arXiv subjects

Siddhartha Sarkar

Publications and source records attributed to Siddhartha Sarkar.

At least 19 recordsLinked to original sources

arXiv2026

Interlayer Exciton Condensate Stiffness Is Non-Monotonic in Quantum Metric

Identifying the origin of the superfluid stiffness of electron-electron and electron-hole pair condensates is an important issue in flat-band physics. Here, we study the stiffness of bilayer exciton condensates using exact diagonalization and realistic Coulomb interactions across a wide variety of flat Chern band systems, including Landau levels, mixed Landau levels, and moiré bands. We find that stiffness is non-monotonic in the trace of the quantum metric and that it develops peaks when the band wavefunctions are engineered to be similar to those of Landau levels. The stiffness predicted by mean-field theory agrees quantitatively with exact diagonalization in these optimal cases, but systematically overestimates it otherwise. Flat bands with identical quantum geometry tensors can exhibit substantial differences in stiffness. The stiffness of condensates formed between moiré flat bands, which typically have strong variations in Berry curvature and quantum metric across their Brillouin zones, tends to be larger when the bands have non-zero Chern numbers and can be larger than that of Landau levels. Our results reveal a behavior that is richer than that suggested by simple geometric bounds and provide new guiding principles for the design of robust flat-band condensates with large superfluid stiffness.

cond-mat.mes-hall↗

arXiv2026

Tunable Multiband Geometry and Fractional Phases in Higher Vortexable Systems

Higher vortexability is often viewed as a route to topological flat bands with higher-Landau-level-like quantum geometry. Here we emphasize a complementary perspective: it provides a tunable multiband structure in which wave function geometry can be varied continuously while the band dispersion, degeneracy, and topology remain fixed. We perform systematic exact-diagonalization studies of many-body phases in fractionally filled higher vortexable moiré systems, retaining the full flat-band Hilbert space rather than projecting onto a single band. The multiband treatment reveals a cascade of Abelian and non-Abelian phases at zero magnetic field, including integer and fractional exciton insulators, Abelian fractional Chern insulators, Moore-Read and Read-Rezayi states. At fixed filling, different phases are connected through transitions or crossovers driven solely by changes in wave function geometry, highlighting quantum geometry itself as a direct tuning parameter between competing topological states. At fillings associated with Moore-Read and Read-Rezayi states, our calculations show that interband mixing shifts the optimal quantum geometry regime without suppressing non-Abelian topological order under screened Coulomb interaction. Our results establish higher vortexable moiré bands as a tunable platform for exploring geometry-driven multiband topological phases at zero magnetic field.

cond-mat.str-el↗

arXiv2026

How Similar Can Fractional Chern Insulators Be to Fractional Quantum Hall States? Moiré-Enhanced Gaps and Excitation-Spectrum Correspondence

Fractional Chern insulators (FCIs) realize fractional quantum Hall topology in lattice bands, but their excitation spectra remain far less understood than their ground states. Here we establish a theoretical principle relating the periodic electron-density modulations of flat Chern bands to the many-body gap and excitation spectrum of FCIs. Contrary to the conventional view that such density modulations are detrimental to fractional topology, we show that different reciprocal-lattice Fourier components play sharply distinct roles: components at smaller reciprocal lattice vectors suppress the FCI gap, whereas components at larger reciprocal lattice vectors enhance it. By suppressing the harmful small-wave-vector components and amplifying the beneficial large-wave-vector components, the gap enhancement can, in principle, be made arbitrarily large within the projected flat-band theory. Moreover, the same enhancement factor rescales the full low-energy spectrum, making the FCI excitation spectrum predictable from the corresponding Landau-level problem. We further generalize this correspondence to non-Abelian states. Applying this principle to moiré Chern bands, we identify these reciprocal-lattice density components as practical diagnostics for robust FCIs.

