# Publications by Steve Simon

## Partial equilibration of the anti-Pfaffian edge due to Majorana Disorder

Physical Review Letters American Physical Society **124** (2020) 126801

We consider electrical and thermal equilibration of the edge modes of the Anti-Pfaffian quantum Hall state at ν = 5/2 due to tunneling of the Majorana edge mode to trapped Majorana zero modes in the bulk. Such tunneling breaks translational invariance and allows scattering between Majorana and other edge modes in such a way that there is a parametric difference between the length scales for equilibration of charge and heat transport between integer and Bose mode on the one hand, and for thermal equilibration of the Majorana edge mode on the other hand. We discuss a parameter regime in which this mechanism could explain the recent observation of quantized heat transport [Banerjee et all, Nature 559, 7713 (2018)].

## Classical dimers on penrose tilings

Physical Review X American Physical Society **10** (2020) 011005

## Transport in bilayer graphene near charge neutrality: Which scattering mechanisms are important?

Physical Review Letters American Physical Society **124** (2020) 026601

## Wavefunctionology: The Special Structure of Certain Fractional Quantum Hall Wavefunctions

in *Fractional Quantum Hall Effects: New Developments*, World Scientific (2020)

## Energetics of Pfaffian–anti-Pfaffian domains

Physical review B: Condensed matter and materials physics American Physical Society **101** (2020) 041302(R)

In several recent works it has been proposed that, due to disorder, the experimentally observed ν = 5/2 quantum Hall state could be microscopically composed of domains of Pfaffian order along with domains of anti-Pfaffian order. We numerically examine the energetics required for forming such domains and conclude that for the parameters appropriate for recent experiments, such domains would not occur.

## Superconducting order of Sr2RuO4 from a three-dimensional microscopic model

Physical Review Research American Physical Society **1** (2019) 033108

## Approximating observables on eigenstates of large many-body localized systems

Physical review B: Condensed matter and materials physics American Physical Society **99** (2019) 104201

Eigenstates of fully many-body localized (FMBL) systems can be organized into spin algebras based on quasilocal operators called l-bits. These spin algebras define quasilocal l-bit measurement (τzi) and l-bit flip (τxi) operators. For a disordered Heisenberg spin chain in the MBL regime we approximate l-bit flip operators by finding them exactly on small windows of systems and extending them onto the whole system by exploiting their quasilocal nature. We subsequently use these operators to represent approximate eigenstates. We then describe a method to calculate products of local observables on these eigenstates for systems of size L in O(L2) time. This algorithm is used to compute the error of the approximate eigenstates.

## Driven quantum dot coupled to a fractional quantum Hall edge

Physical Review B: Condensed Matter and Materials Physics American Physical Society **100** (2019) 245111

## Signatures of the many-body localized regime in two dimensions

Nature Physics Springer Nature **15** (2018) 164–169-

Lessons from Anderson localization highlight the importance of the dimensionality of real space for localization due to disorder. More recently, studies of many-body localization have focused on the phenomenon in one dimension using techniques of exact diagonalization and tensor networks. On the other hand, experiments in two dimensions have provided concrete results going beyond the previously numerically accessible limits while posing several challenging questions. We present the large-scale numerical examination of a disordered Bose–Hubbard model in two dimensions realized in cold atoms, which shows entanglement-based signatures of many-body localization. By generalizing a low-depth quantum circuit to two dimensions, we approximate eigenstates in the experimental parameter regimes for large systems, which is beyond the scope of exact diagonalization. A careful analysis of the eigenstate entanglement structure provides an indication of the putative phase transition marked by a peak in the fluctuations of entanglement entropy in a parameter range consistent with experiments.

## Interaction effects and charge quantization in single-particle quantum dot emitters

Physical Review Letters American Physical Society (2019)

We discuss a theoretical model of an on-demand single-particle emitter that employs a quantum dot, attached to an integer or fractional quantum Hall edge state. Via an exact mapping of the model onto the spin-boson problem we show that Coulomb interactions between the dot and the chiral quantum Hall edge state, unavoidable in this setting, lead to a destruction of precise charge quantization in the emitted wave-packet. Our findings cast doubts on the viability of this set-up as a single-particle source of quantized charge pulses. We further show how to use a spin-boson master equation approach to explicitly calculate the current pulse shape in this set-up.

## Fractional oscillations

Nature Physics Springer Nature **15** (2019) 527-528

An electrical interferometer device has detected interference patterns that suggest anyons could be conclusively demonstrated in the near future.

## Finite temperature effects on Majorana bound states in chiral p-wave superconductors

SciPost Physics SciPost **6** (2019) 1-18

## Reply to “Comment on ‘Interpretation of thermal conductance of the ν=5/2 edge' ”

Physical Review B American Physical Society **98** (2018)

Feldman argues that simply having a large velocity mismatch and long wavelength disorder is not likely to result in sufficient non-equilibration of Majorana edge modes at ν=5/2 to explain recent thermal transport experiments. I agree that this picture alone is probably too simple, although small modifications of the mechanism could still be viable.

