arXiv subjects

Ajit C. Balram

Publications and source records attributed to Ajit C. Balram.

At least 19 recordsLinked to original sources

arXiv2026

Sum rules and density-wave modes in spin-singlet fractional quantum Hall fluids

Fractional quantum Hall (FQH) states are prototypical examples of strongly interacting topologically ordered systems. In this work, we obtain thermodynamic fits on the plane for the pair correlation function, and its Fourier transform, the static structure factor, of two-component spin-singlet Halperin and Jain FQH fluids by expanding them in the recently introduced basis of the orthogonal associated Laguerre polynomials [Fulsebakke et al., SciPost Phys. 14, 149 (2023), https://doi.org/10.21468/SciPostPhys.14.6.149 ] and ascertaining the expansion coefficients by fitting them to large-system Monte Carlo data evaluated using their trial wavefunctions. In this fitting procedure, aside from constraining the exact short-distance behavior of the wavefunction, we also derive and enforce the sum rules that the long-wavelength expansion of the static structure factor must adhere to. We show that incorporating these constraints is crucial for obtaining numerically stable and accurate values of the long-wavelength Girvin-MacDonald-Platzman (GMP)/symmetric density-wave excitation gap. We further extend this approach to spin-resolved density-correlation functions, enabling the evaluation of the gap of the antisymmetric density-wave mode for these spin-singlet FQH states. Finally, we use the density-correlators to compute variational energies of the states and construct phase diagrams for bilayer FQH systems. These could be relevant for understanding recent bilayer FQH experiments that map out the phase diagram by tuning the interlayer separation and density-imbalance/layer-polarization.

cond-mat.str-el↗

arXiv2026

Skyrmion Excitations in the $\nu=-1$ Quantum Hall state in Monolayer Graphene

We investigate the skyrmion excited states atop the $SU(4)$ quantum Hall ferromagnetic ground state at filling factor $\nu=-1$ in monolayer graphene. The competition among short-range anisotropic interactions, the Zeeman coupling, and sublattice symmetry-breaking potential gives rise to four distinct spin-valley-ordered ground-state phases. Combining effective field theory with the Hartree--Fock approximation, we develop a variational framework that incorporates both the long-range Coulomb interaction and the symmetry-breaking terms on an equal footing. Variational minimization determines the optimal skyrmion texture, including both its spatial radial profile and internal $SU(4)$ spinor structure. We establish the phase diagram of skyrmion excitations, identify thirteen distinct skyrmion phases under different external-field conditions, and determine their spin-valley textures, energies, and characteristic sizes. The robustness of the results against different radial ans\"atze demonstrates the reliability of our variational approach. Our work provides a systematic framework for studying skyrmion excitations in multicomponent quantum Hall ferromagnets and can be naturally extended to more general $SU(4)$ quantum Hall systems.

cond-mat.mes-hall↗

arXiv2026

Relations between density-density correlators of states in the maximal spin multiplet

We present identities relating the pair-correlation functions and static structure factors of states in the maximal spin multiplet. This allows us to compute these density-density correlation functions of all members of the multiplet using just these correlation functions of the highest-weight state. We apply these relations to obtain energies for many fractional quantum Hall (FQH) states. In particular, we analytically compute the energies of the Halperin-$(1,1,1)$ state as a function of density imbalance and layer separation, and numerically evaluate these energies for many other FQH states.

cond-mat.str-el↗

arXiv2026

Testing the robustness of topological quantities evaluated from the modular Hamiltonian for a given wavefunction

Topologically ordered states are characterized by topological quantities like the Hall conductance, topological entanglement entropy, and chiral central charge. Techniques based on the modular Hamiltonian have recently been developed to extract these quantities from a wavefunction. Here, we consider a lattice model of fractional quantum Hall states, a prototypical example of topologically ordered systems, and extract their topological content using the modular Hamiltonian-based methods. We consider the Laughlin and Moore-Read states and show that the extracted topological quantum numbers converge to their expected results. As expected, the convergence is slower when the correlation length of the state is longer. Generally, our results show that a reliable extraction of topological content through modular methods requires the usage of large systems.

cond-mat.str-el↗

arXiv2026

Level statistics of the disordered Haldane-Shastry model with $1/r^α$ interaction

