Singlet Phase Research Articles

N2HDECAY: Higgs boson decays in the different phases of the N2HDM

The program N2HDECAY calculates the branching ratios and decay widths of the Higgs bosons of the Next-to-Two-Higgs-Doublet Model (N2HDM). The code incorporates the dominant higher-order effects by including QCD corrections and off-shell decay modes. The N2HDM is an extension of the Standard Model by a Higgs doublet and a real Higgs singlet. Its phenomenology can change dramatically depending on which global symmetries are broken by electroweak symmetry breaking. It can feature a large visible Higgs sector in the broken phase, behave like a 2HDM with scalar singlet dark matter in the dark singlet phase, or, in the inert doublet phase, extend an inert doublet model by mixing a singlet with the SM Higgs boson. N2HDECAY provides precise predictions for the decays of the Higgs bosons in all of these phases. Program summaryProgram Title:N2HDECAYProgram Files doi:http://dx.doi.org/10.17632/n45d9zd5xz.1Licensing provisions: GPLv2Programming language: Fortran 77Nature of problem: Calculation of branching ratios and total widths for the Higgs bosons and the top-quark in the N2HDM. To achieve a high precision, the decay widths are calculated including all available QCD and off-shell corrections.Solution method: The code calculates all required Higgs couplings from a standard set of N2HDM input parameters. The computations of the decay widths use analytic formulas for all two particle final states. Off-shell decays are integrated numerically and a linear interpolation over the resonance is performed.

Slave Boson Analysis of f2-Configuration Systems with Γ1 Singlet Crystalline-Electric-Field Ground State under the Cubic Symmetry

We investigated electron phases in the $f^2$-configuration system with the $\Gamma_1$ crystalline-electric-field (CEF) ground state in cubic symmetry. An extended three-orbital periodic Anderson model, which consists of $j=5/2$ states, is evaluated by using the rotationally invariant slave boson formalism. As a result, we found three phases at zero temperature: the $\Gamma_1$ CEF singlet phase, and two kinds of Fermi liquid (FL). One of the FL arises owing to the presence of the $\Gamma_5$ CEF state, while the other forms a quasi-degenerated CEF state. All these phases are separated by first-order transitions: the charge-transfer transition and the CEF energy-level crossing. We also found heavy quasiparticle behaviors in the intermediate valence region between the $f^2$ and $f^3$ configurations. In this region, the mass enhancement factor exhibits a peak structure by increasing the hybridization. Physical properties of these phases and transitions are discussed.

Phase diagram of the Hubbard-Kondo lattice model from the variational cluster approximation

The interplay between the Kondo effect and magnetic ordering driven by the Ruderman-Kittel-Kasuya-Yosida interaction is studied within the two-dimensional Hubbard-Kondo lattice model. In addition to the antiferromagnetic exchange interaction ${J}_{\ensuremath{\perp}}$ between the localized spins and the conduction electrons, this model also contains the local repulsion $U$ between the conduction electrons. We use variational cluster approximation to investigate the competition between the antiferromagnetic phase, the Kondo singlet phase, and a ferrimagnetic phase on square lattice. At half-filling, the N\'eel antiferromagnetic phase dominates from small to moderate ${J}_{\ensuremath{\perp}}$ and $U{J}_{\ensuremath{\perp}}$, and the Kondo singlet elsewhere. Sufficiently away from half-filling, the antiferromagnetic phase first gives way to a ferrimagnetic phase (in which the localized spins order ferromagnetically, and the conduction electrons do likewise, but the two mutually align antiferromagnetically), and then to the Kondo singlet phase.

Ground-state phase diagram of the frustrated spin- 12 two-leg honeycomb ladder

We investigate a spin-$1/2$ two-leg honeycomb ladder with frustrating next-nearest-neighbor (NNN) coupling along the legs, which is equivalent to two $J_1$-$J_2$ spin chains coupled with $J_\perp$ at odd rungs. The full parameter region of the model is systematically studied using conventional and infinite density-matrix renormalization group as well as bosonization. The rich phase diagram consists of five distinct phases: A Haldane phase, a NNN-Haldane phase and a staggered dimer phase when $J_{\perp} < 0$; a rung singlet phase and a columnar dimer phase when $J_{\perp} > 0$. An interesting reentrant behavior from the dimerized phase into the Haldane phase is found as the frustration $J_2$ increases. The universalities of the critical phase transitions are fully analyzed. Phase transitions between dimerized and disordered phases belong to the two-dimensional Ising class with central charge $c=1/2$. The transition from the Haldane phase to NNN-Haldane phase is of a weak topological first order, while the continuous transition between the Haldane phase and rung singlet phase has central charge $c=2$.

