Entanglement and criticality in quantum impurity systems

We investigate the entanglement between a spin and its environment in impurity systems which exhibit a second-order quantum phase transition separating a delocalized and a localized phase for the spin. As an application, we employ the spin-boson model, describing a two-level system (spin) coupled to a sub-Ohmic bosonic bath with power-law spectral density, J(omega) proportional to omega(s) and 0 < s < 1. Combining Wilson's numerical renormalization group method and hyperscaling relations, we demonstrate that the entanglement between the spin and its environment is always enhanced at the quantum phase transition resulting in a visible cusp (maximum) in the entropy of entanglement. We formulate a correspondence between criticality and impurity entanglement entropy, and the relevance of these ideas to nanosystems is outlined.     

Spin glass models with ferromagnetically biased couplings on the Bethe lattice: analytic solutions and numerical simulations

We derive the zero-temperature phase diagram of spin glass models with a generic fraction of ferromagnetic interactions on the Bethe lattice. We use the cavity method at the level of one-step replica symmetry breaking (1RSB) and we find three phases: a replica-symmetric (RS) ferromagnetic one, a magnetized spin glass one (the so-called mixed phase), and an unmagnetized spin glass one. We are able to give analytic expressions for the critical point where the RS phase becomes unstable with respect to 1RSB solutions: we also clarify the mechanism inducing such a phase transition. Finally we compare our analytical results with the outcomes of a numerical algorithm especially designed for finding ground states in an efficient way, stressing weak points in the use of such numerical tools for discovering RSB effects. Some of the analytical results are given for generic connectivity.     

Nematic and chiral order for planar spins on a triangular lattice

We propose a variant of the antiferromagnetic XY model which includes a biquadratic (J2) as well as the quadratic (J1) interaction on the triangular lattice. The phase diagram for large J2/J1 exhibits a phase with coexisting quasi-long-range nematic, and long-ranged vector spin chirality orders in the absence of magnetic order, which qualifies our model as the first instance of a classical spin model that exhibits a vector chiral spin liquid phase. The interplay of nematic and spin chirality orders is discussed. A variety of critical properties are derived by means of Monte Carlo simulation.     

Low temperature phase diagrams for quantum perturbations of classical spin systems

We consider a quantum spin system with Hamiltonian $$H = H^{(0)} + \lambda V,$$ whereH ⁽⁰⁾ is diagonal in a basis ∣s〉=? _x ∣s _x 〉 which may be labeled by the configurationss={s_x} of a suitable classical spin system on ? ^d , $$H^{(0)} |s\rangle = H^{(0)} (s)|s\rangle .$$ We assume thatH ⁽⁰⁾(s) is a finite range Hamiltonian with finitely many ground states and a suitable Peierls condition for excitation, whileV is a finite range or exponentially decaying quantum perturbation. Mapping thed dimensional quantum system onto aclassical contour system on ad+1 dimensional lattice, we use standard Pirogov-Sinai theory to show that the low temperature phase diagram of the quantum spin system is a small perturbation of the zero temperature phase diagram of the classical HamiltonianH ⁽⁰⁾, provided λ is sufficiently small. Our method can be applied to bosonic systems without substantial change. The extension to fermionic systems will be discussed in a subsequent paper.     

Classical spin systems in the presence of a wall: Multicomponent spins

In this paper we investigate classical spin systems on a semi-infinite lattice. We establish detailed properties of such systems near the surface layer. For the Ising- and the classicalXY models on a semi-infinite lattice we study the phase diagram, the critical properties and the decay of spin-spin correlations near the surface layer.     

Point-contact tunneling spectroscopy between a Nb tip and an ideal topological insulator Sn-doped Bi1.1Sb0.9Te2S

We find that the quantum-classical correspondence in integrable systems is characterized by two time scales. One is the Ehrenfest time below which the system is classical; the other is the quantum revival time beyond which the system is fully quantum. In between, the quantum system can be well approximated by classical ensemble distribution in phase space. These results can be summarized in a diagram which we call Ehrenfest diagram. We derive an analytical expression for Ehrenfest time, which is proportional to h~(-1/2). According to our formula, the Ehrenfest time for the solar-earth system is about 10~(26) times of the age of the solar system. We also find an analytical expression for the quantum revival time, which is proportional to h~(-1). Both time scales involve ω(I), the classical frequency as a function of classical action. Our results are numerically illustrated with two simple integrable models. In addition, we show that similar results exist for Bose gases, where 1/N serves as an effective Planck constant.     

