Impurity and boundary effects in one- and two-dimensional inhomogeneous Heisenberg antiferromagnets

Abstract

We calculate the ground-state energy of one and two-dimensional spatially inhomogeneous antiferromagnetic Heisenberg models for spins 1/2, 1, 3/2 and 2. Our calculations become possible as a consequence of the recent formulation of density-functional theory for Heisenberg models. The method is similar to spin-density-functional theory, but employs a local-density-type approximation designed specifically for the Heisenberg model, allowing us to explore parameter regimes that are hard to access by traditional methods, and to consider complications that are important specifically for nanomagnetic devices, such as the effects of impurities, finite-size, and boundary geometry, in chains, ladders, and higher-dimensional systems.PACS numbers: 71.15. Mb, 75.10.Jm, 75.50.Ee The study of low-dimensional spin systems is one of the central issues in the physics of correlated electrons. Model Hamiltonians of the Heisenberg type are widely used to study, e.g., antiferromagnetically coupled spin chains, ladders, and layers, 1,2 and constitute most useful models for strong correlations in undoped cuprates and manganites. Finite-size Heisenberg models, moreover, serve as paradigmatic models for the emerging field of nanomagnetism and spintronics. However, progress in the analysis of nanomagnetic devices requires capability to deal with 'real-life' complications, such as impurities of arbitrary size and location, boundaries of various shapes, and crossovers between finite and extended systems, or between one and higher dimensions. In the present paper we present a convenient and efficient numerical approach for calculating ground-state energies of antiferromagnetic Heisenberg models subjected to such complications.Traditional numerical methods are well suited for studying generic properties of homogeneous Heisenberg models, and have provided many important insights into the physics of magnetic systems. However, the very significant expenditure of computational effort required by methods such as group-theory-aided exact diagonalization, Quantum Monte Carlo (QMC), 3 or the densitymatrix renormalization group (DMRG), 4 imposes rather strict limits on the size and complexity of systems that can be studied. The mean-field approximation can, in principle, be applied to systems of almost arbitrary size and complexity, but its neglect of correlation makes it unreliable as a tool for studying many issues of current physical interest in strongly correlated systems. In ab initio calculations, density-functional theory (DFT) provides a convenient and reliable way to go beyond the mean-field (Hartree) approximation, allowing to study real systems of considerable size and complexity. 5,6,7 While DFT is in principle an exact reformulation of the many-body problem, 8 its practical implementation requires the use of approximations for the exchange-correlation energy. Among the most important such approximations is the local-density approximation (LDA), the essence of which is to use the exchange-correlation energy of the uniform electron liqui...

Energy of bond defects in quantum spin chains obtained from local approximations and from exact diagonalization

“…This so-called local-spin approximation [4,5] has been applied to investigate the energetics of impurities in one, two and three-dimensional Heisenberg models [4,5,6,7]. Impurities here are defined, relative to a homogeneous model in which all sites have the same spin S, as sites with a spin S I = S (see inset of Fig.…”

Teoria funcional da densidade aplicada ao modelo de Heisenberg

“…[9,10] Os resultados foram obtidos, em sua grande maioria, nas minhas orientações de Iniciação Científica dos alunos Paulo E. G. Assis e Rodrigo S. Veiga, de Mestrado de Poliana H. Penteado [34] e Guilherme N. Prata, [35] e de Doutorado de Fabiano C. de Souza. [36] Nos trabalhos desses alunos está a base da aplicação da DFT ao modelo de Heisenberg.…”

“…(1) da Ref. [10]) 35 4.3 Energia do estado fundamental, por spin, para cadeias abertas com N spins 1/2, com uma impureza de spin S I = 1 na borda (linha tracejada), ou no interior da cadeia (linha cheia), ou uma impureza na borda e outra no interior (linha ponto-tracejada). Os círculos representam os resultados exatos para o caso da impureza S = 1 na borda da cadeia.…”

“…Os funcionais são, até o momento, formulados dentro de aproximações locais a semelhança da LDA, aqui denominada de LSA (de Local Spin Approximation). [10] Queremos sempre que possível confrontar os resultados obtidos através dos funcionais com (lados exatos, mas corno estes são escassos para sistemas em duas ou três dimensões, apresentaremos em sua maioria dados para cadeias unidimensionais.…”

“…utilizamos neste trabalho a DFT, recentemente adaptada por nós para sistemas não-homogêneos descritos pelo Hamiltoniano de Heisenberg. [9,10] Enquanto outros métodos comumente encontrados na literatura se baseiam na função de onda de muitos corpos do sistema, na DFT as propriedades físicas são funcionais de uma densidade eletrônica, em nosso caso funcionais do valor esperado do operador de spin em cada sítio, como veremos. E nessa dependência com unia função densidade 71(0, mais simples que uma função de onda P(Fr , r2 , ...), que a DFT, em geral, ganha enorme vantagem computacional em relação a outros métodos.…”