Cluster mean field theory for two-dimensional spin-1 Bose–Hubbard model

Cluster mean field theory for the two-dimensional spin-1 Bose–Hubbard model is applied to study superfluid (SF) to Mott insulator (MI) phase transitions and various magnetic phases that arise in the presence of spin-dependent anti-ferromagnetic and ferromagnetic interactions. This study clearly shows the nematic behavior of SF and odd-density MI phases, and a continuous phase transition between them for anti-ferromagnetic interaction. The even-density MI shows a nematic or singlet phase depending upon the strength of the interaction, and a continuous crossover between them. The SF to singlet MI transition is discontinuous. The dependence of cluster size on the critical on-site interaction (U0C) for SF to MI transitions is also studied. In the case of anti-ferromagnetic interaction, it is found that U0C for the SF to odd-density MI transition decreases with cluster size; however, no such changes are observed for the SF to singlet MI transition. In the case of ferromagnetic interactions, SF to MI transitions are continuous, and Mott lobes become enlarged with cluster size. Second order Rényi entanglement entropy (EE) is calculated in different phases. The results show that Rényi EE is large in the nematic MI phase.

Spin nematics next to spin singlets

We provide a route to generate nematic order in a spin-1/2 system. Unlike the well-known magnon-binding mechanism, our spin nematics requires neigher the frustration effect nor a spin polarization in a high field or in the vicinity of a ferromagnet, but instead appears next to the spin singlet phase. We start from a state consisting of a quantum spin-1/2 singlet dimer placed on each site of a triangular lattice, and show that inter-dimer ring exchange interactions efficiently dope the SU(2) triplets that itinerate and interact, easily driving a stable singlet state to either Bose Einstein condensates or a triplet crystal, some hosting a spin nematic order. A variety of roles the ring exchange serves include the generation of a bilinear-biquadratic interaction between nearby triplets, which is responsible for the emergent nematic order separated from the singlet phase by a first order transition.

Direct Observation of the Quantum Phase Transition of SrCu2(BO3)2 by High-Pressure and Terahertz Electron Spin Resonance

High-pressure and high-field electron spin resonance (ESR) measurements have been performed on a single crystal of the orthogonal-dimer spin system SrCu$_{2}$(BO$_{3}$)$_{2}$. With frequencies below 1 THz, ESR signals associated with transitions from the singlet ground state to the one-triplet excited states and the two-triplet bound state were observed at pressures up to 2.1 GPa. We obtained directly the pressure dependence of the gap energies, finding a clear first-order phase transition at $P_{c}=1.85\pm0.05$ GPa. By comparing this pressure dependence with the calculated excitation energies obtained from an exact diagonalization, we determined the precise pressure dependence for inter- ($J'$) and intra-dimer ($J$) exchange interactions considering the Dzyaloshinski-Moriya interaction. Thus this system undergoes a first-order quantum phase transition from the dimer singlet phase to a plaquette singlet phase above the ratio $(J'/J)_{c}=0.660\pm0.003$.

Phase transitions and spin excitations of spin-1 bosons in optical lattice

We investigate ground state properties of spin-1 bosonic system trapped in optical lattice with extended standard basis operator (SBO) method. For both ferromagnetic ($U_2<0$) and antiferromagnetic ($U_2>0$) systems, we analytically figure out the symmetry properties in Mott-insulator and superfluid phases, which would provide a deeper insight into the MI-SF phase transition process. Then by applying self-consistent approach to the method, we include the effect of quantum and thermal fluctuations and derive the MI-SF transition phase diagram, which is in quantitative agreement with recent Monte-Carlo simulation at zero temperature, and at finite temperature, we find the underestimation of finite-temperature-effect in the mean-field approximation method. If we further consider the spin excitations in the insulating states of spin-1 system in external field, distinct spin phases are expected. Therefore, in the Mott lobes with $n=1$ and $n=2$ atoms per site, we give analytical and numerical boundaries of the singlet, nematic, partially magnetic and ferromagnetic phases in the magnetic phase diagrams.