Quantum phase transition in spin glasses with multi-spin interactions

We examine the phase diagram of the p-interaction spin glass model in a transverse field. We consider a spherical version of the model and compare with results obtained in the Ising case. The analysis of the spherical model, with and without quantization, reveals a phase diagram very similar to that obtained in the Ising case. In particular, using the static approximation, reentrance is observed at low temperatures in both the quantum spherical and Ising models. This is an artifact of the approximation and disappears when the imaginary time dependence of the order parameter is taken into account. The resulting phase diagram is checked by accurate numerical investigation of the phase boundaries.     

Field-induced supersolid phase in spin-one Heisenberg models

We use numerical methods to demonstrate that the phase diagram of S=1 Heisenberg models with uniaxial anisotropy contains an extended supersolid phase. We show that this Hamiltonian is a particular case of a more general and ubiquitous model that describes the low-energy spectrum of some isotropic and frustrated spin-dimer systems. This result is crucial for finding a spin supersolid state in real magnets.     

Diverse solid and supersolid phases of bosons in a triangular lattice

We investigate the ground state of bosons with long-range interactions in the large U limit on a triangular lattice. By mapping this system to the spin-1/2 XXZ model in a magnetic field, we can apply the spin wave theory to this study. We demonstrate how to construct the phase diagrams within the spin wave theory. The phase diagrams are given in an extensive parameter region, where, besides the superfluid phase, diverse solid and supersolid phases are shown to exist in this model. Especially, we find that the phase diagram obtained in this method is consistent with the one obtained previously using numerical techniques in the Ising limit. This confirms the effectiveness of our method. We analyze the stability of all the obtained supersolids and show that they will not be ruined by the quantum fluctuations. We observe that the quantum fluctuations in the stripe supersolid phase could be enhanced by the external field. We also discuss the relevance of our result with the experiment that may be realized with ultracold bosonic polar molecules in a triangular optical lattice.     

Wang-Landau study of the triangular Blume-Capel ferromagnet

We report on numerical simulations of the two-dimensional Blume-Capel ferromagnet embedded in the triangular lattice. The model is studied in both its first- and second-order phase transition regime for several values of the crystal field via a sophisticated two-stage numerical strategy using the Wang-Landau algorithm. Using classical finite-size scaling techniques we estimate with high accuracy phase-transition temperatures, thermal, and magnetic critical exponents and we give an approximation of the phase diagram of the model.     

Eine phasenraumdarstellung für spinsysteme

We start with the definition of two mapping operators, one of them is the projection operator onto coherent spin states. With the help of these operators we derive a mapping theorem which defines a correspondence between the operators in spin space andc-number functions of a certain class. It is shown that this correspondence is one-to-one. The quantum-mechanical expectation value of an operator is found to be expressible in the form of a phase space average of classical statistical mechanics. We also derive a product theorem which allows us to transcribe the equations of motion for operators into equivalent equations for thec-number functions. As an illustration of the theory, some examples are discussed.     

