arXiv subjects

Mytraya Gattu

Publications and source records attributed to Mytraya Gattu.

10 recordsLinked to original sources

arXiv2026

Shape Deformation and Braid Statistics of Fractional Quantum Hall Quasiparticles

For ``ideal anyons,'' the Berry phase associated with a closed loop of an anyon around another is robust, that is, independent of the size or the shape of the loop, and directly yields the braid statistics. That is not the case for the fractional quantum Hall (FQH) quasiparticles (QPs), which are charged and have finite size. We consider here how the Berry phase depends on the shape of the QP, which, unlike its charge, is not a topological property and varies along the path in response to the local potential. We show that the Berry phase $Θ$ associated with the loop of a fractionally charged QP around another contains three distinct contributions: $Θ=Θ_{\rm AB}+Θ_{\rm shape}+Θ_{\rm braid}$. The Aharonov-Bohm phase $Θ_{\rm AB}$ is dominant, being proportional to the area of the loop, and the shape-dependent term $Θ_{\rm shape}$, identified in this work, can be larger than the order-one contribution from the braid statistics $Θ_{\rm braid}$. A precise determination of the braid statistics is challenging because it can be swamped by practically undetectable uncertainties in its trajectory and shape. We discuss these results in the context of the interference experiments. We also note that the fractional phase jumps in these experiments can be understood without assuming the existence of QPs with sharply quantized fractional charges at the edges of the FQH system, wherein these phase jumps are a direct measure of the fractionally quantized vorticity of the QPs in the bulk of the fractional quantum Hall state.

cond-mat.str-el↗

arXiv2026

Universality of long-wavelength behavior of composite-fermion Fermi liquid

A recent article evaluated the long-wavelength behavior of the projected static structure factor of the composite-fermion (CF) liquid within the zeroth-order microscopic theory and found $\bar{S}(\mathbf{q})\sim q^3$, in disagreement with the $\bar{S}(\mathbf{q})\sim q^3\ln q$ behavior predicted by the Chern-Simons field theory for the Coulomb interaction. Here we consider the possibility that the discrepancy arises because the zeroth-order CF Fermi-liquid wave function used in that work does not properly capture the long wavelength behavior. We use CF diagonalization to significantly improve the wave function but do not find any evidence for $\bar{S}(\mathbf{q})\sim q^3 \ln q$ behavior. Additionally, we find that the small-$q$ behavior of $\bar{S}(\mathbf{q})$ is also insensitive to the form of the interaction between electrons, suggesting universality.

cond-mat.str-el↗

arXiv2025

Dressing composite fermions with artificial intelligence

Recent variational studies have demonstrated that the strongly correlated ground states of the fractional quantum Hall (FQH) effect can be captured using machine learning approaches starting from no prior knowledge of the underlying physics. We introduce a complementary framework that instead starts from Jain's composite-fermion (CF) wavefunctions, which accurately describe FQH states as weakly interacting states of CFs at fillings $ν= n/(2pn+1)$ in an idealized limit. As we move away from this idealized limit to one more in line with experimental reality, we expect CFs to become dressed much like the electrons of a noninteracting system, which are dressed by neutral excitations as interaction is turned on adiabatically, as in Landau's Fermi-liquid theory. We model this dressing using a Feynman-Cohen-style backflow approach, implemented through symmetry-preserving neural networks-a framework we refer to as CF-Flow. CF-Flow achieves competitive accuracy with substantially greater computational efficiency and scales to systems of $\gtrsim 26$ electrons. At fillings $ν= 1/3$ and $2/5$, as a function of Landau-level mixing strength, CF-Flow produces ground-state energies with low local-energy variance that are nearly indistinguishable from those obtained using the fixed-phase diffusion Monte Carlo (fp-DMC) method, even though the latter constrains the wavefunction phase to that of the lowest Landau level-thereby providing insight into why fp-DMC has been successful in giving an accurate quantitative account of several experiments. Finally, the symmetry-preserving architecture of CF-Flow enables access to excited states and computation of the transport gap at $ν= 1/3$, where we find, unexpectedly, that it decays exponentially toward a finite value in the limit of large Landau-level mixing, suggesting a first-order transition from the FQH liquid to a non-FQH state.

