arXiv subjects

Nisarga Paul

Publications and source records attributed to Nisarga Paul.

At least 19 recordsLinked to original sources

arXiv2026

Entangling power of neural networks

Characterizing the complexity of correlations between subsystems is a fundamental task across information theory, machine learning, and science. In quantum physics, neural networks have found increasing application in learning wavefunctions. Here we introduce the entangling power of an encoder-decoder neural network, which quantifies its ability to generate entanglement between subsystems, dependent on a latent space dimension $K$ and the complexity class of the decoder. We exactly calculate this quantity for polynomial decoders of degree $p$ acting on a $K$-dimensional latent space. Our results establish the exponential entangling power of neural networks with modest resources. More broadly, our work provides a framework for analyzing correlations in machine learning that generalizes the notion of the Schmidt rank in entanglement theory.

cond-mat.dis-nn↗

arXiv2026

Learning the closest Slater determinant

Learning compact, interpretable descriptions of quantum many-body states is an important task in quantum science. We study the task of learning the Slater determinant with maximum fidelity to an arbitrary fermionic many-body state, with motivation from both Hartree-Fock methods and agnostic tomography. Given an $n$-fermion wavefunction built from $m$ fermionic modes, we provide classical and quantum algorithms returning a Slater determinant with fidelity within $\varepsilon$ of maximal in time $m^{\text{poly}(n,1/\varepsilon)}$. We prove matching hardness lower bounds, assuming standard complexity conjectures, along some parameter axes. Given access to quantum copies, we prove this can be accomplished with $\text{poly}(m,n,1/\varepsilon)$ copies of $\rho$. We also show that above a fidelity of $2/3$ any stationary point is the unique global maximum while below $2/3$ the optimization landscape can have spurious stationary points, and hence $2/3$ marks a transition point in the optimization landscape for this problem. We apply the algorithm to the Fermi-Hubbard model, extracting the closest Slater determinant from neural quantum state solutions. Together, our results provide algorithmic tools with provable guarantees in understanding fermionic many-body systems with classical or quantum simulation.

quant-ph↗

arXiv2026

Bootstrapping ground state properties of classical frustrated magnets

We introduce a method based on semidefinite programming that produces rigorous two-sided bounds on ground state energy densities and correlation functions of translation-invariant classical spin models on infinite lattices. In this method, the challenge of non-convex optimization on an infinite lattice is replaced with a hierarchy of finite-size convex optimizations arising from positivity conditions that any probability distribution over spin configurations must satisfy. This adapts the Lasserre hierarchy in the theory of polynomial optimization to the context of frustrated magnetism, and we prove convergence of this hierarchy in the thermodynamic limit. Our method subsumes the Luttinger--Tisza method and further applies to non-quadratic Hamiltonians and non-Bravais lattices, thus addressing limitations of prior analytical methods. We apply the method to various two-dimensional frustrated spin models, where it brackets the energy densities and observables accurately across large parameter ranges with typical run times of seconds per parameter point.

cond-mat.stat-mech↗

arXiv2026

Resonant Zener Interferometry in van der Waals Heterostructures

We demonstrate the presence of quantum interference effects in van der Waals heterostructures subject to in-plane electric fields. The in-plane field $F$ accelerates carriers through a hybridized band edge, and interlayer Zener tunneling occurs by distinct pathways, resulting in a solid-state quantum interferometer with imprints in transport observables. For parabolic-band bilayers, we identify two characteristic signatures which are observable in lateral conductance: Landau-Zener-Stuckelberg oscillations in the band-overlap regime periodic in $1/F$ at small fields, resembling electric-field induced quantum oscillations, and a pronounced resonance at $F\propto T_0^{3/2}$ set by the interlayer tunneling $T_0$. These features provide a directly accessible probe of coherent interferometric dynamics in van der Waals heterostructures, and could be harnessed for more precise engineering and characterization.

