Spin-gap Phase Research Articles

Antiferromagnetic and spin-gap phases of the anisotropic Kondo necklace model

We have studied the effect of anisotropies on the quantum phase transition of the Kondo necklace model in dimensions D=1, 2 and 3. Both the anisotropy $\delta$ of the inter-site interaction term and anisotropy $\Delta$ of the on-site Kondo interaction have been included. We use a bond operator method with constraints implemented in mean field approximation. Starting from the paramagnetic phase we determine the critical ratio $(t/J)_c$ of the quantum critical point and associated scaling exponents of the Kondo-singlet gap. We show that in the case of easy-axis type anisotropy $\delta >1$ a qualitatively new behavior in comparison to the conventional Kondo necklace model with ($\delta$,$\Delta$)=(0,1) appears. We have also obtained the antiferromagnetic order parameter in the long range ordered phase for $t > t_c$.

Uniaxial pressure dependencies of the phase boundary of TlCuCl 3

We present a thermal expansion and magnetostriction study of TlCuCl 3, which shows a magnetic-field-induced transition from a spin gap phase to a Néel-ordered phase. Using Ehrenfest relations we derive huge and strongly anisotropic uniaxial pressure dependencies of the respective phase boundary, e.g., the transition field changes by about ± 185 % / GPa depending on the direction of uniaxial pressure.

Phonons in Hubbard ladders studied within the framework of the one-loop renormalization group

We study the effects of phonons in $N$-leg Hubbard ladders within the framework of a one-loop renormalization group. In particular, we explicitly demonstrate that the role of phonons changes {\em qualitatively} even in the simplest two-leg ladder, as compared to the single-chain system where phonons always dominate. Our numerical results suggest that in the spin-gapped phase of the two-leg ladder, the opening of the spin gap by electron-electron interaction also drives the electron-phonon interaction to strong coupling, but in a {\em subdominant} fashion. Therefore, even though the inclusion of phonons does not alter the phase, their subdominant relevance strongly renormalizes some physical properties below the energy scale of the spin gap. This might shine some light on the recent experiments showing an anomalous isotope effects in high-temperature superconductors.

Weak-coupling phase diagrams of bond-aligned and diagonal, doped Hubbard ladders

We study, using a perturbative renormalization group technique, the phase diagrams of bond-aligned and diagonal Hubbard ladders defined as sections of a square lattice with nearest-neighbor and next-nearest-neighbor hopping. We find that for not too large hole doping and small next-nearest-neighbor hopping the bond-aligned systems exhibit a fully spin-gapped phase while the diagonal systems remain gapless. Increasing the next-nearest-neighbor hopping typically leads to a decrease of the gap in the bond-aligned ladders, and to a transition into a gapped phase in the diagonal ladders. Embedding the ladders in an antiferromagnetic environment can lead to a reduction in the extent of the gapped phases. These findings suggest a relation between the orientation of hole-rich stripes and superconductivity as observed in LSCO.

Effect of chiral interactions in frustrated magnetic chains

The Heisenberg model with competing exchanges together with the chiral term is studied using series expansion about the dimer limit and by finite-size diagonalizations. The phase diagram is determined with ground-state orderings and the lowest excitation characteristics. We find that the chiral term induces a gapless line in frustrated spin-gapped phases. A critical chiral strength is also able to change the ground state from spiral to N\'eel quasi-long-range-order phase.

The Stochastic State Selection Method for Energy Eigenvalues in the Shastry–Sutherland Model

We apply a recently developed stochastic method to the Shastry-Sutherland model on 4x4 and 8x8 lattices. This method, which we call the Stochastic State Selection Method here, enables us to evaluate expectation values of powers of the Hamiltonian with very limited number of states. In this paper we first apply it to the 4x4 Shastry-Sutherland system, where one can easily obtain the exact ground state, in order to demonstrate that the method works well for this frustrated system. We numerically show that errors of the evaluations depend much on representations of the states and that the restructured representation is better than the normal one for this model. Then we study the 8x8 system to estimate energy eigenvalues of the lowest S=1 state as well as of the lowest excited S=0 state, where S denotes the total spin of the system. The results, which are in good accordance with our previous data obtained by the Operator Variational method, support that an intermediate spin-gap phase exists between the singlet dimer phase and the magnetically ordered phase. Estimates of the critical coupling and of the spin gap for the transition from the dimer phase to the intermediate phase are also presented.

Optimal inhomogeneity for superconductivity

We study the effect of nonuniform transverse couplings on a quasi-one dimensional superconductor. We show that inhomogeneous couplings quite generally increase the superconducting (pairing) gap relative to the uniform system, but that beyond an ``optimal'' degree of inhomogeneity, they lead to a suppression of the tendency to phase coherence. The optimal conditions for superconductivity are derived. We also show that a {\it delocalized}, spin-gapped phase is stable against weak disorder in a four-leg-ladder with moderate repulsive interactions.

