simulations, and investigate the role of the spin anisotropy of the interchain coupling on the ground state of the system. We find that the Ising anisotropy of the interchain coupling can significantly enhance the longitudinal spin correlations and drive the system to an incommensurate AFM phase at intermediate magnetic fields, which is understood as a longitudinal spin density wave (LSDW). With increasing field, the ground state changes to a canted AFM order with transverse spin correlations. We further provide a global phase diagram showing how the competition between the LSDW and the canted AFM states is tuned by the Ising anisotropy of the interchain coupling.

Phase diagram and quantum criticality of Heisenberg spin chains with Ising anisotropic interchain couplings

Motivated by recent progress on field-induced phase transitions in quasi-one-dimensional quantum antiferromagnets, we study the phase diagram of $S=1/2$ antiferromagnetic Heisenberg chains with Ising anisotropic interchain couplings under a longitudinal magnetic field via large-scale quantum Monte Carlo simulations. The interchain interactions is shown to enhance longitudinal spin correlations to stabilize an incommensurate longitudinal spin density wave order at low temperatures. With increasing field the ground state changes to a canted antiferromagnetic order until the magnetization fully saturates above a quantum critical point controlled by the $(3+2)$D XY universality. Increasing temperature in the quantum critical regime the system experiences a fascinating dimension crossover to a universal Tomonaga-Luttinger liquid. The calculated NMR relaxation rate $1/T_1$ indicates this Luttinger liquid behavior survives a broad field and temperature regime. Our results determine the global phase diagram and quantitative features of quantum criticality of a general model for quasi-one-dimensional spin chain compounds, and thus lay down a concrete ground to the study on these materials.