On $\mathsf{c = 1}$ critical phases in anisotropic spin-1 chains

Quantum spin-1 chains may develop massless phases in presence of Ising-like and single-ion anisotropies. We have studied c = 1 critical phases by means of both analytical techniques, including a mapping of the lattice Hamiltonian onto an O(2) NL M, and a multi-target DMRG algorithm which allows for accurate calculation of excited states. We find excellent quantitative agreement with the theoretical predictions and conclude that a pure Gaussian model, without any orbifold construction, describes correctly the low-energy physics of these critical phases. This combined analysis indicates that the multicritical point at large single-ion anisotropy does not belong to the same universality class as the Takhtajan-Babujian Hamiltonian as claimed in the past. A link between string-order correlation functions and twisting vertex operators, along the c = 1 line that ends at this point, is also suggested.Received: 16 July 2003, Published online: 24 October 2003PACS: 75.40.-s Critical-point effects, specific heats, short-range order - 75.10.Jm Quantized spin models - 02.70.-c Computational techniques     

High-temperature morphology of stepped gold surfaces

Molecular dynamics simulations with a classical many-body potential are used to study the high-temperature stability of stepped non-melting metal surfaces. We have studied in particular the Au(111) vicinal surfaces in the (M + 1,M− 1,M) family and the Au(100) vicinals in the (M,1,1) family. Some vicinal orientations close to the non-melting Au(111) surface become unstable close to the bulk melting temperature and facet into a mixture of crystalline (111) regions and localized surface-melted regions. On the contrary, we do not find high-temperature faceting for vicinals close to Au(100), also a non-melting surface. These (100) vicinal surfaces gradually disorder with disappearance of individual steps well below the bulk melting temperature. We have also studied the high-temperature stability of ledges formed by pairs of monatomic steps of opposite sign on the Au(111) surface. It is found that these ledges attract each other, so that several of them merge into one larger ledge, whose edge steps then act as a nucleation site for surface melting.     

Geometric phase for mixed states: a differential geometric approach

A new definition and interpretation of the geometric phase for mixed state cyclic unitary evolution in quantum mechanics are presented. The pure state case is formulated in a framework involving three selected principal fiber bundles, and the well-known Kostant-Kirillov-Souriau symplectic structure on (co-) adjoint orbits associated with Lie groups. It is shown that this framework generalizes in a natural and simple manner to the mixed state case. For simplicity, only the case of rank two mixed state density matrices is considered in detail. The extensions of the ideas of null phase curves and Pancharatnam lifts from pure to mixed states are also presented.     

Exact entanglement entropy of the XYZ model and its sine-Gordon limit

We obtain the exact expression for the Von Neumann entropy for an infinite bipartition of the XYZ model, by connecting its reduced density matrix to the corner transfer matrix of the eight vertex model. Then we consider the anisotropic scaling limit of the XYZ chain that yields the (1+1)-dimensional sine-Gordon model. We present the formula for the entanglement entropy of the latter, which has the structure of a dominant logarithmic term plus a constant, in agreement with what is generally expected for a massive quantum field theory.