Ginzburg-Landau Theory and Classical Critical Phenomena of Mott Transition

Theory of classical critical phenomena of Mott transition is developed for the dimensionality $d \le \infty$. Reconsidering a cluster dynamical mean-field theory (DMFT), Ginzburg-Landau free energy is derived in terms of hybridization function for a cluster-impurity model. Its expansion around a cluster DMFT solution reduces to a $\phi^4$ model. Inherent thermal Mott transition without spontaneous symmetry breaking is described by a scalar field reflecting the charge degrees of freedom. In the space of local Coulomb repulsion, chemical potential and temperature, a first-order transition surface terminates at a critical end curve. The criticality belongs to the Ising universality as a liquid-gas transition. Various quantities including double occupancy, electron filling and entropy show diverging responses at the criticality and discontinuities at the first-order transition. Particularly, electron effective mass shows a critical divergence in $2\le d\le 4$. Only at a certain curve on the surface, a filling-control transition and its related singularities disappear. We discuss detailed critical behaviors, effects of interplay with other critical fluctuations, and relevant experimental results.Comment: 15 pages including 3 figure

Chiral spin pairing in helical magnets

The Ginzburg-Landau Hamiltonian for incommensurate frustrated classical spin systems is analyzed. The coupling to phonons through the Dzyaloshinskii-Moriya interaction and/or the four-spin exchange interaction of the Coulomb origin under the egde-sharing network of magnetic and ligand ions drive chiral spin piarings, introducing two successive second-order phase transitions upon cooling. First, a vector spin-chiral order appears with an either parity, leaving an O(2) chiral spin liquid. Then, the O(2) symmetry is broken by the spin ordering into a helical magnetic state. Possible candidate materials are also discussed.Comment: 5 pages, inclluding one figure; some detailed derivations added; to appear in Phys. Rev. Let

Magnetic Monopole Supercurrent through a Quantum Spin Ice Tunnel Junction

Magnetic monopoles are hypothetical particles that may exist as quantized sources and sinks of the magnetic field. In materials, they may appear in an emergent quantum electrodynamics described by a U(1) lattice gauge theory. Particularly, quantum spin ice hosts monopoles as bosonic spinons coupled to emergent gauge fields in a U(1) quantum spin liquid, namely, a deconfined Coulomb phase. When monopoles are condensed to form a long-range order, monopoles and gauge fields are screened and confined. Here we show, however, that monopole supercurrent flows across a junction of two ferromagnets that are weakly linked through and placed on top of the U(1) QSL, when a gauge-invariant phase difference of spinons across the junction is generated by quenching or an applied electric voltage parallel to the junction. This novel phenomenon paves the way to a new paradigm of spinonics for a dissipationless control of magnetism.Comment: 6 pages, 2 figures. J. Phys. Soc. Jpn. in pres

Pseudogap and Superconducting Fluctuations in High-Tc Cuprates

We analyze pseudogap phenomena widely observed in the underdoped cuprates. We assume the existence of a strong d-wave pairing force competing with antiferromagnetic(AFM) fluctuations and the formation of flat and damped dispersion around the $(\pi,0)$ and $(0,\pi)$ region as two important elements caused by the proximity from the Mott insulator. Using the mode-mode coupling theory for the d-wave superconducting(dSC) and AFM fluctuations, we reproduce basic properties of the pseudogap seen in the magnetic resonance, neutron scattering, angle resolved photoemission and tunneling measurements in the cuprates. Then minimal requirements to understand the pseudogap phenomena are clarified as the above two elements. A strong competition of the pairing with the antiferromagnetic fluctuations suppresses the transition temperature thereby generates the pseudogap in the underdoped region while the weakness of the AFM fluctuations leads to the absence of the pseudogap at the optimal doping concentration.}Comment: 13 pages including 4 figures, to appear in J. Phys. Soc. Jpn. Supp

Pseudogap and Kinetic Pairing Under Critical Differentiation of Electrons in Cuprate Superconductors

Superconducting mechanism of cuprates is discussed in the light of the proximity of the Mott insulator. The proximity accompanied by suppression of coherence takes place in an inhomogeneous way in the momentum space in finite-dimensional systems. Studies on instabilities of metals consisted of such differentiated electrons in the momentum space are reviewed from a general point of view. A typical example of the differentiation is found in the flattening of the quasiparticle dispersion discovered around momenta $(\pi,0)$ and $(0,\pi)$ on 2D square lattices. This flattening even controls the criticality of the metal-insulator transition. Such differentiation and suppressed coherence subsequently cause an instability to the superconducting state in the second order of the strong coupling expansion. The d-wave pairing interaction is generated from such local but kinetic processes in the absence of disturbance from the coherent single-particle excitations. The superconducting mechanism emerges from a direct kinetic origin which is conceptually different from the pairing mechanism mediated by bosonic excitations as in magnetic, excitonic, and BCS mechanisms. Pseudogap phenomena widely observed in the underdoped cuprates are then naturally understood from the mode-mode coupling of d-wave superconducting (dSC) fluctuations repulsively coupled with antiferromagnetic (AFM) ones. When we assume the existence of a strong d-wave channel repulsively competing with AFM fluctuations under the formation of flat and damped single-particle dispersion, we reproduce basic properties of the pseudogap seen in the magnetic resonance, neutron scattering, angle resolved photoemission and tunneling measurements in the cuprates.Comment: 12pages including 1 figure, Proceedings of Advanced Research Workshop on Open Problems in Strongly Correlated Electron Systems in Ble

