arXiv subjects

Ha Quang Trung

Publications and source records attributed to Ha Quang Trung.

7 recordsLinked to original sources

arXiv2026

Non-Abelian braiding in Abelian Fractional Quantum Hall Phases from realistic interactions

We propose a method of realizing non-Abelian braiding of fractionalized quasiholes in the Laughlin fractional quantum Hall phase at $ν=1/3$ with realistic two-body interactions within the lowest Landau level. It is numerically shown that low-lying gapped excitations near $ν=1/3$ are contained almost entirely within the null space of the three-body Moore-Read model Hamiltonian. They are thus quantum fluids of non-Abelian quasiholes that are in principle physically accessible. In particular, Laughlin ground state can be described as a fluid of ``$ψ$-type" quasiholes formed by binding a magnetic flux with a Majorana fermion (MF), and the Laughlin quasiholes are described by the ``$1$-type'' quasiholes, which are magnetic fluxes without a MF attached. Within the Laughlin phase, Laughlin quasiholes can be locally fractionalized into non-Abelian quasiholes, when the strong attraction between them is overcome by properly designed one-body electronstatic trapping potentials. Extensive numerics with proper finite-size scaling corroborate this physical picture, and our study points to the possibility of realizing non-Abelian braiding within an Abelian topological phase in experiment without the need for fine-tuning realistic electron-electron interaction.

cond-mat.str-el↗

arXiv2026

Many-Anyon Braiding in Non-Abelian Fractional Quantum Hall Effect with Hybrid Monte Carlo Simulation

We employ the hybrid Monte Carlo method to efficiently compute the many-anyon non-Abelian braiding matrices associated with different braiding schemes of the Moore-Read quasiholes. A novel proposal in this work is that anyon braiding schemes based on a global rotation are robust against finite-size effects, as demonstrated by benchmarking their errors in the braiding matrix against those of a simple two-anyon exchange. Moreover, we investigate how electron-electron interactions and local electrostatic trapping potentials influence the energetic preference of different fusion channels. Their effect on the non-Abelian braiding matrices has been verified, a surprising phenomenon that demonstrates long-range entanglement of non-Abelian states. Our results are relevant to the experimental realization of non-Abelian physics in fractional quantum Hall and other analogous systems, including the fast-growing field of fractional quantum anomalous Hall states in moiré materials.

cond-mat.str-el↗

arXiv2026

Hybrid Monte Carlo for Fractional Quantum Hall States

We develop a hybrid Monte Carlo method to efficiently compute the physical observables from the samplings of the Laughlin and the Moore-Read wave functions of fractional quantum Hall (FQH) systems. With the advancements in methodology, including global updates and double stereographic projection on spherical geometry, our hybrid Monte Carlo simulation is significantly faster than the widely used Metropolis Monte Carlo scheme. As a result, we can readily simulate systems with electron numbers $N > 1000$ on both disk and sphere geometries. We apply this method to investigating the topological shift obtained from the edge dipole moment, computed from the density of the wave function on the disk. We also numerically computed the non-Abelian braiding matrices for different braiding schemes of the Moore-Read quasiholes on the sphere. Results with much better quality compared with previous works have been achieved. With the thermodynamic limit results obtained at ease, we also discuss the future usage of our method to clarify the questions on the instability of fractional quantum Hall states in an ideal Chern band setting or under quantum decoherence.

cond-mat.str-el↗

arXiv2025

Dynamics of Anyon Clusters in Fractional Quantum Hall Fluids

In fractional quantum Hall fluids, the quasiparticle excitations are anyons with fractional charges and statistics. Effective interactions among the anyons can be induced by either model or realistic electron-electron (e-e) interactions. Without losing the generality, we investigate such phenomena for the Laughlin 1/3 and Moore-Read (MR) non-Abelian phases. Anyons display rich internal dynamics in both cases that will lead to interesting experimental consequences. In particular, bound states of two Laughlin anyons are preferred under short-range e-e interactions, leading to 2e/3 -- instead of e/3 -- effective charge carriers at low temperatures, which have been seen in several experiments. MR phases host two topologically distinct fusion channels: 1 and psi. The different effective interactions of e/4 anyons in the two sectors suggest the vanishing of the degeneracy of fusion channels when the e-e interaction is no longer its model Hamiltonian, in which case different bound states could also appear. This indicates the possibility of energetically manipulating the two types of anyons by tuning the bare e-e interactions. We point out that the results of recently developed high-resolution STM measurements will be affected by the effective anyon interactions, where anyons are clustered together after the tunneling of electrons. The low-lying parts of the local density of states affected by various anyon clusters are simulated for both Abelian and non-Abelian systems with (screened) Coulomb interactions.

cond-mat.str-el↗

arXiv2025

Long-range Entanglement and Role of Realistic Interaction in Braiding of Non-Abelian Quasiholes in Fractional Quantum Hall Phases

Parity conservation dictates that when fusing pairs of Moore-Read (MR) quasiholes, such that each pair of charge-$e/4$ anyon forms a charge-$e/2$ anyon, the parity of the numbers of $1$-anyon and $ψ$-anyon must be conserved within a given system. This idea is illustrated here using the Jack polynomial formalism, which also provides a basis to numerically study the dynamics of MR anyons. In particular, we examine the effect of two-body electron-electron interaction on the degeneracy of two anyon fusion channels, which affects their mutual statistics of the MR anyons. We find that parity conservation gives rise to a long-range ``entanglement" which affect the experimental measurement of exchange statistics under realistic electron interaction. It is therefore important to account for all quasiholes in an experimental systems in order to accurately predict the outcome of a certain measurement. We also show how understanding the quasihole dynamics can help to fine-tune two-body interactions in order to stabilize any given fusion channel in experiments.

cond-mat.str-el↗

arXiv2023

Spin-statistics relation and the Abelian braiding phase for anyons in fractional quantum Hall effect

Quasihole excitations in fractional quantum Hall (FQH) systems exhibit fractional statistics and fractional spin, but how the spin-statistics relation emerges from many-body physics remains poorly understood. Here we prove a spin-statistics relation using only FQH wave functions, on both the sphere and disk geometry. In particular, the proof on the disk generalizes to all quasiholes in realistic systems, which have a finite size and could be deformed into arbitrary shapes. Different components of the quasihole spins are linked to different conformal Hilbert spaces (CHS), which are nullspaces of model Hamiltonians that host the respective FQH ground states and quasihole states. Understanding how the intrinsic spin of the quasiholes is linked to different CHS is crucial for the generalized spin-statistics relation that takes into account the effect of metric deformation. In terms of the experimental relevance, this enables us to study the effect of deformation and disorder that introduces an additional source of Berry curvature, an aspect of anyon braiding that has been largely neglected in previous literature.

cond-mat.mes-hall↗

arXiv2021

Fractionalisation and dynamics of anyons at $ν=n+1/3$ in fractional quantum Hall effect and their experimental signatures

We show the low-lying excitations at filling factor $ν=n+1/3$ with realistic interactions are contained completely within the well-defined Hilbert space of "Gaffnian quasiholes". Each Laughlin quasihole can thus be understood as a bound state of two Gaffnian quasiholes, which in the lowest Landau level (LLL) behaves like "partons" with "asymptotic freedom" mediated by neutral excitations acting as "gluons". Near the experimentally observed nematic FQH phase in higher LLs, quasiholes become weakly bounded and fractionalise with rich dynamical properties. By studying the effective interactions between quasiholes, we predict a finite temperature phase transition of the Laughlin quasiholes even when the Laughlin ground state remains incompressible, and derive relevant experimental conditions for its possible observations.

cond-mat.str-el↗