cond-mat.str-el↗

arXiv2025

Probing fractional quantum Hall effect by photoluminescence

The recent discovery of fractional quantum anomalous Hall (FQAH) states - fractional quantum Hall (FQH) states realized without an external magnetic field - in twisted transition-metal dichalcogenide (TMD) bilayers represents a significant development in condensed matter physics. Notably, these states were first observed via photoluminescence (PL) spectroscopy. Surprisingly, a general theoretical understanding of PL is not available even for the standard FQH states. For an ideal two-dimensional system, the energy of the emitted photon is predicted to be independent of the correlations, but we show that the PL intensity contains valuable information. Specifically, we predict that at finite temperatures, the PL intensity peaks at the Jain fillings ν= n/(2n \pm 1), and away from these fillings, the binding energies of the composite-fermion excitons and trions can be deduced from the temperature dependence of the intensity. We discuss implications for PL experiments in semiconductor quantum wells and twisted TMD bilayers.

cond-mat.str-el↗

arXiv2025

Exploring the nature of the emergent gauge field in composite-fermion metals: A large-scale microscopic study

Field theories of the composite-fermion (CF) metal model it as a Fermi sea of composite fermions coupled to an emergent gauge field. Within a random phase approximation, these theories predict that the Landau damping of the gauge field resulting from its coupling to the low-energy, long-wavelength CF particle-hole excitations modifies the electrons' density-density correlation function related to the static structure factor $S(q)$ at wave vector $q$. This produces a non-analytic correction $\propto q^{3}\ln q$ to $S(q)$ (with the magnetic length $\ell_{B}=1$). Thanks to the recently developed quaternion formulation for Jain-Kamilla projection of CF wave functions, the evaluation of $S(q)$ from the accurate microscopic theory of composite fermions has now become possible for systems containing as many as $N=900$ CFs, which enables a reliable determination of the small-$q$ behavior of $S(q)$. We study CF metals corresponding to electrons at Landau level filling factors $ν=1/2$ and $1/4$, and for completeness, also of bosons at $ν=1$ and $1/3$. In the $q\rightarrow0$ limit, our microscopic calculation reveals a $q^{3}$ term in $S(q)$ of the CF metals rather than $q^{3} \ln q$. This behavior is well-predicted by a model of a non-interacting Fermi sea of dipolar CFs, which also obtains its coefficient accurately.

cond-mat.str-el↗

arXiv2025

Molecular anyons in fractional quantum Hall effect

One of the profound consequences of the fractional quantum Hall (FQH) effect is the notion of fractionally charged anyons. In spite of extensive experimental study, puzzles remain, however. For example, both shot-noise and Aharonov-Bohm interference measurements sometimes report a charge that is a multiple of the elementary charge. We report here high-precision microscopic calculations that reveal the surprising result that the FQH anyons often bind together into stable clusters, which we term molecular anyons. This is counterintuitive, given that the elementary anyons carry the same charge and are therefore expected to repel one another. The number of anyons in a cluster, its binding energy and its size depend sensitively on the parent FQH state and the interaction between electrons (which is experimentally tunable, e.g., by varying the quantum well width). Our calculations further suggest that the charge-$1/4$ non-Abelian anyons of the $5/2$ FQH state may also bind to form charge-$1/2$ Abelian clusters. The existence of molecular anyons not only can provide a natural explanation for the observed charges, but also leads to a host of new predictions for future experiments and invites a re-analysis of many past ones.