cond-mat.str-el↗

arXiv2026

Hitting Axis-Parallel Segments with Weighted Points

We study a geometric hitting-set problem in which the input consists of a set $P$ of weighted points and a family $S=H\cup V$ of axis-parallel segments in the plane. The goal is to select a minimum-weight subset of $P$ that hits every segment in $S$. Even restricted geometric hitting-set problems are known to be computationally hard, and for axis-parallel segments the standard decomposition into horizontal and vertical sub-instances yields only a simple factor-$2$ approximation. We present an LP-rounding algorithm that breaks the factor-2 barrier. For the weighted problem, we obtain a randomized $(1+2/e)$-approximation by combining systematic rounding on horizontal lines with an exact repair step on residual vertical sub-instances. In the unweighted case, a sharper analysis gives a $(1+1/(e-1))$-approximation. Finally, we consider the case where one of the sub-instances consists of lines instead of line segments, a problem considered by Fekete et al. (Geometric Hitting Set for Segments of Few Orientations, Theor. Comp. Sys., 62 (2) 2018),. In this case, we improve their result to obtain an approximation factor of $1+1/e$ and show that the problem is APX-hard. We also present algorithms for the generalization to $d$ orientations, as well as PTASes for bounded-complexity subclasses of the unweighted Hitting Set problem.

cs.CG↗

arXiv2026

XDiag: Exact Diagonalization for Quantum Many-Body Systems

Exact diagonalization (ED) is a cornerstone technique in quantum many-body physics, enabling precise solutions to the Schrödinger equation for interacting quantum systems. Despite its utility in studying ground states, excited states, and dynamical behaviors, the exponential growth of the Hilbert space with system size presents significant computational challenges. We introduce XDiag, an open-source software package designed to combine advanced and efficient algorithms for ED with and without symmetry-adapted bases with user-friendly interfaces. Implemented in C++ for computational efficiency and wrapped in Julia for ease of use, XDiag provides a comprehensive toolkit for ED calculations. Key features of XDiag include the first publicly accessible implementation of sublattice coding algorithms for large-scale spin system diagonalizations, efficient Lin table algorithms for symmetry lookups, and random-hashing techniques for distributed memory parallelization. The library supports various Hilbert space types (e.g., spin-1/2, electron, and t-J models), facilitates symmetry-adapted block calculations, and automates symmetry considerations. The package is complemented by extensive documentation, a user guide, reproducible benchmarks demonstrating near-linear scaling on thousands of CPU cores, and over 20 examples covering ground-state calculations, spectral functions, time evolution, and thermal states. By integrating high-performance computing with accessible scripting capabilities, XDiag allows researchers to perform state-of-the-art ED simulations and explore quantum many-body phenomena with unprecedented flexibility and efficiency.

cond-mat.str-el↗

arXiv2026

Uni-width subgroups, universal elements, and lambda number of finite groups

A cyclic subgroup $N$ of a finite group $G$ is called a uni-width subgroup of $G$ if $N$ is the unique cyclic subgroup of $G$ of order $|N|$. In this article, we prove that a finite group $G$ admits a unique largest uni-width subgroup denoted by $U(1;G)$. We then show that the prime factors of the order of $U(1;G)$ influence the structure decomposition of its Fitting subgroup ${\mathrm{Fit}}(G)$. A power graph $Γ_G$ of a finite group is defined by $G$ being its set of vertices, and a pair of distinct elements $x,y \in G$ are connected by an edge if either $x \in \langle y \rangle$ or $y \in \langle x \rangle$. A universal element of a graph is a vertex that is adjacent to each of the remaining vertices. Our following result shows that a power graph $Γ_G$ of a finite non-trivial group admits a non-identity universal element if and only if it is either cyclic or a generalized quaternion $2$-group. The lambda number $λ(G)$ of a finite group $G$ is a measure of the least number of colors required for an $L(2,1)$-type of vertex coloring on $Γ_G$, which is known to be $\geq |G|$. Generalizing an earlier result, we then derive a necessary condition on a finite group $G$ such that $λ(G) = |G|$. Finally, we show that this result is best possible by exhibiting a family of groups without the necessary condition for which $λ(G) > |G|$.

