Analytical study of the layered XY model with VCE method

Motivated by experiments on liquid-crystal films, we study the development of specific heat anomaly of finite layer system. With the VCE method, we introduce the strong surface interaction into the layered XY model and get the results of the forth-order analytical expansion. The results show that when the strong surface interaction becomes strong enough, the order trend defeats the quantum noise and the specific heat peak moves abnormally to the high temperature with the number of layers decreasing.

Criticality, factorization, and long-range correlations in the anisotropic XY model

We study the long-range quantum correlations in the anisotropic XY model. By first examining the thermodynamic limit, we show that employing the quantum discord as a figure of merit allows one to capture the main features of the model at zero temperature. Furthermore, by considering suitably large site separations we find that these correlations obey a simple scaling behavior for finite temperatures, allowing for efficient estimation of the critical point. We also address ground-state factorization of this model by explicitly considering finite-size systems, showing its relation to the energy spectrum and explaining the persistence of the phenomenon at finite temperatures. Finally, we compute the fidelity between finite and infinite systems in order to show that remarkably small system sizes can closely approximate the thermodynamic limit.

Monte Carlo study of the XY-model on quasi-periodic lattices

Monte Carlo Simulations were carried out using a nearest neighbour ferromagnetic XYmodel, on both 2-D and 3-D quasi-periodic lattices. In the case of 2-D, both the unfrustrated and frustrated XV-model were studied. For the unfrustrated 2-D XV-model, we have examined the magnetization, specific heat, linear susceptibility, helicity modulus and the derivative of the helicity modulus with respect to inverse temperature. The behaviour of all these quatities point to a Kosterlitz-Thouless transition occuring in temperature range Te == (1.0 -1.05) JlkB and with critical exponents that are consistent with previous results (obtained for crystalline lattices) . However, in the frustrated case, analysis of the spin glass susceptibility and EdwardsAnderson order parameter, in addition to the magnetization, specific heat and linear susceptibility, support a spin glass transition. In the case where the 'thin' rhombus is fully frustrated, a freezing transition occurs at Tf == 0.137 JlkB , which contradicts previous work suggesting the critical dimension of spin glasses to be de > 2 . In the 3-D systems, examination of the magnetization, specific heat and linear susceptibility reveal a conventional second order phase transition. Through a cumulant analysis and finite size scaling, a critical temperature of Te == (2.292 ± 0.003) JI kB and critical exponents of 0:' == 0.03 ± 0.03, f3 == 0.30 ± 0.01 and I == 1.31 ± 0.02 have been obtained.

Topological lattice actions for the 2d XY model

We consider the 2d XY Model with topological lattice actions, which are invariant against small deformations of the field configuration. These actions constrain the angle between neighbouring spins by an upper bound, or they explicitly suppress vortices (and anti-vortices). Although topological actions do not have a classical limit, they still lead to the universal behaviour of the Berezinskii-Kosterlitz-Thouless (BKT) phase transition — at least up to moderate vortex suppression. In the massive phase, the analytically known Step Scaling Function (SSF) is reproduced in numerical simulations. However, deviations from the expected universal behaviour of the lattice artifacts are observed. In the massless phase, the BKT value of the critical exponent ηc is confirmed. Hence, even though for some topological actions vortices cost zero energy, they still drive the standard BKT transition. In addition we identify a vortex-free transition point, which deviates from the BKT behaviour.

Contributions to the theory of the A15 compounds and to the theory of the XY model

The text of this thesis provides historical introduction to the two studies Theoretical Model of Superconductivity and the Martensitic Transformation in A15 Compounds" and "A Comparison of Kadanoff-Migdal Renormalization with New Monte Carlo Results for the XY Model", contained herein as appendices.

Bose-Hubbard model in a strong effective magnetic field: Emergence of a chiral Mott insulator ground state

Motivated by experiments on Josephson junction arrays, and cold atoms in an optical lattice in a synthetic magnetic field, we study the ``fully frustrated'' Bose-Hubbard model with half a magnetic flux quantum per plaquette. We obtain the phase diagram of this model on a two-leg ladder at integer filling via the density matrix renormalization group approach, complemented by Monte Carlo simulations on an effective classical XY model. The ground state at intermediate correlations is consistently shown to be a chiral Mott insulator (CMI) with a gap to all excitations and staggered loop currents which spontaneously break time-reversal symmetry. We characterize the CMI state as a vortex supersolid or an indirect exciton condensate, and discuss various experimental implications.

