Emptiness formation probability in the domain-wall six-vertex model

The emptiness formation probability in the six-vertex model with domain wall boundary conditions is considered. This correlation function allows one to address the problem of limit shapes in the model. We apply the quantum inverse scattering method to calculate the emptiness formation probability for the inhomogeneous model. For the homogeneous model, the result is given both in terms of certain determinant and as a multiple integral representation.     

Competing orders in one-dimensional half-integer fermionic cold atoms: A conformal field theory approach

The physical properties of arbitrary half-integer spins F=N−1/2$F=N-1/2$ fermionic cold atoms loaded into a one-dimensional optical lattice are investigated by means of a conformal field theory approach. We show that for attractive interactions two different superfluid phases emerge for F?3/2$F?3/2$: A BCS pairing phase, and a molecular superfluid phase which is formed from bound-states made of 2N   fermions. In the low-energy approach, the competition between these instabilities and charge-density waves is described in terms of ZN${\mathbb{Z}}_N$ parafermionic degrees of freedom. The quantum phase transition for F=3/2,5/2$F=3/2,5/2$ is universal and shown to belong to the Ising and three-state Potts universality classes respectively. In contrast, for F?7/2$F?7/2$, the transition is non-universal. For a filling of one atom per site, a Mott transition occurs and the nature of the possible Mott-insulating phases are determined.     

Exact results of a mixed spin-1/2 and spin-1 Ising chain with both longitude and transverse single-ion anisotropies

The mixed spin-1/2 and spin-1 Ising chain with both longitude and transverse single-ion anisotropies Dz and Dx is solved exactly by means of a mapping to the spin-1/2 Ising chain with the alternating transverse fields and the Jordan-Wigner transformation. The analytical expressions of the quasi-particles' spectra Λk, the minimal energy gap Δ₀ for exciting a fermion quasi-particle, the minimal energy gap Δh for exciting a hole, and the ground state energy are obtained. The phase diagram of the ground state is also given. The results show that when Dz?0 for any finite value of Dx, there is no quantum critical point and the ground state is always in a spin ordered phase disregard of the boundary condition in the present system.     

Hubbard-like models in high spatial dimensions

The present paper studies the properties of Hubbard-like models in high spatial dimensionsD. In a first par the limit of infinite dimension and its main features-i.e.i) the mapping onto a generalized atomic model with an additional auxiliary field andii) the validity of the local approximation for the self-energy-are worked out in a systematic (1/D)-expansion. Since the hopping matrix elements have to be properly scaled with the dimensionD, the (1/D)-expansion is also an expansion in the hopping amplitude. Thus for small hopping theD-limit may serve as a proper approximation for finite-dimensional systems. The second part of the paper adopts the hybridisation-perturbation theory of the single impurity Anderson model in order to construct a perturbation theory for the auxiliary field of the generalized atom which can also be interpreted as an expansion in the hopping amplitude. The non-crossing approximation (NCA) is used to study the antiferromagnetic phase transtion of theD-Hubbard model in the case of half filling: the critical temperature, the antiferromagnetic order parameter and the free energy of the lattice system are calculated. The NCA-results are in quite good agreement with recent results from the imaginary-time discretisation method.     

Anyonic loops in three-dimensional spin liquid and chiral spin liquid

We established a large class of exactly soluble spin liquids and chiral spin liquids on three-dimensional helix lattices by introducing Kitaev-type's spin coupling. In the chiral spin liquids, exact stable ground states with spontaneous breaking of the time reversal symmetry are found. The fractionalized loop excitations in both the spin and chiral spin liquids obey non-Abelian statistics. We characterize this kind of statistics by non-Abelian Berry phase and quantum algebra relation. The topological correlation of loops is independent of local order parameter and it measures the intrinsic global quantum entanglement of degenerate ground states.     

Matter-wave interference in Bose-Einstein condensates: A dispersive hydrodynamic perspective

The interference pattern generated by the merging interaction of two Bose-Einstein condensates reveals the coherent, quantum wave nature of matter. An asymptotic analysis of the nonlinear Schrödinger equation in the small dispersion (semiclassical) limit, experimental results, and three-dimensional numerical simulations show that this interference pattern can be interpreted as a modulated soliton train generated by the interaction of two rarefaction waves propagating through the vacuum. The soliton train is shown to emerge from a linear, trigonometric interference pattern and is found by use of the Whitham modulation theory for nonlinear waves. This dispersive hydrodynamic perspective offers a new viewpoint on the mechanism driving matter-wave interference.     

Low temperature thermodynamics of inverse square spin models in one dimension

We present a field-theoretic renormalization group calculation in two loop order for classical O(N)-models with an inverse square interaction in the vicinity of their lower critical dimensionality one. The magnetic susceptibility at low temperatures is shown to diverge like with a=(N-2)/(N-1) and . From a comparison with the exactly solvable Haldane-Shastry model we find that the same temperature dependence applies also to ferromagnetic quantum spin chains. Received: 20 February 1998 / Revised: 27 April 1998 / Accepted: 30 April 1998     

Quantum critical phenomena, entanglement entropy and Hubbard model in 1d with the boundary site with a negative chemical potential −p and the Hubbard coupling U positive

Recently the ground state and some excited states of the half-filled case of the 1d Hubbard model were discussed exactly for an open chain with L sites. The case when the boundary site has the chemical potential −p and the Hubbard coupling U is positive was considered. We model CeAl₂ nanoparticles, in which a valence of 4f electron number changes on surface Ce atoms, by this Hubbard model. A surface phase transition exists at some critical value pc3 of chemical potential (its absolute value) p in the model; when p<pc3 all the charge excitations have the gap, while there exists a massless charge mode when p>pc3. The aim of this Letter is to find whether this surface phase transition is of the first order or of the second order. We have found that the entanglement entropy and its derivative has a discontinuity at pc3 in general and thus this transition is of the first order (with exception of two points for the probability w₂ of occurrence of two electrons with opposites spins on the same site). There is a divergence in the difference of entanglement entropy for points w₂=0 and . The first point w₂=0 corresponds to ferro- (antiferro-) magnetic state at half-filled case. The second point does not correspond to any state for halffilled case. In the first case there is present the surface phase transition of the second order type.     