## Behavior of l-bits near the many-body localization transition

Physical Review B American Physical Society **98** (2018) 184201-

Eigenstates of fully many-body localized (FMBL) systems are described by quasilocal operators τzi (l-bits), which are conserved exactly under Hamiltonian time evolution. The algebra of the operators τzi and τxi associated with l-bits (τi) completely defines the eigenstates and the matrix elements of local operators between eigenstates at all energies. We develop a non-perturbative construction of the full set of l-bit algebras in the many-body localized phase for the canonical model of MBL. Our algorithm to construct the Pauli-algebra of l-bits combines exact diagonalization and a tensor network algorithm developed for efficient diagonalization of large FMBL Hamiltonians. The distribution of localization lengths of the l-bits is evaluated in the MBL phase and used to characterize the MBL-to-thermal transition.

## Interpretation of thermal conductance of the ν = 5/2 edge

Physical Review B American Physical Society **97** (2018) 121406(R)

Recent experiments [Banerjee et al, arXiv:1710.00492] have measured thermal conductance of the ν = 5/2 edge in a GaAs electron gas and found it to be quantized as K ≈ 5/2 (in appropriate dimensionless units). This result is unexpected, as prior numerical work predicts that the ν = 5/2 state should be the Anti-Pfaffian phase of matter, which should have quantized K = 3/2. The purpose of this paper is to propose a possible solution to this conflict: if the Majorana edge mode of the Anti-Pfaffian does not thermally equilibrate with the other edge modes, then K = 5/2 is expected. I briefly discuss a possible reason for this nonequilibration, and what should be examined further to determine if this is the case.

## Effective edge state dynamics in the fractional quantum Hall effect

Physical Review B: Condensed Matter and Materials Physics American Physical Society **98** (2018)

We consider the behavior of quantum Hall edges away from the Luttinger liquid fixed point that occurs in the low-energy, large-system limit. Using the close links between quantum Hall wave functions and conformal field theories, we construct effective Hamiltonians from general principles and then constrain their forms by considering the effect of bulk symmetries on the properties of the edge. In examining the effect of bulk interactions on this edge, we find remarkable simplifications to these effective theories which allow for a very accurate description of the low-energy physics of quantum Hall edges relatively far away from the Luttinger liquid fixed point, and which apply to small systems and higher energies.

## Weak-coupling superconductivity in an anisotropic three-dimensional repulsive Hubbard model

Physical Review B American Physical Society **98** (2018) 224515

We study a three-dimensional single-band repulsive Hubbard model at weak coupling. We establish the superconducting phase diagram in the parameter space of the chemical potential and the out-of-plane hopping strength. The model continuously connects the Hubbard model in two and three dimensions. We confirm previously established results in these limits, and identify a rich structure of competing order parameters in between. Specifically, we find five types of p- and d-wave orders. In several regions of the phase diagram, even when the Fermi surface is a corrugated cylinder, the ground state is a time-reversal-symmetry-breaking superconductor with nodes, i.e., a Weyl superconductor.

## Structure of edge-state inner products in the fractional quantum Hall effect

Physical Review B American Physical Society **97** (2018) 155108

We analyze the inner products of edge state wave functions in the fractional quantum Hall effect, specifically for the Laughlin and Moore-Read states. We use an effective description for these inner products given by a large-N expansion ansatz proposed in a recent work by J. Dubail, N. Read, and E. Rezayi [Phys. Rev. B 86, 245310 (2012)]. As noted by these authors, the terms in this ansatz can be constrained using symmetry, a procedure we perform to high orders. We then check this conjecture by calculating the overlaps exactly for small system sizes and compare the numerics with our high-order expansion. We find the effective description to be very accurate.

## Theory of the Josephson Junction Laser

Physical Review Letters American Physical Society **121** (2018)

We develop an analytic theory for the recently demonstrated Josephson Junction laser (Science 355, 939, 2017). By working in the time-domain representation (rather than the frequency-domain) a single non-linear equation is obtained for the dynamics of the device, which is fully solvable in some regimes of operation. The nonlinear drive is seen to lead to mode-locked output, with a period set by the round-trip time of the resonant cavity.

## Size constraints on a Majorana beam-splitter interferometer: Majorana coupling and surface-bulk scattering

Physical Review B American Physical Society **97** (2018) 115424

Topological insulator surfaces in proximity to superconductors have been proposed as a way to produce Majorana fermions in condensed matter physics. One of the simplest proposed experiments with such a system is Majorana interferometry. Here we consider two possibly conflicting constraints on the size of such an interferometer. Coupling of a Majorana mode from the edge (the arms) of the interferometer to vortices in the center of the device sets a lower bound on the size of the device. On the other hand, scattering to the usually imperfectly insulating bulk sets an upper bound. From estimates of experimental parameters, we find that typical samples may have no size window in which the Majorana interferometer can operate, implying that a new generation of more highly insulating samples must be explored.