math.GR↗

arXiv2025

Mechanochemical feedback drives complex inertial dynamics in active solids

Active solids combine internal active driving with elasticity to realize states with nonequilibrium mechanics and autonomous motion. They are often studied in overdamped settings, e.g., in soft materials, and the role of inertia is less explored. We construct a model of a chemically active solid that incorporates mechanochemical feedback and show that, when feedback overwhelms mechanical damping, autonomous inertial dynamics can spontaneously emerge through sustained consumption of chemical fuel. By combining numerical simulations, analysis and dynamical systems approaches, we show how active feedback drives complex nonlinear dynamics on multiple time-scales, including limit cycles and chaos. Our results suggest design principles for creating ultrafast actuators and autonomous machines from soft, chemically-powered solids.

cond-mat.soft↗

arXiv2025

Unconventional Fractional Phases in Multi-Band Vortexable Systems

In this Letter, we study topological flat bands with distinct features that deviate from conventional Landau level behavior. We show that even in the ideal quantum geometry limit, moire flat band systems can exhibit physical phenomena fundamentally different from Landau levels without lattices. In particular, we find new fractional quantum Hall states emerging from multi-band vortexable systems, where multiple exactly flat bands appear at the Fermi energy. While the set of bands as a whole exhibits ideal quantum geometry, individual bands separately lose vortexability, and thus making them very different from a stack of Landau levels. At certain filling fractions, we find fractional states whose Hall conductivity deviates from the filling factor. Through careful numerical and analytical studies, we rule out all known mechanisms--such as fractional quantum Hall crystals or separate filling of trivial and topological bands--as possible explanations. Leveraging the exact solvability of vortexable systems, we use analytic Bloch wavefunctions to uncover the origin of these new fractional states, which arises from the commensurability between the moire unit cell and the magnetic unit cell of an emergent effective magnetic field.

cond-mat.str-el↗

arXiv2025

Beyond the Lowest Landau Level: Unlocking More Robust Fractional States Using Flat Chern Bands with Higher Vortexability

Enhancing the many-body gap of a fractional state is crucial for realizing robust fractional excitations. For fractional Chern insulators, existing studies suggest that making flat Chern bands closely resemble the lowest Landau level (LLL) seems to maximize the excitation gap, providing an apparently optimal platform. In this work, we demonstrate that deforming away from the LLL limit can, in fact, produce substantially larger FQH gaps. Using moiré flat bands with strongly non-Landau-level wavefunctions, we show that the gap can exceed that of the LLL by more than two orders of magnitude for short-range interactions and by factors of two to three for long-range interactions. This enhancement is generic across Abelian FCI states and follows a universal enhancement factor within each hierarchy. Using the Landau level framework, we identify the amplification of pseudopotentials as the microscopic origin of the observed enhancement. This finding demonstrates that pseudopotential engineering can substantially strengthen fractional topological phases. We further examined non-Abelian states and found that, within finite-size resolution, this wavefunction construction method can also be used to manipulate and enhance the gap for certain interaction parameters.

cond-mat.str-el↗

arXiv2025

Tunable symmetry breaking in a hexagonal-stacked moiré magnet

Symmetry plays a central role in defining magnetic phases, making tunable symmetry breaking across magnetic transitions highly desirable for discovering non-trivial magnetism. Magnetic moiré superlattices, formed by twisting two-dimensional (2D) magnetic crystals, have been theoretically proposed and experimentally explored as platforms for unconventional magnetic states. However, despite recent advances, tuning symmetry breaking in moiré magnetism remains limited, as twisted 2D magnets, such as rhombohedral (R)-stacked twisted CrI_3, largely inherit the magnetic properties and symmetries of their constituent layers. Here, in hexagonal-stacked twisted double bilayer (H-tDB) CrI_3, we demonstrate clear symmetry evolution as the twist angle increases from 180^{\circ} to 190^{\circ}. While the net magnetization remains zero across this twist angle range, the magnetic phase breaks only the three-fold rotational symmetry at 180^{\circ}, but it breaks all of the rotational, mirror, and time-reversal symmetries at intermediate twist angles between 181^{\circ} and 185^{\circ}, and all broken symmetries are recovered at 190^{\circ}. These pronounced symmetry breakings at intermediate twist angles are accompanied by metamagnetic behaviors, evidenced by symmetric double hysteresis loops around zero magnetic field. Together, these results reveal that H-tDB CrI_3 at intermediate twist angles host a distinct moiré magnetic phase, featuring periodic in-plane spin textures with broken rotational, mirror, and time-reversal symmetries, which is markedly different from the out-of-plane layered antiferromagnetism in bilayer CrI_3 and the predominantly out-of-plane moiré magnetism in R-tDB CrI_3. Our work establishes H-stacked CrI_3 moiré magnets as a versatile platform for engineering magnetic properties, including and likely beyond complex spin textures.