Understanding how the interaction range and various types of disorder affect the level statistics of many-body quantum systems and lead to the emergence of many-body localization (MBL) is a challenging open frontier. We study the level statistics of a variant of the spin-$1/2$ Haldane-Shastry model with $1/r^α$ interactions, where $α{\geq}0$ parametrizes the range of the interactions, in the presence of position disorder and/or random magnetic fields. We find that neither position disorder nor random magnetic fields alone yields pristine Poisson statistics in this long-range interacting system; however, Poisson statistics emerge in their combined presence, suggesting the emergence of MBL when both types of disorder coexist. Interestingly, once random magnetic fields break the $SU(2)$ symmetry, the strength of the position disorder, $δ$, appears to play an important role, as evidenced by an approximate scaling collapse of the disorder-averaged gap ratios that is parametrized in terms of a single parameter, $αδ$.

cond-mat.str-el↗

arXiv2026

Additional quantum many-body scars of the spin-$1$ $XY$ model with Fock-space cages and commutant algebras

Quantum many-body scars (QMBS) represent a mechanism for weak ergodicity breaking, characterized by the coexistence of atypical non-thermal eigenstates within an otherwise thermalizing many-body spectrum. In this work, we revisit the spin-$1$ $XY$ model on a periodic chain and construct several new families of exact scar eigenstates embedded within its extensively degenerate manifolds that owe their origins to an interplay of $U(1)$ magnetization conservation and chiral symmetries. We go beyond previously studied towers of states and first identify a novel set of interference-protected eigenstates resembling Fock space cage states, where destructive interference confines the wave function to sparse subgraphs of the Fock space. These states exhibit subextensive entanglement entropy, and when subjected to a transverse magnetic field, form equally spaced ladders whose coherent superpositions display long-lived fidelity oscillations. We further reveal a simpler organizing principle behind these nonthermal states by using the commutant algebra framework, in particular by showing that they are simultaneous eigenstates of non-commuting local operators. Moreover, in doing so, we uncover two more novel families of exact scars: a tower of volume-entangled states, and a set of mirror-dimer states with some free local degrees of freedom. Our results illustrate the power and interplay of interference-based and algebraic mechanisms of non-ergodicity, offering systematic routes to identifying and classifying QMBS in generic many-body quantum systems.

cond-mat.str-el↗

arXiv2025

Numerical demonstration of Abelian fractional statistics of composite fermions in the spherical geometry

Fractional quantum Hall (FQH) fluids host quasiparticle excitations that carry a fraction of the electronic charge. Moreover, in contrast to bosons and fermions that carry exchange statistics of $0$ and $π$ respectively, these quasiparticles of FQH fluids, when braided around one another, can accumulate a Berry phase, which is a fractional multiple of $π$. Deploying the spherical geometry, we numerically demonstrate that composite fermion particle (CFP) excitations in the Jain FQH states carry Abelian fractional statistics. Previously, the exchange statistics of CFPs were studied in the disk geometry, where the statistics get obscured due to a shift in the phase arising from the addition of another CFP, making its determination cumbersome without prior knowledge of the shift. We show that on the sphere this technical issue can be circumvented and the statistics of CFPs can be obtained more transparently. The ideas we present can be extended to determine the statistics of quasiparticles arising in certain non-Abelian partonic FQH states.

cond-mat.str-el↗

arXiv2025

Monte Carlo Sampling for Wave Functions Requiring (Anti)Symmetrization

Many strongly correlated states, such as those arising in the fractional quantum Hall effect and spin liquids, are described by wave functions obtained by dividing particles into multiple clusters, constructing a readily evaluable wave function in each cluster, and (anti)symmetrizing across these clusters. We introduce a method to compute quantities such as energies and correlators, using Monte Carlo simulations for these states. Our framework overcomes the factorial scaling of explicit (anti)symmetrization, allowing for studies of systems beyond the reach of exact diagonalization.