Construction of Hamiltonians by supervised learning of energy and entanglement spectra

Correlated many-body problems ubiquitously appear in various fields of physics such as condensed matter physics, nuclear physics, and statistical physics. However, due to the interplay of the large number of degrees of freedom, it is generically impossible to treat these problems from first principles. Thus the construction of a proper model, namely effective Hamiltonian, is essential. Here, we propose a simple scheme of constructing Hamiltonians from given energy or entanglement spectra with machine learning. We apply the proposed scheme to the Hubbard model at the half-filling, and compare the obtained effective low-energy spin-1/2 model with several analytic results based on the high order perturbation theory which have been inconsistent with each other. We also show that our approach can be used to construct the entanglement Hamiltonian of a quantum many-body state from its entanglement spectrum as well. We exemplify this using the ground states of the $S=1/2$ two-leg Heisenberg ladders. We observe a qualitative difference between the entanglement Hamiltonians of the two phases (the Haldane phase and the Rung Singlet phase) of the model due to the different origin of the entanglement. In the Haldane phase, we find that the entanglement Hamiltonian is non-local by nature, and the locality can be restored by introducing the anisotropy and turning the system into the large-$D$ phase. Possible applications to the study of strongly-correlated systems and the model construction from experimental data are discussed.

Electric field induced irreversible change and asymmetric butterfly strain loops in Pb(Zr,Ti)O3-Pb(Ni1/3Nb2/3)O3-Bi(Zn1/2Ti1/2)O3 quaternary ceramics

The phase transformation and strain characteristics of (0.9-x)Pb(Zr0.54Ti0.46)O3−0.1Pb(Ni1/3Nb2/3)O3-xBi(Zn1/2Ti1/2)O3 (0.1PNN-(0.9-x)PZT-xBZT) solid-solution ceramics were investigated. The substitution of BZT for PZT can effectively decrease the sintering temperature from 1150 °C at x = 0–975 °C at x = 0.24. A typical morphotropic phase boundary (MPB) between ferroelectric rhombohedral (R) phases and relaxor tetragonal (T) phases was identified in the composition range of x = 0.12–0.18, resulting in enhanced dielectric, piezoelectric and electromechanical properties of d33 = 610 pC/N, kp = 58% an ε33T/εo = 2518 at x = 0.16. Most interestingly, exceptionally asymmetric butterfly strain loops were observed in the first-cycle electric loading, and found to obviously change with increasing the BZT content. The X-ray diffraction analysis on virgin and poled samples suggests that the observed asymmetric strain curves should stem from the electric field induced irreversible lattice shrinkage or lattice elongation in the single-R or single-T phase compositions, respectively. For MPB compositions, a combined effect of both opposite strain contributions would result in a maximum value (in absolute value) in the observed irreversible strain Sirr at x = 0.12, together with the effect of the electric field induced irreversible T-R phase transition. These results provide useful insights into the mechanism of forming asymmetric bipolar strains observed in BZT-substituted PZT-PNN piezoelectric ceramics.

Groundstate fidelity phase diagram of the fully anisotropic two-leg spin-½ XXZ ladder

The fully anisotropic two-leg spin- XXZ ladder model is studied in terms of an algorithm based on the tensor network (TN) representation of quantum many-body states as an adaptation of projected entangled pair states to the geometry of translationally invariant infinite-size quantum spin ladders. The TN algorithm provides an effective method to generate the groundstate wave function, which allows computation of the groundstate fidelity per lattice site, a universal marker to detect phase transitions in quantum many-body systems. The groundstate fidelity is used in conjunction with local order and string order parameters to systematically map out the groundstate phase diagram of the ladder model. The phase diagram exhibits a rich diversity of quantum phases. These are the ferromagnetic, stripe ferromagnetic, rung singlet, rung triplet, Néel, stripe Néel and Haldane phases, along with the two XY phases XY1 and XY2.