cond-mat.mes-hall↗

arXiv2025

Higher-dimensional Fermiology in bulk moir\'e metals

In the past decade, moir\'e materials have revolutionized how we engineer and control quantum phases of matter. Among incommensurate materials, moir\'e materials are aperiodic composite crystals whose long-wavelength moir\'e superlattices enable tunable properties without chemically modifying their layers. To date, nearly all reports of moir\'e materials have investigated van der Waals heterostructures assembled far from thermodynamic equilibrium. Here we introduce a conceptually new approach to synthesizing high-mobility moir\'e materials in thermodynamic equilibrium. We report a new family of foliated superlattice materials (Sr$_6$TaS$_8$)$_{1+\delta}$(TaS$_2$)$_8$ that are exfoliatable van der Waals crystals with atomically incommensurate lattices. Lattice mismatches between alternating layers generate moir\'e superlattices, analogous to those of 2D moir\'e heterobilayers, that are coherent throughout these crystals and are tunable through their synthesis conditions without altering their chemical composition. High-field quantum oscillation measurements map the complex Fermiology of these moir\'e metals, which can be tuned via the moir\'e superlattice structure. We find that the Fermi surface of the structurally simplest moir\'e metal is comprised of over 40 distinct cross-sectional areas, the most observed in any material to our knowledge. This can be naturally understood by postulating that bulk moir\'e materials can encode electronic properties of higher-dimensional superspace crystals in ways that parallel well-established crystallographic methods used for incommensurate lattices. More broadly, our work demonstrates a scalable synthesis approach potentially capable of producing moir\'e materials for electronics applications and evidences a novel material design concept for accessing a broad range of physical phenomena proposed in higher dimensions.

cond-mat.mtrl-sci↗

arXiv2025

Bound on entanglement in neural quantum states

Variational wavefunctions offer a practical route around the exponential complexity of many-body Hilbert spaces, but their expressive power is often sharply constrained. Matrix product states, for instance, are efficient but limited to area law entangled states. Neural quantum states (NQS) are widely believed to overcome such limitations, yet little is known about their fundamental constraints. Here we prove that feed-forward neural quantum states acting on $n$ spins with $k$ scalar nonlinearities, under certain analyticity assumptions, obey a bound on entanglement entropy for any subregion: $S \leq c k\log n$, for a constant $c$. This establishes an NQS analog of the area law constraint for matrix product states and rules out volume law entanglement for NQS with $O(1)$ nonlinearities. We demonstrate analytically and numerically that the scaling with $n$ is tight for a wide variety of NQS. Our work establishes a fundamental constraint on NQS that applies broadly across different network designs, while reinforcing their substantial expressive power.

quant-ph↗

arXiv2025

Reconstructing the Hamiltonian from the local density of states using neural networks

Reconstructing a quantum system's Hamiltonian from limited yet experimentally observable information is interesting both as a practical task and from a fundamental standpoint. We pose and investigate the inverse problem of reconstructing a Hamiltonian from a spatial map of the local density of states (LDOS) near a fixed energy. We demonstrate high-quality recovery of Hamiltonians from the LDOS using supervised learning. In particular, we generate synthetic data from single-particle Hamiltonians in 1D and 2D, train convolutional neural networks, and obtain models that solve the inverse problem with remarkably high accuracy. Moreover, we are able to generalize beyond the training distribution and develop models with strong robustness to noise. Finally, we comment on possible experimental applications to scanning tunneling microscopy, where we propose that maps of the electronic local density of states might be used to reveal a sample's unknown underlying energy landscape.

cond-mat.dis-nn↗

arXiv2025

Emergent curved space and gravitational lensing in quantum materials

We show that an effective gravitational field naturally emerges in quantum materials with long-wavelength spin (or pseudospin) textures. When the itinerant electrons' spin strongly couples to the background spin texture, it effectively behaves as a spinless particle in a curved space, with the curvature arising from quantum corrections to the electron's spin orientation. The emergent curved space gives rise to the electron lensing effect, an analog of the gravitational lensing. The lensing effect can appear in systems without (emergent) magnetic fields, such as those with coplanar spin textures. Our work shows that novel ``gravitational'' phenomena generically appear in quantum systems due to nonadiabaticity, opening new research directions in quantum physics.

cond-mat.mes-hall↗

arXiv2025

Compressible quantum liquid with vanishing Drude weight

We explore the possibility of quantum liquids that are compressible but have vanishing DC conductivity in the absence of disorder. We show that the composite Fermi liquid emerging from strong interaction in a generic Chern band has zero Drude weight, in stark contrast to normal Fermi liquids. Our work establishes the absence of Drude weight as the defining property of the composite Fermi liquid phase, which distinguishes it from the Fermi liquid or other types of non-Fermi liquids. Our findings point to a possibly wide class of gapless quantum phases with unexpected transport and optical properties.