Numerical evidence of quantum melting of spin ice: quantum-classical crossover

Unbiased quantum Monte-Carlo simulations are performed on the nearest-neighbor spin-$\frac{1}{2}$ pyrochlore XXZ model with an antiferromagnetic longitudinal and a weak ferromagnetic transverse exchange couplings, $J$ and $J_\perp$. The specific heat exhibits a broad peak at $T_{\mathrm{CSI}}\sim0.2J$ associated with a crossover to a classical Coulomb liquid regime showing a suppressed spin-ice monopole density, a broadened pinch-point singularity, and the Pauling entropy for $|J_\perp|\ll J$, as in classical spin ice. On further cooling, the entropy restarts decaying for $J_\perp>J_{\perp c}\sim-0.104J$, producing another broad specific heat peak for a crossover to a bosonic quantum Coulomb liquid, where the spin correlation contains both photon and quantum spin-ice monopole contributions. With negatively increasing $J_\perp$ across $J_{\perp c}$, a first-order thermal phase transition occurs from the quantum Coulomb liquid to an XY ferromagnet. Relevance to magnetic rare-earth pyrochlore oxides is discussed.Comment: 7 pages, 7 figures, accepted for publication in Phys. Rev. Let

Quantum Melting of Spin Ice: Emergent Cooperative Quadrupole and Chirality

A quantum melting of the spin ice is proposed for pyrochlore-lattice magnets Pr$_2TM_2$O$_7$ ($TM=$Ir, Zr, and Sn). The quantum superexchange Hamiltonian having a nontrivial magnetic anisotropy is derived in the basis of atomic non-Kramers magnetic doublets. The ground states exhibit a cooperative ferroquadrupole and pseudospin chirality, forming a magnetic analog of smectic liquid crystals. Our theory accounts for dynamic spin-ice behaviors experimentally observed in Pr$_2TM_2$O$_7$.Comment: 4 pages including 4 fgures; accepted for publication in Phys. Rev. Lett.; powder-neutron scatteing profile added in favorable comparison with experimen

Vector-spin-chirality order in a dimerized frustrated spin-1/2 chain

A frustrated spin-$1/2$ XXZ chain model comprising a ferromagnetic nearest-neighbor coupling with the bond alternation, $J_1(1\pm\delta)<0$, and an antiferromagnetic second-neighbor exchange coupling $J_2>0$ is studied at zero and weak magnetic fields by means of density matrix renormalization group calculations of order parameters, correlation functions and the entanglement entropy as well as an Abelian bosonization analysis. At zero magnetic field, the bond alternation $\delta>0$ suppresses the gapless phase characterized by a vector-chiral (VC) long-range order (LRO) and a quasi-LRO of an incommensurate spin spiral, whereas this phase occupies a large region in the space of $J_1/J_2$ and the easy-plane exchange anisotropy for $\delta=0$ [S. Furukawa \textit{et al.}, Phys. Rev. Lett. \textbf{105}, 257205 (2010)]. Then, four gapped phases are found to appear as the exchange anisotropy varies from the SU(2)-symmetric case to the U(1)-symmetric case; the Haldane dimer (D$_+$) phase with the same sign of the $x,y$- and $z$-component dimer order parameters, two VC dimer (VCD$_+$/VCD$_-$) phases with the sign of the $z$-component dimer order parameter being unaltered/reversed, and the even-parity dimer (D$_-$) phase. At small magnetic fields, a field-induced ring-exchange interaction, which is proportional to a staggered scalar chirality and a magnetic flux penetrating the associated triangle, drives a transition from the D$_-$ phase into a VC-Neel-dimer (VCND) phase, but not from the D$_+$ phase. This VCND phase is stable up to the large magnetic field at which the Zeeman term closes the spin gap. A possible relevance to Rb$_2$Cu$_2$Mo$_3$O$_{12}$ is discussed.Comment: 15 pages, 10 figure

Quantum spin ice under a [111] magnetic field: from pyrochlore to kagom\'e

Quantum spin ice, modeled for magnetic rare-earth pyrochlores, has attracted great interest for hosting a U(1) quantum spin liquid, which involves spin-ice monopoles as gapped deconfined spinons, as well as gapless excitations analogous to photons. However, the global phase diagram under a [111] magnetic field remains open. Here we uncover by means of unbiased quantum Monte-Carlo simulations that a supersolid of monopoles, showing both a superfluidity and a partial ionization, intervenes the kagom\'e spin ice and a fully ionized monopole insulator, in contrast to classical spin ice where a direct discontinuous phase transition takes place. We also show that on cooling, kagom\'e spin ice evolves towards a valence bond solid similar to what appears in the associated kagom\'e lattice model [S. V. Isakov et al., Phys. Rev. Lett. 97, 147202 (2006)]. Possible relevance to experiments is discussed.Comment: 5 pages, 4 figures; accepted for publication in PR

Chiral order and electromagnetic dynamics in one-dimensional multiferroic cuprates

We show by unbiased numerical calculations that the ferromagnetic nearest-neighbor exchange interaction stabilizes a vector spin chiral order against the quantum fluctuation in a frustrated spin-1/2 chain relevant to multiferroic cuprates, LiCu2O2 and LiCuVO4. Our realistic semi-classical analyses for LiCu2O2 resolve controversies on the helical magnetic structure and unveil the pseudo-Nambu-Goldstone modes as the origin of experimentally observed electromagnons.Comment: 4 pages including 3 figures (main text); 7 pages including 4 figures and 1 table (supplement); accepted for publication in Phys. Rev. Let