Quantum Phase Transitions of theS=1 Shastry–Sutherland Model

We investigate quantum phase transitions of the two-dimensional S =1 Shastry–Sutherland model, which is characterized by the frustrated orthogonal-dimer structure, by means of the exact diagonalization method and the Ising-type series expansion method. We clarify how distinct spin gap phases realized in the chain system are adiabatically connected to those in the two-dimensional Shastry–Sutherland model. The effect of single-ion anisotropy is also discussed.

Quantum phase transitions in a frustrated orthogonal-dimer S=1 spin system

We investigate quantum phase transitions in a quasi-one-dimensional orthogonal-dimer S=1 spin chain by means of the exact diagonalization. By taking into account the effect of the interchain coupling, we discuss how the distinct spin-gap phases found in the orthogonal-dimer chain are adiabatically connected to those in the two-dimensional Shastry–Sutherland model for the compounds SrCu 2(BO 3) 2 and Nd 2BaZnO 5.

HIGH TEMPERATURE SUPERCONDUCTIVITY AND BERRY PHASE

We have analyzed the mechanism of high Tcsuperconductivity from the viewpoint of chirality and Berry phase. It is observed that spin pairing and charge pairing is caused by a gauge force generated by magnetic flux quanta attached to them. Different phase structures associated with high Tcsuperconductivity have been studied from an analysis of the renormalization group equation involving the Berry phase factor μ. It is found that there are two crossovers above the superconducting temperature Tc, one corresponding to the glass phase and the other represents spin gap phase. However, the spin gap temperature [Formula: see text] is found to be dependent on Tcand [Formula: see text] shows a universal behaviour with respect to the hole doping δ/δ0with δ0being the optimal doping rate.

Thermodynamics and crossover phenomena in the correlation lengths of the one-dimensionalt-Jmodel

We investigate the thermodynamics of the one-dimensional t-J model using transfer matrix renormalization group (TMRG) algorithms and present results for quantities like particle number, specific heat, spin susceptibility and compressibility. Based on these results we confirm a phase diagram consisting of a Tomonaga-Luttinger liquid (TLL) phase for small J/t and a phase separated state for J/t large. Close to phase separation we find a spin-gap (Luther-Emery) phase at low densities consistent with predictions by other studies. At the supersymmetric point we compare our results with exact results from the Bethe ansatz and find excellent agreement. In particular we focus on the calculation of correlation lengths and static correlation functions and study the crossover from the non-universal high T lattice into the quantum critical regime. At the supersymmetric point we compare in detail with predictions by conformal field theory (CFT) and TLL theory and show the importance of logarithmic corrections.

Frustration-induced phase transitions in the spin-Sorthogonal-dimer chain

We investigate quantum phase transitions in the frustrated orthogonal-dimer chain with an arbitrary spin $S \geq 1/2$. When the ratio of the competing exchange couplings is varied, first-order phase transitions occur 2S times among distinct spin-gap phases. The introduction of single-ion anisotropy further enriches the phase diagram. The phase transitions described by the present model possess most of the essential properties inherent in frustrated quantum spin systems.

Hole-Doping Effects on a Frustrated Spin Ladder

Hole-doping effects are investigated on the t – J ladder model with the linked-tetrahedra structure. We discuss how a metal–insulator transition occurs upon hole doping with particular emphasis on the effects of geometrical frustration. By computing the electron density and the spin correlation function by the density matrix renormalization group, we show that strong frustration triggers a first-order transition to a metallic phase, when holes are doped into the plaquette-singlet phase. By examining spin excitations in a metallic case in detail, we discuss whether the spin-gap phase persists upon hole doping according to the strength of frustration. It is further shown that the lowest excited state in a spin-gap metallic phase can be described in two independent quasiparticles.

Ground-state phase diagram of quantum Heisenberg antiferromagnets on the anisotropic dimerized square lattice

The $S=1/2$ and $S=1$ two-dimensional quantum Heisenberg antiferromagnets on the anisotropic dimerized square lattice are investigated by the quantum Monte Carlo method. By finite-size-scaling analyses on the correlation lengths, the ground-state phase diagram parametrized by strengths of the dimerization and of the spatial anisotropy is determined much more accurately than the previous works. It is confirmed that the quantum critical phenomena on the phase boundaries belong to the same universality class as that of the classical three-dimensional Heisenberg model. Furthermore, for $S=1,$ we show that all the spin-gapped phases, such as the Haldane and dimer phases, are adiabatically connected in the extended-parameter space, though they are classified into different classes in terms of the string order parameter in the one-dimensional, i.e., the zero-interchain-coupling, case.