cond-mat.str-el↗

arXiv2025

Berry Curvature Dipole-induced Non-linear Hall Effect in Oxide Heterostructures

The observation of non-linear Hall effects in time-reversal invariant systems has established the intriguing role of band topology beyond Berry curvature in determining transport phenomena. Many of these non-linear responses owe their origin to the Berry curvature dipole (BCD), which, like the Berry curvature (monopole), is also an electronic band structure effect, but is routinely strongly constrained by crystalline symmetries. Here, we propose non-centrosymmetric transition metal oxide heterostructures as promising platforms for realizing and tuning BCD-induced non-linear Hall effects. Specifically, we investigate superlattices of the form $(\mathrm{Ba(Os,Ir)}\mathrm{O}_3)_n/(\mathrm{BaTiO}_3)_4$ ($n{=}1, 2$), comprising metallic perovskite layers ($\mathrm{BaOsO_3}$ or $\mathrm{BaIrO_3}$) sandwiched between insulating ferroelectric $\mathrm{BaTiO_3}$ (BTO). The ferroelectric distortion in BTO breaks inversion symmetry of the superlattice, giving rise to a finite BCD with two symmetry-allowed components of equal magnitude and opposite sign. Our first-principles calculations demonstrate that the magnitude of the BCD -- and consequently the nonlinear Hall response -- can be effectively tuned by varying the number of metallic layers or the choice of the B-site cation in these $\mathrm{ABO_3}$ perovskites. Since Rashba splitting and ferroelectric distortion in these systems are readily controllable via an external electric field or strain, the non-linear Hall response in these materials can be directly engineered. Our findings establish non-centrosymmetric oxide perovskite heterostructures as a versatile platform for exploring and manipulating BCD-driven non-linear transport phenomena.

cond-mat.mtrl-sci↗

arXiv2025

Dispersion of collective modes in spinful fractional quantum Hall states on the sphere

Collective modes capture the dynamical aspects of fractional quantum Hall (FQH) fluids. Depending on the active degrees of freedom, different types of collective modes can arise in a FQH state. In this work, we consider spinful FQH states in the lowest Landau level (LLL) along the Jain sequence of fillings $\nu{=}n/(2n{\pm}1)$ and compute the Coulomb dispersion of their spin-flip and spin-conserving collective modes in the spherical geometry. We use the LLL-projected density-wave and composite fermion (CF) exciton states as trial wave functions for these modes. To evaluate the dispersion of density-wave states, we derive the commutation algebra of spinful LLL-projected density operators on the sphere, which enables us to extract the gap of the density-wave excitations from the numerically computed density-density correlation function, i.e., the static structure factor, of the FQH ground state. We find that the CF excitons provide an accurate description of the collective modes at all wavelengths, while the density-wave states fail to do so. Specifically, the spin-flip density wave reliably captures the spin-flip collective mode only for the Laughlin and Halperin states, and that too only in the long-wavelength limit. Interestingly, for spin-singlet primary Jain states, the spin-conserving density mode is inaccurate even in the long-wavelength regime. We show that this discrepancy stems from the presence of an additional high-energy spin-conserving parton mode, similar to that found in fully polarized secondary Jain states at $\nu{=}n/(4n{\pm}1)$. We propose an ansatz for this parton mode and compute its Coulomb dispersion in the singlet state at $\nu{=}2/5$. The predicted parton mode can be observed in circularly polarized inelastic light scattering experiments.

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

Dispersion of neutral collective modes in partonic fractional quantum Hall states and its applications to paired states of composite fermions

The Moore-Read Pfaffian (Pf) state exhibits two distinct neutral excitation modes, the bosonic magnetoroton mode, and the neutral fermion mode. These two modes have been conjectured to be supersymmetric (SUSY) partners in the long-wavelength limit. Previous studies on these neutral excitations of the Pf state have shown evidence in favor of SUSY in the vicinity of the second Landau level (SLL) Coulomb interaction. Inspired by that, using the framework of parton theory, we test the SUSY conjecture for a state that lies in the same universality class as the particle-hole conjugate of the Pf, namely the anti-Pf (aPf) state, by constructing explicit wave functions for its magnetoroton and neutral fermion excitations and evaluating them for very large system sizes. As with the previous studies on the Pf state, we find that the long-wavelength gaps of the neutral modes of the parton state belonging to the same topological class as the aPf are close to each other for the SLL Coulomb interaction. Furthermore, using the parton wave functions, we compute the dispersion of various neutral collective excitations, including the magnetoroton, neutral fermion, and parton-excitons, for several notable non-Abelian and Abelian states. Finally, we propose a parton-exciton ansatz for the gapped neutral excitation of the composite fermion Fermi liquid at quarter filling and compute its dispersion for the Coulomb interaction in the lowest Landau level.