cond-mat.str-el↗

arXiv2025

Gyrotropic magnetic effect in metallic chiral magnets

We study the gyrotropic magnetic effect (GME), the low-frequency limit of optical gyrotropy, in metals and semimetals coupled to chiral spin textures. In these systems, the chiral spin texture which lacks inversion symmetry can imprint itself upon the electronic structure through Hund's coupling, leading to novel low-frequency optical activity. Using perturbation theory and numerical diagonalization of both relativistic and non-relativistic models of conduction electrons coupled to spin textures, we analyze how the GME manifests in both single-$q$ and multi-$q$ textures. Analytical expressions for the rotatory power are derived in terms of universal scaling functions. Estimates based on realistic material parameters reveal an experimentally viable range of values for the rotatory power. The GME arises from the orbital and spin magnetic moments of conduction electrons, with the orbital part closely tied to Berry curvature and playing a significant role in relativistic metals but not so in non-relativistic metals where there is no inherent Berry curvature. The spin contribution to the GME can be significant in non-relativistic metals with a large Fermi energy. Our work establishes the GME as a sensitive probe of magnetic chirality and symmetry breaking in metallic chiral magnets.

cond-mat.mes-hall↗

arXiv2025

Shining light on collective modes in moiré fractional Chern insulators

We show that collective excitations and optical responses of moiré fractional Chern insulators (FCIs) drastically differ from those of standard fractional quantum Hall (FQH) states in a Landau level. By constructing a variational wavefunction that incorporates the moiré lattice effect, we capture the collective modes in FCIs across a range of crystal momenta including the roton minimum. Interestingly, new collective modes -- ``fractional excitons'' -- are found in the long wavelength limit ($\boldsymbol{q} \rightarrow 0$) at low energy below the excitation continuum, distinct from the FQH case. Some of these modes are optically active and manifest as sharp peaks in optical conductivity at THz frequency. We further show that intraband optical absorption and spectral weight in twisted ${\rm MoTe}_2$ are highly tunable by the displacement field. Our work thus establishes optical spectroscopy as a powerful tool to illuminate the unique collective modes of moiré FCIs.

cond-mat.mes-hall↗

arXiv2024

Non-Abelian fractionalization in topological minibands

Motivated by the recent discovery of fractional quantum anomalous Hall states in moiré systems, we consider the possibility of realizing non-Abelian phases in topological minibands. We study a family of moiré systems, skyrmion Chern band models, which can be realized in two-dimensional semiconductor-magnet heterostructures and also capture the essence of twisted transition metal dichalcogenide homobilayers. We show using many-body exact diagonalization that, in spite of strong Berry curvature variations in momentum space, the non-Abelian Moore-Read state can be realized at half filling of the second miniband. These results demonstrate the feasibility of non-Abelian fractionalization in moiré systems without Landau levels and shed light on the desirable conditions for their realization. In particular, we highlight the prospect of realizing the Moore-Read state in twisted semiconductor bilayers.

cond-mat.mes-hall↗

arXiv2024

Stability of sub-dimensional localization to electronic interactions

Sub-dimensional localization, also known as directional localization, arises when 2d electrons are subject to a periodic potential and incommensurate magnetic field which cause them to become exponentially localized along one crystal axis, while remaining extended in the orthogonal direction. We establish that sub-dimensional localization is robust to the presence of electronic interactions, which are known to generically destabilize single-particle localization. Consequently we predict that sub-dimensional localization may occur in moire materials, where it is manifest as a total absence of conductivity in the localized (transverse) direction, with finite conductivity in the extended (longitudinal) direction. We find the electrons form longitudinal charge density waves which are incommensurate with the moire potential, allowing them to slide and hence conduct in the longitudinal direction. The conductivity remains prohibited in the transverse direction due an emergent charge dipole moment conservation law.

cond-mat.mes-hall↗

arXiv2024

Designing (higher) Hall crystals

We introduce a novel platform for realizing interaction-induced Hall crystals with diverse Chern numbers $C$. This platform consists of a two-dimensional semiconductor or graphene subjected to an out-of-plane magnetic field and a one-dimensional modulation, which can be realized by moir\'e or dielectric engineering. We show that interactions drive the system to spontaneously break the residual translational symmetry, resulting in Hall crystals with various $C$ (including $|C|>1$). Remarkably, these phases persist across continuous ranges of filling and magnetic field, and the global phase diagram can be understood in a unified manner.

