Dimensional Quantum Spin Research Articles

(2 + 1)-dimensional quantum gravity, spin networks and asymptotics

A method to evaluate spin networks for (2 + 1)-dimensional quantum gravity is given. We analyse the evaluation of spin networks for Lorentzian, Euclidean and a new limiting case of Newtonian quantum gravity. Particular attention is paid to the tetrahedron and to the study of its asymptotics. Moreover, we propose that all this technique can be extended to spin networks for quantum gravity in any dimension.

Frustrated three-dimensional quantum spin liquid in CuHpCl

Inelastic neutron scattering measurements are reported for the quantum antiferromagnetic material Cu_2(C_5H_12N_2)_2Cl_4 (CuHpCl). The magnetic excitation spectrum forms a band extending from 0.9 meV to 1.4 meV. The spectrum contains two modes that disperse throughout the a-c plane of the monoclinic unit cell with less dispersion along the unique b-axis. Simple arguments based on the measured dispersion relations and the crystal structure show that a spin ladder model is inappropriate for describing CuHpCl. Instead, it is proposed that hydrogen bond mediated exchange interactions between the bi-nuclear molecular units yield a three-dimensional interacting spin system with a recurrent triangular motif similar to the Shastry-Sutherland Model (SSM). Model independent analysis based on the first moment sum rule shows that at least four distinct spin pairs are strongly correlated and that two of these, including the dimer bond of the corresponding SSM, are magnetically frustrated. These results show that CuHpCl should be classified as a frustration induced three dimensional quantum spin liquid.

Resonant electron transmission through a finite quantum spin chain.

Electron transport in a finite one-dimensional quantum spin chain (with ferromagnetic exchange) is studied within an s-d exchange Hamiltonian. Spin transfer coefficients strongly depend on the sign of the s-d exchange constant. For a ferromagnetic coupling, they exhibit a novel resonant pattern, reflecting the salient features of the combined electron-spin system. Spin-flip processes are inelastic and feasible at finite voltage or at finite temperature.

Time-reversal in NMR of solids

The behavior of multiple spin dynamics under time-reversal excitation is investigated in strongly dipolar coupled spin networks. It is demonstrated that the typical physical intuition that NMR spectroscopists have of time- reversal in such systems is erroneous. By studying the equation of motion of the spin system in an infinite one- dimensional quantum spin chain with nearest-neighbor dipolar interactions and evolving under time-reversal excitation, a more appropriate physical picture emerges. Implications of these new findings are briefly discussed in the context of error propagation and teleportation in NMR quantum information processing.

Commutation relations of vertex operators related with the spin representation of Uq(Dn

A new scheme to study the XXZ spin chain in massive regime is introduced by Davies et al in [1]. In this scheme, which is called symmetry approach, the space of states is identified with some Uq(A\_ ) -module. Under this identification, the XXZ Hamiltonian can be constructed on this module as an operator which commutes with the action of Uq(A '). Furthermore, the row transfer matrix and creation (annihilation) operators can be constructed by using vertex operators. In a similar way to [1], the higher spin chain [2] and the models related to the vector representation ofUq(A^) [3], Uq(B^ U q ( D ( n } ) [5] are studied. In this paper, we consider the model related with the spin representation of Uq(Dn ). In physics the model that we consider here is explained as follows. It is a one dimensional quantum spin chain model constructed from the spin representation of Uq(Dn )• The Hamiltonian acts on the space of the infinite tensor product

Translational Symmetry Breaking and Soliton Sectors for Massive Quantum Spin Models in 1 + 1 Dimensions

We consider the classification of pure infinite volume ground states and that of soliton sectors for 1+1 dimensional massive quantum spin models. We obtain a proof that non-translationally invariant ground state cannot exist for a class of translationally invariant Hamiltonians including the spin 1 AKLT (Affleck Kennedy Lieb Tasaki) antiferromagnetic spin model. We also obtain a complete classification of soliton sectors (up to unitary equivalence) for certain massive models (e.g. ferromagnetic XXZ models).

Remarks on duality of 1 dimensional quantum spin models

We present some results on duality maps and ground states of 1 dimensional quantum spin models. We also give some applications to Kramers Wannier duality and the nonlocal transformation that Kennedy and Tasaki discovered in their study of Haldane phase of quantum antiferromagnetic spin models.

A New Approach to Quantum Spin Chains at Finite Temperature

Presented is a new approach to the study of one dimensional quantum spin systems at finite temperature. The approach is based upon a general structure of solvable models; the Yang-Baxter equation and the Bethe ansatz equation, and in addition the evaluation of finite size corrections. Provided that the ground state is constructed by the Bethe ansatz method, exact low temperature expansions of physical quantities are given without further assumption.

A note on the Monte Carlo simulation of one dimensional quantum spin systems

The one dimensional Ising model in a transverse field is treated by Monte Carlo methods in order to study the approach originally proposed by Suzuki, Miyashita and Kuroda.

Gibbs states of a one dimensional quantum lattice

A one dimensional infinite quantum spin lattice with a finite range interaction is studied. The Gibbs state in the infinite volume limit is shown to exist as a primary state of a UHF algebra. The expectation value of any local observables in the state as well as the mean free energy depend analytically on the potential, showing no phase transition. The Gibbs state is an extremal KMS state.