Healing of defects in random antiferromagnetic spin chains

We study the effects of a weakened link in random antiferromagnetic spin chains. We show that healing occurs, and that homogeneity is restored at low energy, in a way that is qualitatively similar to the fate of impurities in clean ferromagnetic spin chains, or in Luttinger liquids with attractive interactions. Healing in the random case occurs even without interactions, and is characteristic of the random singlet phase. Using real-space renormalization group and exact diagonalization methods, we characterize this universal healing crossover by studying the entanglement across the weak link. We identify a crossover healing length that separates a regime where the system is cut in half by the weak link from a fixed point where the spin chain is healed. Our results open the way to the study of impurity physics in disordered spin chains.

Dynamic zero modes of Dirac fermions and competing singlet phases of antiferromagnetic order

In quantum spin systems, singlet phases often develop in the vicinity of an antiferromagnetic order. Typical settings for such problems arise when itinerant fermions are also present. In this work, we develop a theoretical framework for addressing such competing orders in an itinerant system, described by Dirac fermions strongly coupled to an O(3) nonlinear sigma model. We focus on two spatial dimensions, where upon disordering the antiferromagnetic order by quantum fluctuations the singular tunneling events also known as (anti)hedgehogs can nucleate competing singlet orders in the paramagnetic phase. In the presence of an isolated hedgehog configuration of the nonlinear sigma model field, we show that the fermion determinant vanishes as the dynamic Euclidean Dirac operator supports fermion zero modes of definite chirality. This provides a topological mechanism for suppressing the tunneling events. Using the methodology of quantum chromodynamics, we evaluate the fermion determinant in the close proximity of magnetic quantum phase transition, when the antiferromagnetic order parameter field can be described by a dilute gas of hedgehogs and antihedgehogs. We show how the precise nature of emergent singlet order is determined by the overlap between dynamic fermion zero modes of opposite chirality, localized on the hedgehogs and antihedgehogs. For a Kondo-Heisenberg model on the honeycomb lattice, we demonstrate the competition between spin Peierls order and Kondo singlet formation, thereby elucidating its global phase diagram. We also discuss other physical problems that can be addressed within this general framework.

Quantum phases of frustrated two-leg spin- 12 ladders with skewed rungs

The quantum phases of 2-leg spin-1/2 ladders with skewed rungs are obtained using exact diagonalization of systems with up to 26 spins and by density matrix renormalization group calculations to 500 spins. The ladders have isotropic antiferromagnetic (AF) exchange $J_2 > 0$ between first neighbors in the legs, variable isotropic AF exchange $J_1$ between some first neighbors in different legs, and an unpaired spin per odd-membered ring when $J_1 \gg J_2$. Ladders with skewed rungs and variable $J_1$ have frustrated AF interactions leading to multiple quantum phases: AF at small $J_1$, either F or AF at large $J_1$, as well as bond-order-wave phases or reentrant AF (singlet) phases at intermediate $J_1$.

Preparation of Structural Phase Diagram of Ln2Ni1-X Cu x O4+δ (Ln=La, Pr, Nd, Sm, Eu) as New Cathode Materials: Variation of Structural Phase Diagram on Kinds of Ln

Crystal structure of Ln2Ni1-x Cu x O4+δ (Ln= La, Pr, Nd, Sm and Eu), which are expected as new cathode materials for solid fuel cells, was investigated. Single phase with K2NiF4 structure, so-called T-phase, was obtained for La2Ni1-x Cu x O4+δ regardless of Cu content. Single phase with Nd2CuO4 structure, so-called T’-phase, was obtained for Sm2Ni1-x Cu x O4+δ and Eu2Ni1-x Cu x O4+δ for only 0.95≤x≤1.0 and x=1.0 respectively. No T-phase was obtained for the other composition of Ln2Ni1-x Cu x O4+δ (Ln=Sm, Eu). The single T-phase and T’-phase were obtained for Pr2Ni1-x Cu x O4+δ with x≤0.4 and x=1.0, respectively. For Pr2Ni1-x Cu x O4+δ with x between 0.5 and 0.9, phase separation into T-phase and T’-phase due to miscibility gap was observed, showing similar behavior with Nd2Ni1-x Cu x O4+δ except for little smaller x range of the miscibility gap. From high temperature X-ray diffraction measurements, it was revealed that the miscibility gap between 0.5 and 0.9 of Pr2Ni1-x Cu x O4+δ remained up to 700 °C. Variation of the crystal structure of Ln2Ni1-x Cu x O4+δ on kinds of Ln and Cu content could be explained by using tolerance factor calculated from ionic radius of Ln3+, Ni2+ and Cu2+.