cond-mat.str-el↗

arXiv2025

Hetero-Orbital Two-Component Fractional Quantum Hall States in Bilayer Graphene

A two-dimensional electron system exposed to a strong magnetic field produces a plethora of strongly interacting fractional quantum Hall (FQH) states, the complex topological orders of which are revealed through exotic emergent particles, such as composite fermions, fractionally charged Abelian and non-Abelian anyons. Much insight has been gained by the study of multi-component FQH states, where spin and pseudospin indices of the electron contribute additional correlation. Traditional multi-component FQH states develop in situations where the components share the same orbital states and the resulting interactions are pseudospin independent; this homo-orbital nature was also crucial to their theoretical understanding. Here, we study "hetero-orbital" two-component FQH states, in which the orbital index is part of the pseudospin, rendering the multi-component interactions strongly SU(2) anisotropic in the pseudospin space. Such states, obtained in bilayer graphene at the isospin transition between N = 0 and N = 1 electron Landau levels, are markedly different from previous homo-orbital two-component FQH states. In particular, we observe strikingly different behaviors for the parallel-flux and reverse-flux composite fermion states, and an anomalously strong two-component 2/5 state over a wide range of magnetic field before it abruptly disappears at a high field. Our findings, combined with detailed theoretical calculations, reveal the surprising robustness of the hetero-orbital FQH effects, significantly enriching our understanding of FQH physics in this novel regime.

cond-mat.mes-hall↗

arXiv2025

Interplay of superconducting, metallic, and crystalline states of composite fermions at $ν{=}1/6$ in wide quantum wells

Evidence for developing fractional quantum Hall effect (FQHE) at filling fraction $ν{=}1/6$ and $1/8$ has recently been reported in wide GaAs quantum wells [Wang \emph{et al.}, PRL {\bf 134}, 046502 (2025)]. In this article, we theoretically investigate the nature of the state at $ν{=}1/6$ as a function of the quantum well width and the density by considering composite-fermion (CF) crystals, CF Fermi sea, and various kinds of paired CF states. The $f$-wave paired state has the lowest energy among the paired CF states. However, for parameters of interest, the energies of the CF crystal, the CF Fermi liquid, and the $f$-wave paired CF state are too close to call. We, therefore, predict that {\it if} the FQHE at $ν{=}1/6$ is experimentally confirmed, this state would be an $f$-wave paired state of CFs, which can be verified by measurement of its thermal Hall conductance. Exact diagonalization studies for systems with up to 8 electrons show that the ground states at $ν{=}n/(6n{\pm} 1)$ are incompressible for all widths and densities we have considered and well described by the corresponding Laughlin and Jain states. We propose a phase diagram for large quantum well widths and densities in which at zero disorder, incompressible FQHE states are stabilized at $ν{=}n/(6n{\pm} 1)$ and $ν{=}1/6$, but in between these fillings the CF crystal is stabilized. With disorder, which creates a spatial variation in the filling factor, two regimes are identified: (i) for small disorder, when the incompressible states percolate at the special fillings, FQHE with quantized Hall plateaus and vanishing longitudinal resistance should occur; and (ii) for larger disorder, when the CF crystal percolates, the longitudinal resistance rises with decreasing temperature but the domains of FQHE liquid produce minima at the special filling factors. The experiments are consistent with the latter scenario.

cond-mat.str-el↗

arXiv2025

Exact volume-law entangled zero-energy eigenstates in a large class of spin models

Exact solutions for excited states in non-integrable quantum Hamiltonians have revealed novel dynamical phenomena that can occur in quantum many-body systems. This work proposes a method to analytically construct a specific set of volume-law-entangled zero-energy exact excited eigenstates in a large class of spin Hamiltonians. In particular, we show that all spin chains that satisfy a simple set of conditions host exact volume-law zero-energy eigenstates in the middle of their spectra. Examples of physically relevant spin chains of this type include the transverse-field Ising model, PXP model, spin-$S$ $XY$ model, and spin-$S$ Kitaev chain. Although these eigenstates are highly atypical in their structure, they are thermal with respect to local observables. Our framework also unifies many recent constructions of volume-law entangled eigenstates in the literature. Finally, we show that a similar construction also generalizes to spin models on graphs in arbitrary dimensions.