Magnetic phase diagram of the dimerized spin S = 1/2 ladder

The ground-state magnetic phase diagram of a spin S=1/2 two-leg ladder with alternating rung exchange J_⊥(n)=J_⊥[1 + (-1)ⁿ δ] is studied using the analytical and numerical approaches. In the limit where the rung exchange is dominant, we have mapped the model onto the effective quantum sine-Gordon model with topological term and identified two quantum phase transitions at magnetization equal to the half of saturation value from a gapped to the gapless regime. These quantum transitions belong to the universality class of the commensurate-incommensurate phase transition. We have also shown that the magnetization curve of the system exhibits a plateau at magnetization equal to the half of the saturation value. We also present a detailed numerical analysis of the low energy excitation spectrum and the ground state magnetic phase diagram of the ladder with rung-exchange alternation using Lanczos method of numerical diagonalizations for ladders with number of sites up to N = 28. We have calculated numerically the magnetic field dependence of the low-energy excitation spectrum, magnetization and the on-rung spin-spin correlation function. We have also calculated the width of the magnetization plateau and show that it scales as δ^ν, where critical exponent varies from ν = 0.87±0.01 in the case of a ladder with isotropic antiferromagnetic legs to ν = 1.82±0.01 in the case of ladder with ferromagnetic legs. Obtained numerical results are in an complete agreement with estimations made within the continuum-limit approach.     

Supersolid phase in spin dimer XXZ systems under a magnetic field

Using the quantum Monte Carlo method, we study, under external magnetic fields, the ground state phase diagram of the two-dimensional spin S=1/2 dimer model with an anisotropic intraplane antiferromagnetic coupling. With the anisotropy 4 greater/approximately Delta greater/approximately 3, a supersolid phase characterized by a nonuniform Bose condensate density that breaks translational symmetry is found. The rich phase diagram also contains a checkerboard solid, an antiferromagnet in the z axis, and a superfluid phase formed by S(z)= +1 spin triplets which has a finite staggered magnetization in the in-plane direction. As we show, the model can be realized as a consequence of including the next nearest neighbor coupling among dimers and our results suggest that spin dimer systems may be an ideal model system to study the supersolid phase.     

Unveiling new magnetic phases of undoped and doped manganites

Novel ground-state spin structures in undoped and lightly doped manganites are investigated based on the orbital-degenerate double-exchange model, via mean-field and numerical techniques. In undoped manganites, a new antiferromagnetic (AFM) state, called the E-type phase, is found adjacent in parameter space to the A-type AFM phase. Its structure is in agreement with recent experimental results. This insulating E-AFM state is also competing with a ferromagnetic metallic phase as well. For doped layered manganites, the phase diagram includes another new AFM phase of the CxE1-x type. Experimental signatures of the new phases are discussed.     

Classial and quantum solitons in the transverse field Ising model

We investigate the shape and the dynamics of domain walls in the one-dimensional Ising model with spin S, exchange constant J and external transverse field Γ using numerical calculations up to S = 20 and analytical approximations. For $\tfrac{\Gamma } {{JS}}$ \] we describe classical domain walls as strongly localized excitations, which have either central spin or central bond symmetry. These symmetries are identified also in the quantum case, when solitary excitations develop into energy bands. In the classical limit S → ∞ localization results from the exponential vanishing of the bandwidth for the lowest bands. We describe the relation between the spectrum of moving classical solitons and the quantum band structure.     

Generalized nonlinear sigma model approach to alternating spin chains and ladders

We generalize the nonlinear sigma model treatment of quantum spin chains to cases including ferromagnetic bonds. When these bonds are strong enough, the classical ground state is no longer the standard Néel order and we present an extension of the known formalism to deal with this situation. We study the alternating ferromagnetic-antiferromagnetic spin chain introduced by Hida. The smooth crossover between decoupled dimers and the Haldane phase is semi-quantitatively reproduced. We study also a spin ladder with diagonal exchange couplings that interpolates between the gapped phase of the two-leg spin ladder and the Haldane phase. Here again we show that there is a good agreement between DMRG data and our analytical results. Received 6 September 1999     

Spin and charge ordering in three-leg ladders in oxyborates

We study the spin ordering within the three-leg ladders present in the oxyborate Fe3O2BO3 consisting of localized classical spins interacting with conduction electrons (one electron per rung). We also consider the competition with antiferromagnetic superexchange interactions to determine the magnetic phase diagram. Besides a ferromagnetic phase we find (i) a phase with ferromagnetic rungs ordered antiferromagnetically and (ii) a zigzag canted spin ordering along the legs. We also determine the induced charge ordering within the different phases and the interplay with lattice instability. Our model is discussed in connection with the lattice dimerization transition observed in this system, emphasizing the role of the magnetic structure.