Multicritical behavior in topological phase transitions

Rufo, S.; Lopes, Nei; Continentino, M. A.; Griffith, M. A. R.

doi:10.1103/physrevb.100.195432

Cited by 49 publications

(53 citation statements)

References 26 publications

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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 symmetry-protected topological phases [18,[29][30][31][32][33][34][35][36][37][38].…”

Section: Discussionmentioning

confidence: 99%

Multicriticality in a one-dimensional topological band insulator

Malard

Brandão

Brito

et al. 2020

Phys. Rev. Research

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A central tenet in the theory of quantum phase transitions (QPTs) is that a nonanalyticity in a ground-state energy 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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Section: Discussionmentioning

confidence: 99%

Multicriticality in a one-dimensional topological band insulator

Malard

Brandão

Brito

et al. 2020

Phys. Rev. Research

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“…3 d. Therefore the spectra is non-relativistic (breaks Lorentz invariance) and become quadratic in nature instead of linear. Energy dispersion for one dimensional system close quantum critical point can be written as , where is correlation length critical exponent and z is dynamical critical exponent 23 . At the critical point the gap function should go to zero, therefore .…”

Section: Resultsmentioning

confidence: 99%

“…At QCP energy dispersion is found to be , where z is dynamical critical exponent. Expanding the energy dispersion around the QCP and identifying the dominant momentum one can find the value of z , which governs the shape of the spectra at the gap closing point 23 .…”

Section: Introductionmentioning

confidence: 99%

Multi-critical topological transition at quantum criticality

Kumar

Kartik

Sinha

et al. 2021

Sci Rep

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The investigation and characterization of topological quantum phase transition between gapless phases is one of the recent interest of research in topological states of matter. We consider transverse field Ising model with three spin interaction in one dimension and observe a topological transition between gapless phases on one of the critical lines of this model. We study the distinct nature of these gapless phases and show that they belong to different universality classes. The topological invariant number (winding number) characterize different topological phases for the different regime of parameter space. We observe the evidence of two multi-critical points, one is topologically trivial and the other one is topologically active. Topological quantum phase transition between the gapless phases on the critical line occurs through the non-trivial multi-critical point in the Lifshitz universality class. We calculate and analyze the behavior of Wannier state correlation function close to the multi-critical point and confirm the topological transition between gapless phases. We show the breakdown of Lorentz invariance at this multi-critical point through the energy dispersion analysis. We also show that the scaling theories and curvature function renormalization group can also be effectively used to understand the topological quantum phase transitions between gapless phases. The model Hamiltonian which we study is more applicable for the system with gapless excitations, where the conventional concept of topological quantum phase transition fails.

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“…The fidelity susceptibility has been widely used [56][57][58][59]; it represents energy fluctuations in the ground state and thus is something like a quantum specific heat. Another important quantity is the correlation length ξ , which has been extracted from the penetration of edge states into the bulk [60]. A different scheme for calculating ξ has been proposed in terms of the Berry connection ( u k |i∂ k u k ) in one dimension and the Berry curvature in two dimensions; their Fourier transforms can be interpreted as real-space correlation functions involving the electric polarization and orbital currents in one and two dimensions, respectively [61,62].…”

Section: Critical Behaviormentioning

confidence: 99%

“…These phases in general do not differ with respect to symmetry and therefore the transitions are of genuine topological nature. Fortunately, in the present case it is very simple to determine the critical behavior, which depends only on the single-particle spectrum close to the k point where the gap closes at criticality [60].…”

Section: Critical Behaviormentioning

confidence: 99%

Topological and nontopological features of generalized Su-Schrieffer-Heeger models

2020

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The (one-dimensional) Su-Schrieffer-Heeger Hamiltonian, augmented by spin-orbit coupling and longerrange hopping, is studied at half filling for an even number of sites. The ground-state phase diagram depends sensitively on the symmetry of the model. Charge-conjugation (particle-hole) symmetry is conserved if hopping is only allowed between the two sublattices of even and odd sites. In this case, we find a variety of topologically nontrivial phases, characterized by different numbers of edge states (or, equivalently, different quantized Zak phases). The transitions between these phases are clearly signalled by the entanglement entropy. Charge-conjugation symmetry is broken if hopping within the sublattices is admitted. We study specifically next-nearest-neighbor hopping with amplitudes t a and t b for the A and B sublattices, respectively. For t a = t b , parity is conserved, and also the quantized Zak phases remain unchanged in the gapped regions of the phase diagram. However, metallic patches appear due to the overlap between conduction and valence bands in some regions of parameter space. The case of alternating next-nearest-neighbor hopping, t a = −t b , is also remarkable, as it breaks both charge-conjugation C and parity P but conserves the product CP. Both the Zak phase and the entanglement spectrum still provide relevant information, in particular about the broken parity. Thus the Zak phase for small values of t a measures the disparity between bond strengths on A and B sublattices, in close analogy to the proportionality between the Zak phase and the polarization in the case of the related Aubry-André model.

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Multicritical behavior in topological phase transitions

Cited by 49 publications

References 26 publications

Multicriticality in a one-dimensional topological band insulator

Multicriticality in a one-dimensional topological band insulator

Multi-critical topological transition at quantum criticality

Topological and nontopological features of generalized Su-Schrieffer-Heeger models

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