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Disorder and interaction in chiral chains: Majoranas vs complex fermions
Disordered Systems and Neural Networks · Submitted 29 May 2019
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim On the other hand, the Majorana fermion chain experiences a spontaneous symmetry breaking and localizes for repulsive interaction.
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The abstract, sentence by sentence
We study the low-energy physics of a chain of Majorana fermions in the presence of interaction and disorder, emphasizing the difference between Majoranas and conventional (complex) fermions. While in the non-interacting limit both models are equivalent (in particular, belong to the same symmetry class BDI and flow towards the same infinite-randomness critical fixed point), their behavior differs drastically once interaction is added. Our density-matrix renormalization group calculations show that the complex-fermion chain remains at the non-interacting fixed point. On the other hand, the Majorana fermion chain experiences a spontaneous symmetry breaking and localizes for repulsive interaction. To explain the instability of the critical Majorana chain with respect to a combined effect of interaction and disorder, we consider interaction as perturbation to the infinite-randomness fixed point and calculate numerically two-wavefunction correlation functions that enter interaction matrix elements. The numerical results supported by analytical arguments exhibit a rich structure of critical eigenstate correlations. This allows us to identify a relevant interaction operator that drives the Majorana chain away from the infinite randomness fixed point. For the case of complex fermions, the interaction is irrelevant.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study the low-energy physics of a chain of Majorana fermions in the presence of interaction and disorder, emphasizing the difference between Majoranas and conventional (complex) fermions. | contribution 0.93 | 0.81 | 0.07 | asserted 0.74 |
| s1 | While in the non-interacting limit both models are equivalent (in particular, belong to the same symmetry class BDI and flow towards the same infinite-randomness critical fixed point), their behavior differs drastically once interaction is added. | background 0.89 | 0.19 | 0.15 | asserted 1.00 |
| s2 | Our density-matrix renormalization group calculations show that the complex-fermion chain remains at the non-interacting fixed point. | result 1.00 | 0.93 | 0.15 | asserted 1.00 |
| s3 | On the other hand, the Majorana fermion chain experiences a spontaneous symmetry breaking and localizes for repulsive interaction. | result 1.00 | 0.89 | 0.51 | asserted 1.00 |
| s4 | To explain the instability of the critical Majorana chain with respect to a combined effect of interaction and disorder, we consider interaction as perturbation to the infinite-randomness fixed point and calculate numerically two-wavefunction correlation functions that enter interaction matrix elements. | method 0.94 | 0.93 | 0.06 | asserted 0.96 |
| s5 | The numerical results supported by analytical arguments exhibit a rich structure of critical eigenstate correlations. | result 0.97 | 0.93 | 0.05 | asserted 0.98 |
| s6 | This allows us to identify a relevant interaction operator that drives the Majorana chain away from the infinite randomness fixed point. | result 0.64 | 0.93 | 0.31 | asserted 0.99 |
| s7 | For the case of complex fermions, the interaction is irrelevant. | result 0.99 | 0.78 | 0.11 | asserted 1.00 |
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Original abstract
We study the low-energy physics of a chain of Majorana fermions in the presence of interaction and disorder, emphasizing the difference between Majoranas and conventional (complex) fermions. While in the non-interacting limit both models are equivalent (in particular, belong to the same symmetry class BDI and flow towards the same infinite-randomness critical fixed point), their behavior differs drastically once interaction is added. Our density-matrix renormalization group calculations show that the complex-fermion chain remains at the non-interacting fixed point. On the other hand, the Majorana fermion chain experiences a spontaneous symmetry breaking and localizes for repulsive interaction. To explain the instability of the critical Majorana chain with respect to a combined effect of interaction and disorder, we consider interaction as perturbation to the infinite-randomness fixed point and calculate numerically two-wavefunction correlation functions that enter interaction matrix elements. The numerical results supported by analytical arguments exhibit a rich structure of critical eigenstate correlations. This allows us to identify a relevant interaction operator that drives the Majorana chain away from the infinite randomness fixed point. For the case of complex fermions, the interaction is irrelevant.
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What this paper does with the arXiv papers it cites
What it cites · 20 sentences without a confident label
Uses the method or tool of 1 paper
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In the MPS representation the (von Neumann) entanglement entropy between two subsystems split by a bond is readily available [ref] .
The density-matrix renormalization group in the age of matrix product states · Interacting Majorana chain with staggering · 0.80
Compares with 1 paper
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On the no-staggering (self-dual) line we observe the Ising (central charge $c=1/2$) and Ising+LL ($c=3/2$) phases, in agreement with Ref. [ref] .
Phase Diagram of the Interacting Majorana Chain Model · Summary and Outlook · 0.81
Cites as background 4 papers
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In this work, we explore the the effect of disorder and interaction on the low energy physics of a chain of Majorana quasiparticles commonly called Kitaev chain [ref] .
Unpaired Majorana fermions in quantum wires · Introduction · 0.80
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The phase diagram of a clean interacting Kitaev chain was studied in Ref. [ref] .
Phase Diagram of the Interacting Majorana Chain Model · Introduction · 0.87
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We start by writing the most general non-interacting Hamiltonian of a 1D system of size $L$ of symmetry class BDI [ref] : [equation] where $h$ is a real matrix and $c_A,B$, $c_A,B^†$ are onsite operators acting on the two sublattices.
Anderson Transitions · Scaling of interaction · 0.81
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