Deconfined quantum criticality in SU(3) antiferromagnets on the triangular lattice

We propose field theories for a deconfined quantum critical point in SU(3) antiferromagnets on the triangular lattice. In particular we consider the continuous transition between a magnetic, three-sublattice color-ordered phase and a trimerized SU(3) singlet phase. Starting from the magnetically ordered state we derive a critical theory in terms of fractional bosonic degrees of freedom, in close analogy to the well-developed description of the SU(2) N\'eel---valence bond solid (VBS) transition on the square lattice. Our critical theory consists of three coupled $C{P}^{2}$ models and we study its fixed point structure using a functional renormalization group approach in a suitable large $N$ limit. We find a stable critical fixed point and estimate its critical exponents, thereby providing an example of deconfined criticality beyond the universality class of the $C{P}^{N}$ model. In addition we present a complementary route towards the critical field theory by studying topological defects of the trimerized SU(3) singlet phase.

Competing phases in spin ladders with ring exchange and frustration

The ground state properties of spin-1/2 ladders are studied, emphasizing the role of frustration and ring exchange coupling. We present a unified field theory for ladders with general coupling constants and geometry. Rich phase diagrams can be deduced by using a renormalization group calculation for ladders with in--chain next nearest neighbor interactions and plaquette ring exchange coupling. In addition to established phases such as Haldane, rung singlet, and dimerized phases, we also observe a surprising instability towards an incommensurate phase for weak interchain couplings, which is characterized by an exotic coexistence of self-consistent ferromagnetic and anti-ferromagnetic order parameters.

Full counting statistics in the Haldane-Shastry chain

We present analytical and numerical results regarding the magnetization full counting statistics (FCS) of a subsystem in the ground-state of the Haldane-Shastry chain. Exact Pfaffian expressions are derived for the cumulant generating function, as well as any observable diagonal in the spin basis. In the limit of large systems, the scaling of the FCS is found to be in agreement with the Luttinger liquid theory. The same techniques are also applied to inhomogeneous deformations of the chain. This introduces a certain amount of disorder in the system; however we show numerically that this is not sufficient to flow to the random singlet phase, that corresponds to $XXZ$ chains with uncorrelated bond disorder.

Impurity-induced antiferromagnetic domains in the periodic Anderson model

A central feature of the Periodic Anderson Model is the competition between antiferromagnetism, mediated by the Ruderman-Kittel-Kasuya-Yosida interaction at small conduction electron-local electron hybridization $V$, and singlet formation at large $V$. At zero temperature, and in dimension $d>1$, these two phases are separated by a quantum critical point $V_c$. We use Quantum Monte Carlo simulations to explore the effect of impurities which have a local hybridization $V_{*} < V_c$ in the AF regime which are embedded in a bulk singlet phase with $V > V_c$. We measure the suppression of singlet correlations and the antiferromagnetic correlations which form around the impurity, as well as the size of the resulting domain. Our calculations agree qualitatively with NMR measurements in CeCoIn$_{5-x}$Cd$_x$.

Mixed parity pairing in a dipolar gas

We show that fermionic dipoles in a two-layer geometry form Cooper pairs with both singlet and triplet components when they are tilted with respect to the normal of the planes. The mixed parity pairing arises because the interaction between dipoles in the two different layers is not inversion symmetric. We use an efficient eigenvalue approach to calculate the zero-temperature phase diagram of the system as a function of the dipole orientation and the layer distance. The phase diagram contains purely triplet as well as mixed singlet and triplet superfluid phases. We show in detail how the pair wave function for dipoles residing in different layers smoothly changes from singlet to triplet symmetry as the orientation of the dipoles is changed. Our results indicate that dipolar quantum gases can be used to unambiguously observe mixed parity pairing.