Electronic quasiparticle structure of ferromagnetic bcc iron

We investigate the influence of electron correlations on the temperature-dependence of the electronic structure of ferromagnetic bcc iron by use of a manybody evaluation of a generalized model of magnetism. The single-particle part of the model-Hamiltonian is taken from an LDA band structure calculation. The manybody interactions are described by only two parameters, an intraband Coulomb interactionU and an interband exchangeJ. WithU=1.8 eV andJ=0.2 eV the self-consistent model solution yields aT=0 moment of about 2.04 µ_B and a Curie-temperature of 1044K. Details of the magnetic behaviour of Fe can be traced back to a striking temperature variation of the quasiparticle density of states. A novel explanation for the experimentally-observed non-collapsing exchange splitting is demonstrated in terms of the temperature-dependent spectral density for wave-vectors near the -point. Typical differences in the magnetic behaviour of Fe and Ni are worked out.     

Spin current in quantum XXZ spin chain

The spin current in the one-dimensional quantum XXZ spin chain is studied based on the exact solutions. It is found that the spin voltage controlled by the unparallel boundary magnetic fields can induce the pure longitudinal spin current in the system. By using Wiener–Hopf and generalized algebraic Bethe ansatz methods, the analytic expressions for the spin current and the spin conductance are obtained. The spin current is proportional to the inverse of the length of the spin chain. The magnitude of spin current can be manipulated by the strength and the twist angle of two boundary magnetic fields. The exact analysis also shows that there exist an Ohm law or London equation type relation between the spin current and the spin conductance.     

The Berry phase: A topological test for the spectrum structure of frustrated quantum spin systems

The nature of the low energy spectrum of frustrated quantum spin systems is investigated by means of a topological test introduced by Hatsugai [Y. Hatsugai, J. Phys. Soc. Jpn. 73 (2004) 2604; Y. Hatsugai, J. Phys. Soc. Jpn. 74 (2005) 1374; Y. Hatsugai, J. Phys. Soc. Jpn. 75 (2006) 123601] which enables to infer the possible existence or absence of a gap between the ground state and excited states of these systems. The test relies on the determination of an order parameter which is a Berry phase. The structure of the spectra of even and odd-legged systems in 2d and 3d is analysed. Results are confronted with previous work.     

The spin-ladder and spin-chain system (La,Y,Sr,Ca)14Cu24O41: Electronic phases,charge and spin dynamics

The quasi-one-dimensional cuprates (La,Y,Sr,Ca)₁₄Cu₂₄O₄₁, consisting of spin-chains and spin-ladders, have attracted much attention, mainly because they represent the first superconducting copper oxide with a non-square lattice. Theoretically, in isolated hole-doped two-leg ladders, superconductivity is tightly associated with the spin gap, although in competition with a charge-density wave (CDW). Indeed, both the gapped spin-liquid and CDW states have been established in the doped spin-ladders of _{Sr14-xCaxCu24O41}${\mathrm{Sr}}_{14-x}{\mathrm{Ca}}_x{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$, however the relevance of these objects to electronic properties and superconductivity is still subject of intensive discussion. In this treatise, an appreciable set of experimental data is reviewed, which has been acquired in recent years, indicating a variety of magnetic and charge arrangements found in the chains and ladders of underdoped (La,Y)_y(S,Ca)_14−yCu₂₄O₄₁ and fully doped _{Sr14-xCaxCu24O41}${\mathrm{Sr}}_{14-x}{\mathrm{Ca}}_x{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$. Based on these data, phase diagrams are constructed for the chains of underdoped systems (as a function of La, Y-substitution), as well as for the chains and ladders of the fully doped ones (as a function of Ca-substitution). We try to reconcile contradictory results concerning the charge dynamics in the ladders, like the hole redistribution between ladders and chains, collective modes and pseudogap, field-dependent transport and the temperature scales and doping levels at which the two-dimensional CDW develops in the ladder planes. The remaining open issues are clearly extracted. In the discussion the experimental results are contrasted with theoretical predictions, which allows us to conclude with two important remarks concerning the nature of the competing CDW and superconducting ground states. A density wave in ladders, characterized by a sinusoidal charge modulation, belongs to the class of broken symmetry patterns, which is theoretically predicted for strongly correlated low-dimensional electron systems; however its precise texture and nature is still an open issue. As for superconductivity, the presence of the spin gap in the normal state points towards d  -wave symmetry and magnetic origin of the attractive interaction. However, there is a finite density of mobile quasi-particles that appears for high Ca contents and increases with pressure, concomitantly with increased two-dimensionality and metallicity. For this reason the superconductivity in the doped ladders of _{Sr14-xCaxCu24O41}${\mathrm{Sr}}_{14-x}{\mathrm{Ca}}_x{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ which occurs under high pressure cannot simply be a stabilization of the d-wave superconductivity expected for a pure single ladder system.     

Effect of twist inhomogeneity on soliton spin excitations in a helimagnet

The effect of twist inhomogeneity on the soliton spin excitations in a one-dimensional inhomogeneous helimagnet in the semiclassical limit is investigated by solving a generalised perturbed fourth order nonlinear Schrödinger equation in the continuum limit. A multiple scale perturbation analysis shows that the amplitude of the perturbed soliton depends on the nature of the inhomogeneity, but its velocity remains constant.