Topology of many-body edge and extended quantum states in an open spin chain: 1/3 plateau, Kosterlitz-Thouless transition, and Luttinger liquid

Montenegro-Filho, R. R.; Matias, Fernanda S.; Coutinho‐Filho, M. D.

doi:10.1103/physrevb.102.035137

Cited by 19 publications

(12 citation statements)

References 73 publications

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“…We also observe the occupancy of the edge states of the ferrimagnetic plateau by one magnon at the indicated magnetic fields. These edge states appears in finite-size open systems associated with topological aspects [3,45] of the ferrimagnetic state.…”

Section: B Magnetization Curves and Local Magnetizationsmentioning

confidence: 99%

“…and was investigated in the isotropic [40][41][42] and anisotropic [41,43,44] cases. Ferrimagnetic systems İn particular, the behavior of the edge states associated with the 1/3 magnetization plateau of the AB 2 anisotropic chain was recently investigated [45]. Furthermore, rich phase diagrams are observed through doping [46][47][48][49][50] or adding geometric frustration [51][52][53][54][55][56][57][58] to the ferrimagnetic models.…”

Section: Introductionmentioning

confidence: 99%

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The role of density-dependent magnon hopping and magnon-magnon repulsion in ferrimagnetic spin-(1/2, $S$) chains in a magnetic field

da Silva,

Montenegro-Filho

2021

Preprint

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We compare the ground-state features of alternating ferrimagnetic chains (1/2, S) with S = 1, 3/2, 2, 5/2 in a magnetic field and the corresponding Holstein-Primakoff bosonic models up to order s/S, with s = 1/2, considering the fully polarized magnetization as the boson vacuum. The singleparticle Hamiltonian is a Rice-Mele model with uniform hopping and modified boundaries, while the interactions have a correlated (density-dependent) hopping term and magnon-magnon repulsion. The magnon-magnon repulsion increases the many-magnon energy and the density-dependent hopping decreases the kinetic energy. We use density matrix renormalization group calculations to investigate the effects of these two interaction terms in the bosonic model, and display the quantitative agreement between the results from the spin model and the full bosonic approximation. In particular, we verify the good accordance in the behavior of the edge states, associated with the ferrimagnetic plateau, from the spin and from the bosonic models. Furthermore, we show that the boundary magnon density strongly depends on the interactions and particle statistics..

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Section: B Magnetization Curves and Local Magnetizationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The role of density-dependent magnon hopping and magnon-magnon repulsion in ferrimagnetic spin-(1/2, $S$) chains in a magnetic field

da Silva,

Montenegro-Filho

2021

Preprint

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“…In this case there is no symmetry breaking associated with an ordered phase when the system undergoes a TPT 6 . For this reason, many different approaches have been proposed recently to identify the universality classes of topological transitions using scaling ideas [6][7][8][9][10][11][12][13][14][15][16][17][18] .…”

Section: Introductionmentioning

confidence: 99%

Anisotropic scaling in 3D topological models: fromWeyl semimetal to Hopf insulator

Rufo

Griffith

Lopes

et al. 2021

Preprint

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A proposal to study topological models beyond the standard topological classification and that exhibit breakdown of Lorentz invariance is presented. The focus of the investigation relies on their anisotropic quantum critical behavior. We study anisotropic effects on three-dimensional (3D) topological models, computing their anisotropic correlation length critical exponent ν obtained from numerical calculations of the penetration length of the zero-energy surface states as a function of the distance to the topological quantum critical point. A generalized Weyl semimetal model with broken time-reversal symmetry is introduced and studied using a modified Dirac equation. An approach to characterize topological surface states in topological insulators when applied to Fermi arcs allows to capture the anisotropic critical exponent θ = νx/νz. We also consider the Hopf insulator model, for which the study of the topological surface states yields unusual values for ν and for the dynamic critical exponent z. From an analysis of the energy dispersions, we propose a scaling relation να¯ zα¯ = 2q and θ = νx/νz = zz/zx for ν and z that only depends on the Hopf insulator Hamiltonian parameters p and q and the axis direction α¯ . An anisotropic quantum hyperscaling relation is also obtained.

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“…Interestingly, more complicated cases can appear if one introduces inhomogeneities into the quantum spin chains. In general, quantum mixed spin chains possess two types of inhomogeneities, [16,17] the alternation of coupling strengths and spin magnitudes within a unit cell, and have attracted a great interest for their exotic low-energy physics, like the magnetization plateau and Luttinger liquid shown in various ferrimagnetic Heisenberg chains, [18][19][20] the Kosterlitz-Thouless and Gaussian criticalities recently studied in the mixed spin-(1∕2, 5∕2, 1∕2) Heisenberg branched chain, [21,22] and the quantum spin liquid phases appeared in the mixed spin-1 and spin-1∕2 Heisenberg octahedral chain. [23] Additionally, these mixed spin chains are also of experimental interest and have several realistic realizations.…”

Section: Introductionmentioning

confidence: 99%

Quantum Phase Transition of a Quantum Mixed Spin Chain by Employing Density Matrix Renormalization Group Method

Yang

2021

Annalen der Physik

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The fidelity susceptibility and trace distance in the valence‐bond‐solid (VBS) transition of a quantum mixed spin chain is investigated, which consists of unit cells arrayed as 1/2‐1/2‐1‐1 with alternating Heisenberg antiferromagnetic exchange couplings, by using the density matrix renormalization group (DMRG) method in the matrix product state (MPS) form. It is observed that the fidelity susceptibility and the first derivative of the trace distance display explicit divergence near the quantum critical point. The information about the quantum criticality, such as the quantum critical point and correlation length critical exponent, is extracted from the finite size scaling behaviors. The obtained quantum critical point is more accurate than previous work, and the existence of the scaling function of the trace distance near the critical point is observed numerically for the first time. In addition, it is also found that the trace distance between two sites can supplement the VBS picture for describing the change of the ground state as the control parameter is varied through the quantum critical point.

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Topology of many-body edge and extended quantum states in an open spin chain: 1/3 plateau, Kosterlitz-Thouless transition, and Luttinger liquid

Cited by 19 publications

References 73 publications

The role of density-dependent magnon hopping and magnon-magnon repulsion in ferrimagnetic spin-(1/2, $S$) chains in a magnetic field

The role of density-dependent magnon hopping and magnon-magnon repulsion in ferrimagnetic spin-(1/2, $S$) chains in a magnetic field

Anisotropic scaling in 3D topological models: fromWeyl semimetal to Hopf insulator

Quantum Phase Transition of a Quantum Mixed Spin Chain by Employing Density Matrix Renormalization Group Method

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