cond-mat.str-el↗

arXiv2025

Anomalous Transport Gaps of Fractional Quantum Hall Phases in Graphene Landau Levels are Induced by Spin-Valley Entangled Ground States

We evaluate the transport gaps in the most prominent fractional quantum Hall states in the $\mathbf{n}{=}0$ and $\mathbf{n}{=}1$ Landau Levels of graphene, accounting for the Coulomb interaction, lattice-scale anisotropies, and one-body terms. We find that the fractional phases in the $\mathbf{n}{=}0$ Landau level are bond-ordered, while those in the $\mathbf{n}{=}1$ Landau level are spin-valley entangled. This resolves a long-standing experimental puzzle [Amet, $\textit{et al.}$, Nat. Comm. $\mathbf{6}$, 5838 (2015)] of the contrasting Zeeman dependence of the transport gaps in the two Landau levels. The spin-valley entangled phases host gapless Goldstone modes that can be probed via bulk thermal transport measurements. As a byproduct of our computations, we place strong constraints on the values of the microscopic anisotropic couplings such that these are consistent with all known experimental results.

cond-mat.mes-hall↗

arXiv2025

Entanglement scaling and charge fluctuations in a Fermi liquid of composite fermions

The composite fermion Fermi liquid (CFL) state at $ν=1/2$ filling of a Landau level is a paradigmatic non-Fermi liquid borne out purely by Coulomb interactions. But in what ways is this exotic state of matter different from a Fermi liquid? The CFL entanglement entropy was indeed found to exhibit a significant enhancement compared to free electrons [Shao et al., Phys. Rev. Lett. 114, 206402 (2015)], which was subsequently ruled out as a finite-size effect by the study of a lattice CFL analog [Mishmash and Motrunich, Phys. Rev. B 94, 081110 (2016)]. Moreover, the enhancement was not observed in a quasi-one-dimensional limit of the Coulomb ground state at $ν=1/2$ [Geraedts et al., Science 352, 197 (2016)]. Here, we revisit the problem of entanglement scaling in the CFL state realized in a two-dimensional electron gas. Using Monte Carlo evaluation of the second Rényi entropy $S_2$ for the CFL variational wave function, we show that the entanglement enhancement is present not only at $ν=1/2$ but also at $ν=1/4$, as well as in bosonic CFL states at $ν=1$ and $ν=1/3$ fillings. In all cases, we find the scaling of $S_2$ with subsystem size to be enhanced compared to the non-interacting case, and insensitive to the choice of geometry and projection to the lowest Landau level. We also demonstrate that, for CFL states, the variance of the particle number in a subsystem obeys area-law scaling with a universal subleading corner contribution, in stark contrast with free fermions. Our results establish the enhanced entanglement scaling and suppressed charge fluctuations as fingerprints of non-Fermi-liquid correlations in CFL states.

cond-mat.str-el↗

arXiv2025

Even-denominator fractional quantum Hall states in the zeroth Landau level of ABA trilayer graphene

Even-denominator fractional quantum Hall states (FQHSs) at half filling are of particular interest because they can host non-Abelian quasiparticles. Here we report the emergence of such states in the zeroth Landau level ($N=0$) of ABA trilayer graphene (TLG), challenging the conventional expectation that they are confined to the first excited Landau level. We observe robust incompressible states at $\nu=7/2$, $9/2$, and $5/2$ with their associated Levin--Halperin daughter states: $\nu=59/17$ and $46/13$ near $7/2$; $\nu=58/13$ and $77/17$ near $9/2$; and $\nu=43/17$ near $5/2$. These states appear exclusively within a finite displacement-field window coincident with crossings between symmetry-broken $N=0$ Landau levels carrying distinct isospin indices. The quantitative correspondence between the calculated crossing loci and the experimentally determined stability regions identifies Landau-level mixing as the microscopic origin. We attribute the stabilization of these even-denominator states to inversion-symmetry breaking in TLG, which enhances valley-resolved Landau-level hybridization and renormalizes short-range Coulomb interactions. Our results expand the landscape of even-denominator FQHSs to multilayer graphene and establish TLG as a tunable platform for realizing non-Abelian anyons.

cond-mat.mes-hall↗