Jordan-Wigner approach to dynamic correlations in spin ladders

Nunner, Tamara S.; Kopp, Thilo

doi:10.1103/physrevb.69.104419

Cited by 18 publications

(14 citation statements)

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“…To proceed further we will replace n ␣,i by its mean value. Although this simplification cannot be rigorously justified 54 and more elaborate treatments are possible in a Jordan-Wigner approach, 55 we show now that it qualitatively reproduces the results available by more sophisticated methods.…”

Section: Discussionsupporting

confidence: 58%

Asymmetric spin-12two-leg ladders: Analytical studies supported by exact diagonalization, DMRG, and Monte Carlo simulations

et al. 2010

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We consider asymmetric spin-1 2 two-leg ladders with nonequal antiferromagnetic ͑AF͒ couplings J ʈ and J ʈ along legs ͑ Յ 1͒ and ferromagnetic rung coupling, J Ќ . This model is characterized by a gap ⌬ in the spectrum of spin excitations. We show that in the large J Ќ limit this gap is equivalent to the Haldane gap for the AF spin-1 chain, irrespective of the asymmetry of the ladder. The behavior of the gap at small rung coupling falls in two different universality classes. The first class, which is best understood from the case of the conventional symmetric ladder at = 1, admits a linear scaling for the spin gap ⌬ ϳ J Ќ . The second class appears for a strong asymmetry of the coupling along legs, J ʈ Ӷ J Ќ Ӷ J ʈ and is characterized by two energy scales: the exponentially small spin gap ⌬ ϳ J Ќ exp͑−J ʈ / J Ќ ͒, and the bandwidth of the low-lying excitations induced by a Suhl-Nakamura indirect exchange ϳJ Ќ 2 / J ʈ . We report numerical results obtained by exact diagonalization, densitymatrix renormalization group and quantum Monte Carlo simulations for the spin gap and various spin correlation functions. Our data indicate that the behavior of the string order parameter, characterizing the hidden AF order in Haldane phase, is different in the limiting cases of weak and strong asymmetries. On the basis of the numerical data, we propose a low-energy theory of effective spin-1 variables, pertaining to large blocks on a decimated lattice.

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Section: Discussionsupporting

confidence: 58%

Asymmetric spin-12two-leg ladders: Analytical studies supported by exact diagonalization, DMRG, and Monte Carlo simulations

et al. 2010

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“…The two-component system can be regarded as a two-leg ladder with one component on each site 41,42 . For two-leg ladders Jordan-Wigner transformation can be applied directly when all sites are arranged in a 1D sequence (the zigzag path in Fig.6).…”

Section: Mapping Hard-core Bosons To Spinless Fermionsmentioning

confidence: 99%

Hard-core bosons in one-dimensional interacting topological bands

Guo

2012

Phys. Rev. A

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We study the hard-core bosons in one-dimensional (1D) interacting topological bands at different filling factors using exact diagonalization. At the filling factor $\nu=1$ and in the presence of on-site Hubbard interaction, we find no sign of the existence of the bosonic topological phase, which is in contrast to the fermionic case. Instead by studying the momentum distribution and the condensate fraction we find a superfluid (SF) to Mott-insulator transition driven by the Hubbard interaction. At the filling factor $\nu=1/3$ and in the presence of longer-ranged interactions, we identify the bosonic fractional topological phase (FTP) whose ground-states are characterized by the three-fold degeneracy and quantized total Berry phase, which is very similar to the fermionic case. Finally we discuss the reason of the different behaviors of hard-core bosons at different filling factors by mapping them to spinless fermions. Our these results can be realized in cold-atom experiments.Comment: PHYSICAL REVIEW A 86, 055604 (2012), brief repor

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“…В качестве 1D-магнетиков могут выступать как простые цепочки с различными типами взаимодействий и анизотропии, так и сложные структуры: лестничные системы, периодические группы магнитных ионов -декорированные цепочки и т. д. [3]. Гейзенберговская цепочка спина 1/2 является одной из фундаментальных и наиболее тщательно исследованных моделей магнетизма [4]: известны строгие решения методом анзаца Бете, а также различные аналитические и численные методы.…”

Section: Introductionunclassified

Вариационная Модель Низкоразмерного Магнетика

Кудасов¹,

Козабаранов²

2020

Физика Твердого Тела

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A variational method with nonlocal trial function is developed for quantum one-dimensional systems. It is applied to the XXZ spin-1/2 chain with an alternating magnetic field. A four-node trial wave function for the fermionic representation of the model is constructed. The results obtained in the model with an extended trial wave function demonstrate a significant increase in the accuracy of the ground state energy in the region of critical behavior compared with the solutions obtained previously. A method for calculation of the spin correlation function are discussed.

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Jordan-Wigner approach to dynamic correlations in spin ladders

Cited by 18 publications

References 50 publications

Asymmetric spin-12two-leg ladders: Analytical studies supported by exact diagonalization, DMRG, and Monte Carlo simulations

Asymmetric spin-12two-leg ladders: Analytical studies supported by exact diagonalization, DMRG, and Monte Carlo simulations

Hard-core bosons in one-dimensional interacting topological bands

Вариационная Модель Низкоразмерного Магнетика

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