cond-mat.str-el↗

arXiv2024

Unlocking new regimes in fractional quantum Hall effect with quaternions

We demonstrate that formulating the composite-fermion theory of the fractional quantum Hall (FQH) effect in terms of quaternions greatly expands its reach and opens the door into many interesting issues that were previously beyond the reach of quantitative theoretical investigation. As an illustration, we investigate the possibility of a nematic or a charge-density wave instability of the composite-fermion Fermi sea at half-filled Landau level and of the nearby FQH states by looking for a magneto-roton instability. Our quaternion formulation of the FQH effect has been inspired by mathematical developments in the theoretical analyses of gravitational wave modes and cosmic microwave background radiation, where an important role is played by spin-weighted spherical harmonics which are nothing but monopole harmonics appearing in the spherical geometry for the FQH effect.

cond-mat.str-el↗

arXiv2024

Proposal for bulk measurement of braid statistics in fractional quantum Hall effect

The quasiparticles (QPs) or quasiholes (QHs) of fractional quantum Hall states have been predicted to obey fractional braid statistics, which refers to the Berry phase (in addition to the usual Aharonov-Bohm phase) associated with an exchange of two QPs or two QHs, or equivalently, to half of the phase associated with a QP/QH going around another. Certain phase slips in interference experiments in the fractional quantum Hall regime have been attributed to fractional braid statistics, where the interference probes the Berry phase associated with a closed path which has segments along the edges of the sample as well as through the bulk (where tunneling occurs). Noting that QPs / QHs with sharply quantized fractional charge and fractional statistics do not exist at the edge of a fractional quantum Hall state due to the absence of a gap there, we provide arguments that the existence of composite fermions at the edge is sufficient for understanding the primary experimental observations; composite fermions are known to occur in compressible states without a gap. We further propose that transport through a closed $\textit{tunneling}$ loop contained entirely in the bulk can, in principle, allow measurement of the braid statistics in a way that the braiding object explicitly has a fractionally quantized charge over the entire loop. Optimal parameters for this experimental geometry are determined from quantitative calculations.

cond-mat.str-el↗

arXiv2024

Extended Uncertainty Principle via Dirac Quantization

Unifying quantum theory and gravity remains a fundamental challenge in physics. While most existing literature focuses on the ultraviolet (UV) modifications of quantum theory due to gravity, this work shows that generic infrared (IR) modifications arise when we describe quantum theory in curved spacetime. We explicitly demonstrate that the modifications to the position-momentum algebra are proportional to curvature invariants (such as the Ricci scalar and Kretschmann scalar). Our results, derived through a rigorous application of Dirac's quantization procedure, demonstrate that infrared effects in quantum systems can be axiomatically derived. We study particle dynamics in an arbitrary curved spacetime by embedding them in a higher-dimensional flat geometry. Our approach, which involves embedding particle dynamics in a higher-dimensional flat geometry and utilizing Dirac's quantization procedure, allows us to capture the dynamics of a particle in 4-dimensional curved spacetime through a modified position-momentum algebra. When applied to various spacetimes, this method reveals that the corrections due to the spacetime curvature are universal. We further compare our results with those derived using extended uncertainty principles. Finally, we discuss the implications of our work for black holes and entanglement.

gr-qc↗

arXiv2023

STM in the fractional quantum Hall effect: Spectroscopy of composite-fermion bound states

The fractional quantum Hall states are non-Fermi liquids of electrons, in that their ground states and low energy excitations are described not in terms of electrons but in terms of composite fermions which are bound states of electrons and $2p$ quantized vortices. An electron or a hole at filling factor $ν=n/(2pn+1)$, where $p,n$ are integers, is a complex molecule of $2pn+ 1$ quasiparticles (excited composite fermions) or quasiholes (missing composite fermions) and has its own internal excitations. Recent scanning tunneling microscopy experiments have succeeded in measuring the electron spectral functions of these states, which provides valuable information on the nature of these strongly correlated molecules and thereby on the short-distance correlations in the fractional quantum Hall liquids. These experiments exhibit several sharp peaks in the tunneling spectra. Detailed calculations based on the composite-fermion theory demonstrate multiple peaks in the local density of states, and we argue that the separation between the peaks represents interaction-corrected composite-fermion cyclotron energy. We discuss what aspects of experiments are explained by our model and which ones remain to be explained.

cond-mat.str-el↗