Magnetization process of random quantum spin chains

The magnetization process of spin chains with randomness is discussed. We emphasize a close analogy between these systems and disordered particle systems and pay particular attention to the (in)stability of spin-gapped phases against several types of randomness. Generically, spin-gap states (plateaus) and Bose-glass-like localized states compete and stable plateaus are possible only for special magnetizations determined by spin S and the period of a pure system. When no external field is applied, the random-singlet state or the Griffith's phase is possible.

Effective gauge-field theory of thet−Jmodel in the charge-spin separated state and its transport properties

We study the slave-boson t-J model of cuprates with high superconducting transition temperatures, and derive its low-energy effective field theory for the charge-spin separated state in a self-consistent manner. The phase degrees of freedom of the mean field for hoppings of holons and spinons can be regarded as a U(1) gauge field, $A_i$. The charge-spin separation occurs below certain temperature, $T_{\rm CSS}$, as a deconfinement phenomenon of the dynamics of $A_i$. Below certain temperature $T_{\rm SG} (< T_{\rm CSS})$, the spin-gap phase develops as the Higgs phase of the gauge-field dynamics, and $A_i$ acquires a mass $m_A$. The effective field theory near $T_{\rm SG}$ takes the form of Ginzburg-Landau theory of a complex scalar field $\lambda$ coupled with $A_i$, where $\lambda$ represents d-wave pairings of spinons. Three dimensionality of the system is crucial to realize a phase transition at $T_{\rm SG}$. By using this field theory, we calculate the dc resistivity $\rho$. At $T > T_{\rm SG}$, $\rho$ is proportional to $T$. At $T < T_{\rm SG}$, it deviates downward from the $T$-linear behavior as $\rho \propto T \{1 -c(T_{\rm SG}-T)^d \}$. When the system is near (but not) two dimensional, due to the compactness of the phase of the field $\lambda$, the exponent $d$ deviates from its mean-field value 1/2 and becomes a nonuniversal quantity which depends on temperature and doping. This significantly improves the comparison with the experimental data.

Competing Spin-Gap Phases in a Frustrated Quantum Spin System in Two Dimensions

We investigate quantum phase transitions among the spin-gap phases and the magnetically ordered phases in a two-dimensional frustrated antiferromagnetic spin system, which interpolates several important models such as the orthogonal-dimer model as well as the model on the 1/5-depleted square lattice. By computing the ground state energy, the staggered susceptibility and the spin gap by means of the series expansion method, we determine the ground-state phase diagram and discuss the role of geometrical frustration. In particular, it is found that a RVB-type spin-gap phase proposed recently for the orthogonal-dimer system is adiabatically connected to the plaquette phase known for the 1/5-depleted square-lattice model.

Staggered liquid phases of the one-dimensional Kondo-Heisenberg lattice model

We describe a family of one-dimensional (1D) liquids, which we call ``staggered liquids,'' in the phase diagram of the 1D Kondo-Heisenberg model. It encompasses three distinct spin-gapped liquids and a Luttinger liquid (LL) phase. A staggered liquid is characterized by gapless modes with a large Fermi-sea signature in the charge-density wave (CDW) mode, and the superconducting order involves the near condensation of charge-$2e$ Cooper pairs with finite center-of-mass momentum. In particular, the conventional gapless ${2k}_{F}$ CDW and $k=0$ pairing modes are absent. We analytically derive the phase transition from an intermediate-coupling spin-gap phase to the strong-coupling gapless LL phase of the Kondo-Heisenberg lattice model.

Frustrated Heisenberg antiferromagnet on the pyrochlore lattice

We investigate quantum phase transitions for the $s=1/2$ antiferromagnetic Heisenberg model on a pyrochlore lattice. By means of a series expansion starting from isolated tetrahedra, the ground-state phase diagram is determined. When the ratio of the two competing exchange couplings is varied, the first-order (second-order) quantum phase transition occurs between the two spin gap phases (the spin-gap and the antiferromagnetic phases). We also discuss some properties expected for the s=1 pyrochlore spin system.

Single-hole dynamics in dimerized and frustrated spin chains

We present a unified account for the coupled single-hole and spin dynamics in the spin-gap phase of dimerized and frustrated spin chains and two-leg spin ladders. Based on the strong dimer limit of a one-dimensional ${t}_{1,2,3}$-${J}_{1,2,3}$ model a diagrammatic approach is presented that employs a mapping of the spin Hamiltonian onto a pseudofermion bond-boson model. Results for the single-hole spectrum are detailed. A finite quasiparticle weight is observed and studied for a variety of system parameters. A comparison with existing exact-diagonalization data is performed and good agreement is found.