cond-mat.mtrl-sci↗

arXiv2025

Minimum Membership Geometric Set Cover in the Continuous Setting

We study the minimum membership geometric set cover, i.e., MMGSC problem [SoCG, 2023] in the continuous setting. In this problem, the input consists of a set $P$ of $n$ points in $\mathbb{R}^{2}$, and a geometric object $t$, the goal is to find a set $\mathcal{S}$ of translated copies of the geometric object $t$ that covers all the points in $P$ while minimizing $\mathsf{memb}(P, \mathcal{S})$, where $\mathsf{memb}(P, \mathcal{S})=\max_{p\in P}|\{s\in \mathcal{S}: p\in s\}|$. For unit squares, we present a simple $O(n\log n)$ time algorithm that outputs a $1$-membership cover. We show that the size of our solution is at most twice that of an optimal solution. We establish the NP-hardness on the problem of computing the minimum number of non-overlapping unit squares required to cover a given set of points. This algorithm also generalizes to fixed-sized hyperboxes in $d$-dimensional space, where an $1$-membership cover with size at most $2^{d-1}$ times the size of a minimum-sized $1$-membership cover is computed in $O(dn\log n)$ time. Additionally, we characterize a class of objects for which a $1$-membership cover always exists. For unit disks, we prove that a $2$-membership cover exists for any point set, and the size of the cover is at most $7$ times that of the optimal cover. For arbitrary convex polygons with $m$ vertices, we present an algorithm that outputs a $4$-membership cover in $O(n\log n + nm)$ time.

cs.CG↗

arXiv2025

Omnidirectional domain wall modes protected by fragile topological states

So-called fragile topological states of matter challenge our conventional notion of topology by lacking the robustness typically associated with topological protection, thereby displaying elusive manifestations that are difficult to harness for wave control. In this Letter, we leverage the recent discovery of fragile topological states in special classes of structural kagome lattices to document the availability of domain wall elastic wave modes that are directly traceable to fragile topology and, yet, exhibit remarkably strong signatures that support omni-directionality. We design twisted kagome bi-domains comprising two topologically distinct sublattices - one trivial and the other fragile topological - sharing a common bandgap and meeting at a domain wall. The two phases are achieved via carefully engineered surface cut patterns that modify the band landscape of the underlying lattices in complementary fashions, leading to dichotomous irreps landscapes. Under these circumstances, a domain wall-bound mode emerges within the shared bandgap and displays remarkable stability against domain wall orientation and introduced defects. We corroborate these findings via $\mathbf{k}\cdot\mathbf{p}$ Hamiltonian and Jackiw-Rabbi analysis and validate them experimentally through laser vibrometry tests on a prototype endowed with water jet-induced perforation patterns.

cond-mat.mtrl-sci↗

arXiv2025

Dynamics of self-dual kagome metamaterials and the emergence of fragile topology

Recent years have seen the discovery of systems featuring fragile topological states. These states of matter lack certain protection attributes typically associated with topology and are therefore characterized by weaker signatures that make them elusive to observe. Moreover, they are typically confined to special symmetry classes and, in general, rarely studied in the context of phononic media. In this Letter, we theoretically predict the emergence of fragile topological bands in the spectrum of a twisted kagome elastic lattice with three-fold rotational symmetry, in the so-called self-dual configuration. A necessary requirement is that the lattice is a structural metamaterial, in which the role of the hinges is played by elastic finite-thickness ligaments. The interplay between the edge modes appearing in the bandgaps bounding the fragile topological states is also responsible for the emergence of corner modes at selected corners of a finite hexagonal domain, which qualifies the lattice as a second-order topological insulator. We demonstrate our findings through a series of experiments via 3D Scanning Laser Doppler Vibrometry conducted on a physical prototype. The selected configuration stands out for its remarkable geometric simplicity and ease of physical implementation in the panorama of dynamical systems exhibiting fragile topology.

