Exact and density matrix renormalization group studies of two mixed spin-
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 branched-chain models developed for a heterotrimetallic Fe-Mn-Cu coordination polymer

Souza, Fabiana; Veríssimo, Luan M.; Strečka, Jozef; Lyra, Marcelo L.; Pereira, Maria S. S.

doi:10.1103/physrevb.102.064414

Cited by 22 publications

(10 citation statements)

References 79 publications

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“…This behavior is presented in the inset Fig. 11(b), where the gapped side (Y > Y c ) is similar to the finite-order Gaussian transition [45,46]. In this case, on one hand, there is still a point, where the rescaled energy gaps have minimal distances, that plays the same role as the crossing point in BKT transition.…”

Section: Now We Fit the Extrapolated Energy Gap With ∆E =mentioning

confidence: 74%

“…The level crossing can be between different types of excitations for different systems. After obtaining the results from LS, we test a universal method to detect quantum phase transitions: the scaling of the energy gap between the ground state and the first excited state [42][43][44][45][46]. The truncation effects in this energy gap that contains information on the divergent behavior of the correlation length, are also important indicators for different types of phase transitions.…”

Section: Introductionmentioning

confidence: 99%

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Truncation effects in the charge representation of the O(2) model

Zhang,

Meurice,

Tsai

2021

Preprint

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The O(2) model in Euclidean space-time is the zero-gauge-coupling limit of the compact scalar quantum electrodynamics. We obtain a dual representation of it called the charge representation. We study the quantum phase transition in the charge representation with a truncation to "spin S", where the quantum numbers have an absolute value less or equal to S. The charge representation preserves the gapless-to-gapped phase transition even for the smallest spin truncation S = 1. The phase transition for S = 1 is an infinite-order Gaussian transition with the same critical exponents δ and η as the Berezinskii-Kosterlitz-Thouless (BKT) transition, while there are true BKT transitions for S ≥ 2. The essential singularity in the correlation length for S = 1 is different from that for S ≥ 2. The exponential convergence of the phase transition point is studied in both Lagrangian and Hamiltonian formulations. We discuss the effects of replacing the truncated Û ± = exp(±i θ) operators by the spin ladder operators Ŝ± in the Hamiltonian. The marginal operators vanish at the Gaussian transition point for S = 1, which allows us to extract the η exponent with high accuracy.

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Section: Now We Fit the Extrapolated Energy Gap With ∆E =mentioning

confidence: 74%

Section: Introductionmentioning

confidence: 99%

Truncation effects in the charge representation of the O(2) model

Zhang,

Meurice,

Tsai

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…For example, the Ising class features a crossing behavior of the scaled excitation gap curves in the vicinity of the critical point. On the other hand, the scaled excitation gap curves behaves differently in Gaussian critical points, presenting a tangential scaling in the vicinity of the transition [43,44]. Exploring these ideas, we develop a simple method to determine the critical points and correlation length critical exponents directly from the scaled excitation gap data for the Gaussian class of quantum phase transitions.…”

Section: Model and The O(2) Nonlinear σ Model Mappingmentioning

confidence: 99%

“…An improved error protocol method for DMRG was introduced [42], where the critical Gaussian points was obtained with high accuracy exploring the von Neumann entropy behavior for large system sizes. Recently, a finite-size scaling analysis of the energy gaps in the vicinity of Gaussian transitions was introduced [43,44] in prototype models of heterotrimetallic compounds described as branched chains with alternate S = 1/2 and larger spins. It was shown that the closing of the gap on both phases meeting at the Gaussian critical point requires a proper tangential scaling form.…”

Section: Introductionmentioning

confidence: 99%

Tangential finite-size scaling of the Gaussian topological transition in the quantum spin-1 anisotropic chain

Veríssimo,

Pereira,

Lyra

2021

Preprint

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Scaling aspects of Gaussian topological phase-transitions in quantum spin chains are investigated using the prototypical one-dimensional spin-1 XXZ Heisenberg model with uniaxial single-ion anisotropy D. This model presents a critical line separating the gaped Haldane and large-D phases, with the relevant energy gap closing at the transition point. We show that a proper tangential finite-size scaling analysis is able to accurately locate the Gaussian critical line and to probe the continuously varying set of correlation length critical exponents. The specific features of the tangential scaling are highlighted in contrast with the standard scaling holding in the Ising-like transition between the gapless AF-Néel and gaped Haldane phases. Our results are compared with fieldtheoretic predictions and available high-accuracy data for specific points along the Gaussian line.

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“…Quantum Heisenberg spin chains provide an intriguing platform for an investigation of quantum magnetism using fully rigorous calculation methods being completely free of any uncontrolled approximation [1]. A few exactly solved Ising-Heisenberg and Heisenberg branched spin chains have recently attracted considerable attention, because they may exhibit striking quantum critical points of Kosterlitz-Thouless and Gaussian type [2][3][4]. Moreover, the Ising-Heisenberg and Heisenberg branched spin chains are not only purely theoretical models, but they are closely related to a few real-world experimental realizations from the family of polymeric coordination compounds [5,6].…”

Section: Introductionmentioning

confidence: 99%

Influence of a spatial anisotropy on presence of the intermediate one-half magnetization plateau of a spin-1/2 Ising-Heisenberg branched chain

Strecka,

Karlova,

Ghannadan

2021

Preprint

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A spin-1/2 Ising-Heisenberg branched chain constituted by regularly alternating Ising spins and Heisenberg dimers involving an additional side branching is exactly solved in a magnetic field by the transfer-matrix method. The spin-1/2 Ising-Heisenberg branched chain involves two different Ising and one Heisenberg coupling constants. The overall ground-state phase diagram is formed by three different ground states emergent depending on a mutual interplay between the magnetic field and three considered coupling constants: the modulated quantum antiferromagnetic phase, the quantum ferrimagnetic phase, and the classical ferromagnetic phase. It is shown that the interaction anisotropy connected to two different Ising coupling constants substantially influences a breakdown of the intermediate one-half magnetization plateau, which represents a macroscopic manifestation of the quantum ferrimagnetic phase.

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Exact and density matrix renormalization group studies of two mixed spin- (12,52,12) branched-chain models developed for a heterotrimetallic Fe-Mn-Cu coordination polymer

Cited by 22 publications

References 79 publications

Truncation effects in the charge representation of the O(2) model

Truncation effects in the charge representation of the O(2) model

Tangential finite-size scaling of the Gaussian topological transition in the quantum spin-1 anisotropic chain

Influence of a spatial anisotropy on presence of the intermediate one-half magnetization plateau of a spin-1/2 Ising-Heisenberg branched chain

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