cond-mat.mes-hall↗

arXiv2024

Band structure engineering using a moiré polar substrate

Applying long wavelength periodic potentials on quantum materials has recently been demonstrated to be a promising pathway for engineering novel quantum phases of matter. Here, we utilize twisted bilayer boron nitride (BN) as a moiré substrate for band structure engineering. Small-angle-twisted bilayer BN is endowed with periodically arranged up and down polar domains, which imprints a periodic electrostatic potential on a target two-dimensional (2D) material placed on top. As a proof of concept, we use Bernal bilayer graphene as the target material. The resulting modulation of the band structure appears as superlattice resistance peaks, tunable by varying the twist angle, and Hofstadter butterfly physics under a magnetic field. Additionally, we demonstrate the tunability of the moiré potential by altering the dielectric thickness underneath the twisted BN. Finally, we find that near-60°-twisted bilayer BN provides a unique platform for studying the moiré structural effect without the contribution from electrostatic moiré potentials. Tunable moiré polar substrates may serve as versatile platforms to engineer the electronic, optical, and mechanical properties of 2D materials and van der Waals heterostructures.

cond-mat.mes-hall↗

arXiv2023

Dimensional reduction from magnetic field in moiré superlattices

Moiré materials provide a highly tunable platform in which novel electronic phenomena can emerge. We study strained moiré materials in a uniform magnetic field and predict highly anisotropic electrical conductivity which switches easy-axis as magnetic field or strain is varied. The dramatic anisotropy reflects one-dimensional localization (dimensional reduction) of the electron wavefunctions along a crystal axis due to quantum interference effects. This can be understood in an effective one-dimensional quasiperiodic Aubry-André-like models, or in a complementary semiclassical picture. This phenomenon should be observable in strained moiré materials at realistic fields and low strain disorder, as well as unstrained systems with anisotropic Fermi surfaces.

cond-mat.mes-hall↗

arXiv2023

Zero-field composite Fermi liquid in twisted semiconductor bilayers

Recent experiments have produced evidence for fractional quantum anomalous Hall (FQAH) states at zero magnetic field in the semiconductor moiré superlattice system $t$MoTe$_2$. Here we argue that a composite fermion description, already a unifying framework for the phenomenology of 2d electron gases at high magnetic fields, provides a similarly powerful perspective in this new context. To this end, we present exact diagonalization evidence for composite Fermi liquid states at zero magnetic field in $t$MoTe$_2$ at fillings $n=\frac{1}{2}$ and $n=\frac{3}{4}$. We dub these non-Fermi liquid metals anomalous composite Fermi liquids (ACFLs), and we argue that they play a central organizing role in the FQAH phase diagram. We proceed to develop a long wavelength theory for this ACFL state that offers concrete experimental predictions upon doping the composite Fermi sea, including a Jain sequence of FQAH states and a new type of commensurability oscillations originating from the superlattice potential intrinsic to the system.

cond-mat.mes-hall↗

arXiv2023

Electronic ratchet effect in a moiré system: signatures of excitonic ferroelectricity

Electronic ferroelectricity represents a new paradigm where spontaneous symmetry breaking driven by electronic correlations, in contrast to traditional lattice-driven ferroelectricity, leads to the formation of electric dipoles. Despite the potential application advantages arising from its electronic nature, switchable electronic ferroelectricity remains exceedingly rare. Here, we report the discovery of an electronic ratchet effect that manifests itself as switchable electronic ferroelectricity in a layer-contrasting graphene-boron nitride moiré heterostructure. Our engineered layer-asymmetric moiré potential landscapes result in layer-polarized localized and itinerant electronic subsystems. At particular fillings of the localized subsystem, we find a ratcheting injection of itinerant carriers in a non-volatile manner, leading to a highly unusual ferroelectric response. Strikingly, the remnant polarization can be stabilized at multiple (quasi-continuous) states with behavior markedly distinct from known ferroelectrics. Our experimental observations, simulations, and theoretical analysis suggest that dipolar excitons are the driving force and elementary ferroelectric units in our system. This signifies a new type of electronic ferroelectricity where the formation of dipolar excitons with aligned moments generates a macroscopic polarization and leads to an electronically-driven ferroelectric response, which we term excitonic ferroelectricity. Such new ferroelectrics, driven by quantum objects like dipolar excitons, could pave the way to innovative quantum analog memory and synaptic devices.

cond-mat.mes-hall↗