Wilson chiral perturbation theory for dynamical twisted mass fermions vs lattice data—A case study

Cichy, Krzysztof; Zafeiropoulos, Savvas

doi:10.1016/j.cpc.2018.11.020

Cited by 1 publication

(4 citation statements)

References 111 publications

(180 reference statements)

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“…Especially, we recover the critical scaling of α found in lattice QCD with Wilson fermions [38][39][40]42] and in the RMT-models for Majorana modes in disordered quantum wires [31,64].…”

Section: Discussionsupporting

confidence: 71%

“…An analogous structure is found in Quantum Chromodynamics (QCD) for discretised fermions on a lattice [41,[60][61][62]. Surprisingly in the latter example, the broadening of the zero eigenvalues coincides with the statistics of a finite-dimensional Gaussian random matrix model [41,[60][61][62], which have been corroborated by lattice simulations [38][39][40]42]. These observations were surprising because universality of the spectral statistics, and thus agreement with RMT, usually only holds in the limit of a large number of eigenvalues, while the number of zero modes has been finite in these systems.…”

Section: Introductionsupporting

confidence: 62%

“…In the present work, we have averaged over all bases transformations U 2 drawn from the Haar measure of the group associated to the respective symmetry class. Yet lattice simulations in QCD [38][39][40]42] strongly suggest that the measure can be relaxed to something non-uniform. As a further study it is natural to investigate what happens if the assumption of an average over the full Haar measure is loosened.…”

Section: Discussionmentioning

confidence: 99%

“…For example topological zero modes are broadened due to residual interactions that break topology. This broadening can be used as a measure of the perturbation strength [38][39][40][41][42]. Topological modes are relevant in both high energy physics [4][5][6][7][43][44][45][46][47] and condensed matter systems [20,[48][49][50][51][52][53][54][55].…”

Section: Introductionmentioning

confidence: 99%

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Universal broadening of zero modes: A general framework and identification

2019

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We consider the smallest eigenvalues of perturbed Hermitian operators with zero modes, either topological or system specific. To leading order for small generic perturbation we show that the corresponding eigenvalues broaden to a Gaussian random matrix ensemble of size ν × ν, where ν is the number of zero modes. This observation unifies and extends a number of results within chiral random matrix theory and effective field theory and clarifies under which conditions they apply. The scaling of the former zero modes with the volume differs from the eigenvalues in the bulk, which we propose as an indicator to identify them in experiments. These results hold for all ten symmetric spaces in the Altland-Zirnbauer classification and build on two facts. Firstly, the broadened zero modes decouple from the bulk eigenvalues and secondly, the mixing from eigenstates of the perturbation form a Central Limit Theorem argument for matrices.

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“…Especially, we recover the critical scaling of α found in lattice QCD with Wilson fermions [38][39][40]42] and in the RMT-models for Majorana modes in disordered quantum wires [31,64].…”

Section: Discussionsupporting

confidence: 71%