Chiral Mott insulator with staggered loop currents in the fully frustrated Bose-Hubbard model

Motivated by experiments on Josephson junction arrays in a magnetic field and ultracold interacting atoms in an optical lattice in the presence of a ``synthetic'' orbital magnetic field, we study the ``fully frustrated'' Bose-Hubbard model and quantum XY model with half a flux quantum per lattice plaquette. Using Monte Carlo simulations and the density matrix renormalization group method, we show that these kinetically frustrated boson models admit three phases at integer filling: a weakly interacting chiral superfluid phase with staggered loop currents which spontaneously break time-reversal symmetry, a conventional Mott insulator at strong coupling, and a remarkable ``chiral Mott insulator'' (CMI) with staggered loop currents sandwiched between them at intermediate correlation. We discuss how the CMI state may be viewed as an exciton condensate or a vortex supersolid, study a Jastrow variational wave function which captures its correlations, present results for the boson momentum distribution across the phase diagram, and consider various experimental implications of our phase diagram. Finally, we consider generalizations to a staggered flux Bose-Hubbard model and a two-dimensional (2D) version of the CMI in weakly coupled ladders.

Classical two-site fidelity and quantum phase transitions in the Ising model and the extended Hubbard model

In this Letter, the classical two-site-ground-state fidelity (CTGF) is exploited to identify quantum phase transitions (QPTs) for the transverse field Ising model (TFIM) and the one-dimensional extended Hubbard model (EHM). Our results show that the CTGF exhibits an abrupt change around the regions of criticality and can be used to identify QPTs in spin and fermionic systems. The method is especially convenient when it is connected with the density-matrix renormalization group (DMRG) algorithm. (C) 2008 Elsevier B.V. All rights reserved.

Quantum coherence and uncertainty in the anisotropic XY chain

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Factorization and criticality in the anisotropic XY chain via correlations

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Static and dynamic properties of incommensurate smectic-AIC liquid crystals

We study the elasticity, topological defects, and hydrodynamics of the recently discovered incommensurate smectic (AIC) phase, characterized by two collinear mass density waves of incommensurate spatial frequency. The low-energy long-wavelength excitations of the system can be described by a displacement field u(x) and a ��phason�� field w(x) associated, respectively, with collective and relative motion of the two constituent density waves. We formulate the elastic free energy in terms of these two variables and find that when w=0, its functional dependence on u is identical to that of a conventional smectic liquid crystal, while when u=0, its functional dependence on w is the same as that for the angle variable in a slightly anisotropic XY model. An arbitrariness in the definition of u and w allows a choice that eliminates all relevant couplings between them in the long-wavelength elastic energy. The topological defects of the system are dislocations with nonzero u and w components. We introduce a two-dimensional Burgers lattice for these dislocations, and compute the interaction between them. This has two parts: one arising from the u field that is short ranged and identical to the interaction between dislocations in an ordinary smectic liquid crystal, and one arising from the w field that is long ranged and identical to the logarithmic interaction between vortices in an XY model. The hydrodynamic modes of the AIC include first- and second-sound modes whose direction-dependent velocities are identical to those in ordinary smectics. The sound attenuations have a different direction dependence, however. The breakdown of hydrodynamics found in conventional smectic liquid crystals, with three of the five viscosities diverging as 1/? at small frequencies ?, occurs in these systems as well and is identical in all its details. In addition, there is a diffusive phason mode, not found in ordinary smectic liquid crystals, that leads to anomalously slow mechanical response analogous to that predicted in quasicrystals, but on a far more experimentally accessible time scale.

Dualidade na teoria de Landau-Ginzburg da supercondutividade

Neste trabalho abordamos a teoria de Ginzburg-Landau da supercondutividade (teoria GL). Apresentamos suas origens, características e resultados mais importantes. A idéia fundamental desta teoria e descrever a transição de fase que sofrem alguns metais de uma fase normal para uma fase supercondutora. Durante uma transição de fase em supercondutores do tipo II é característico o surgimento de linhas de fluxo magnético em determinadas regiões de tamanho finito chamadas comumente de vórtices. A dinâmica destas estruturas topológicas é de grande interesse na comunidade científica atual e impulsiona incontáveis núcleos de pesquisa na área da supercondutividade. Baseado nisto estudamos como essas estruturas topológicas influenciam em uma transição de fase em um modelo bidimensional conhecido como modelo XY. No modelo XY vemos que os principais responsáveis pela transição de fase são os vórtices (na verdade pares de vórtice-antivórtice). Villain, observando este fato, percebeu que poderia tornar explícita a contribuição desses defeitos topológicos na função de partição do modelo XY realizando uma transformação de dualidade. Este modelo serve como inspiração para a proposta deste trabalho. Apresentamos aqui um modelo baseado em considerações físicas sobre sistemas de matéria condensada e ao mesmo tempo utilizamos um formalismo desenvolvido recentemente na referência [29] que possibilita tornar explícita a contribuição dos defeitos topológicos na ação original proposta em nossa teoria. Após isso analisamos alguns limites clássicos e finalmente realizamos as flutuações quânticas visando obter a expressão completa da função correlação dos vórtices o que pode ser muito útil em teorias de vórtices interagentes (dinâmica de vórtices).