Finite Size Effects in Topological Quantum Phase Transitions

Continentino, Mucio A.; Rufo, S.; M., Rufo, Griffith

doi:10.48550/arxiv.1903.00758

Cited by 2 publications

(2 citation statements)

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“…Starting to address this issue, a new branch in the study of TQPTs is currently being developed. Recent works [6][7][8][9][10][11][12][13][14][15][16][17][18] have explored the question as to whether TQPTs possess a critical behavior analogous to that of symmetry-breaking phase transitions, with scaling of observables controlled by universal critical exponents 19,20 . One approach 9,10 suggests that the topological invariants of the Altland-Zirnbauer classification 4 can be expressed as an integral of a function of momentum and the Hamiltonian parameters -a curvature function -whose asymptotic scaling behavior near the transition is governed by critical exponents and can be analyzed using a curvature renormalization group (CRG) method.…”

Section: Introductionmentioning

confidence: 99%

Scaling behavior in a multicritical one-dimensional topological insulator

2020

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A class of Aubry-André-Harper models of spin-orbit coupled electrons exhibits a topological phase diagram where two regions belonging to the same phase are split up by a multicritical point. The critical lines which meet at this point each defines a topological quantum phase transition with a second-order nonanalyticity of the ground-state energy, accompanied by a linear closing of the spectral gap with respect to the control parameter; except at the multicritical point which supports fourth-order transitions with parabolic gap-closing. Here both types of criticality are characterized through a scaling analysis of the curvature function defined from the topological invariant of the model. We extract the critical exponents of the diverging curvature function at the nonhigh symmetry points in the Brillouin zone where the gap closes, and also apply a renormalization group approach to the flattening curvature function at high symmetry points. We also derive a basis-independent correlation function between Wannier states to characterize the transition. Intriguingly, we find that the critical exponents and scaling law defined with respect to the spectral gap remain the same regardless of the order of the transition.

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Section: Introductionmentioning

confidence: 99%

Scaling behavior in a multicritical one-dimensional topological insulator

2020

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“…It is an open problem to explore the full implications of our finding, maybe taking off from recent attempts to formulate an RG approach to QPTs between symmetryprotected topological phases [25][26][27][28][29][30][31][32][33][34][35].…”

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confidence: 99%

Multicriticality in a one-dimensional topological band insulator

Malard,

Brandao,

de Brito

et al. 2020

Preprint

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A central tenet in the theory of quantum phase transitions (QPTs) is that a nonanalyticity in the ground-state energy in the thermodynamic limit implies a QPT. Here we report on a finding that challenges this assertion. As a case study we take a phase diagram of a one-dimensional band insulator with spin-orbit coupled electrons, supporting trivial and topological gapped phases separated by intersecting critical surfaces. The intersections define multicritical lines across which the ground-state energy becomes nonanalytical, concurrent with a closing of the band gap, but with no phase transition taking place.

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Finite Size Effects in Topological Quantum Phase Transitions

Cited by 2 publications

References 0 publications

Scaling behavior in a multicritical one-dimensional topological insulator

Scaling behavior in a multicritical one-dimensional topological insulator

Multicriticality in a one-dimensional topological band insulator

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