cond-mat.mtrl-sci↗

arXiv2024

Novel mechanical response of parallelogram-face origami governed by topological characteristics

Origami principles are used to create strong, lightweight structures with complex mechanical response. However, identifying the fundamental physical principles that determine a sheet's behavior remains a challenge. We introduce a new analytic theory in which commonly studied origami sheets fall into distinct topological classes that predict sharply varying mechanical behavior, including effective stiffness and smoothness of mechanical response under external loads. Origami sheets with negative Poisson's ratios, such as the Miura ori, have conventional, smooth mechanical response amenable to continuum-based approaches. In contrast, positive Poisson's ratio, as in the Eggbox ori, generates a topological transition to lines of doubly degenerate zero modes that lead to dramatically softer structures with uneven, complex patterns of spatial response. These patterns interact in complicated ways with origami boundary conditions and source terms, leading to rich physical phenomena in experimentally accessible systems. This approach highlights topological mechanics, with deep connections to topologically protected quantum-mechanical systems, as a design principle for controlling the mechanical response of thin, complex sheets.

cond-mat.soft↗

arXiv2024

Quantum-metric-induced quantum Hall conductance inversion and reentrant transition in fractional Chern insulators

The quantum metric of single-particle wave functions in topological flatbands plays a crucial role in determining the stability of fractional Chern insulating (FCI) states. Here, we unravel that the quantum metric causes the many-body Chern number of the FCI states to deviate sharply from the expected value associated with partial filling of the single-particle topological flatband. Furthermore, the variation of the quantum metric in momentum space induces band dispersion through interactions, affecting the stability of the FCI states. This causes a reentrant transition into the Fermi liquid from the FCI phase as the interaction strength increases.

cond-mat.str-el↗

arXiv2024

Ideal topological flat bands in chiral symmetric moiré systems from non-holomorphic functions

Recent studies on topological flat bands and their fractional states have revealed increasing similarities between moiré flat bands and Landau levels (LLs). For instance, like the lowest LL, topological exact flat bands with ideal quantum geometry can be constructed using the same holomorphic function structure, $ψ_{\mathbf{k}} = f_{\mathbf{k}-\mathbf{k}_0}(z) ψ_{\mathbf{k}_0}$, where $f_{\mathbf{k}}(z)$ is a holomorphic function. This holomorphic structure has been the foundation of existing knowledge on constructing ideal topological flat bands. In this Letter, we report a new family of ideal topological flat bands where the $f$ function does not need to be holomorphic. We provide both model examples and universal principles, as well as an analytic method to construct the wavefunctions of these flat bands, revealing their universal properties, including ideal quantum geometry and a Chern number of $C = \pm 2$ or higher.

cond-mat.mes-hall↗

arXiv2024

Lower Bounds for Multicolor Star-Critical Ramsey Numbers

The star-critical Ramsey number is a refinement of the concept of a Ramsey number. In this paper, we give equivalent criteria for which the star-critical Ramsey number vanishes. Next, we provide a new general lower bound for multicolor star-critical Ramsey numbers whenever it does not vanish. As an application, we evaluate $r_*(P_k, P_3, P_3)$, where $P_n$ is a path of order $n$. In the process of proving these results, we also show that $r_*(C_5, P_3)=3$, where $C_5$ is a cycle of order $5$.

math.CO↗

arXiv2024

A note on a Conjecture of Gao and Zhuang for groups of order $27$

The small Davenport constant ${\mathsf{d}}(G)$ of a finite group $G$ is defined to be the maximal length of a sequence over $G$ which has no non-trivial product-one subsequence. In this paper, we prove that ${\mathsf{d}}(G) = 6$ for the non-abelian group of order $27$ and exponent $3$ and thereby establish a conjecture by Gao and Zhuang for this group.

math.GR↗