arXiv subjects

Yogeshwar Prasad

Publications and source records attributed to Yogeshwar Prasad.

10 recordsLinked to original sources

arXiv2026

Hamiltonian fingerprints of a collective mode across the BCS-BEC crossover

Collective excitations can survive profound changes in the microscopic degrees of freedom that generate them. We track a layer-odd collective response from an exact weak-coupling hybridisation anchor into the paired regime of an attractive Hubbard bilayer and find that its Hamiltonian sensitivities evolve in a manner consistent with a crossover from single-particle interlayer hybridisation towards collective pair superexchange. At weak coupling, an exact identity for identical tunnel-coupled layers fixes a relative-phase Gaussian kernel zero at $2t_h$, independent of the intralayer hopping. Sign-free determinant quantum Monte Carlo reveals an interaction-driven softening of the many-body spectral scale without analytic continuation, while Gaussian response theory supplies the continuous pole interpretation and shows a shift from layer-density to relative-pair-phase character. In the paired regime, the characteristic response scale acquires a growing fractional sensitivity to the intralayer hopping and an interaction dependence partway towards the $1/U$ law. These results show how a collective excitation can be tracked across a fermion-to-composite-boson crossover while constraining changes in its microscopic drive.

cond-mat.str-el↗

arXiv2026

Hartree Fragmentation and Long-Range Pair Networks in Aperiodic Chains

For fermions in a slowly varying aperiodic potential with random interactions $V_{ij}/|i-j|^{\alpha}$, the potential fixes the resonance supply $N_0 \propto L^{2-n}/h$. On crossing ${\alpha}-2n$, wherever Hartree fragmentation is operative, the resonant-object ensemble reconstructs: turning-point runs fragment into clusters whose intrinsic matching law resolves no logarithmic singularity, while isolated wing bonds survive at finite density and restore a reduced logarithm. The scaling $x^{4-2n-{\alpha}}_{pair} ln{x_{pair}} \propto h^2/(V t0)$ is unchanged. Random coefficient fluctuations sustain the $R^{-{\alpha}}$ coupling; uniform ones cancel to $R^{-{\alpha}-2}$.

cond-mat.dis-nn↗

arXiv2026

Resonance statistics, Fock-space branching, and long-range pair networks in slowly varying interacting chains

In a slowly varying aperiodic potential $h_i=h\cos(2\pi\beta i^n+\phi)$ with random power-law density interactions $V_{ij}/|i-j|^\alpha$, the resonant-object ensemble changes across $\alpha=2n$, wherever Hartree fragmentation is operative, from isolated two-level bonds to a mixture of fragmented multi-site clusters and isolated wing bonds that survive at finite density, while the pair-resonance scaling $x_{\rm pair}^{4-2n-\alpha}\ln x_{\rm pair}\propto h^2/(Vt_0)$ is unchanged~\cite{letter}. Here we develop the microscopic resonance theory underlying these results, together with its domain of validity. We derive the exact phase-averaged resonance statistics --- the supply $N_0\propto L^{2-n}/h$, the correlated common-phase comb, and the closed-form Hartree variance --- proving that the interaction leaves the leading supply law unchanged. Exact construction of the resonant Fock-space graph at $L\le18$ shows that the order-one forward-branching scale $h_{\rm FB}\propto L^{2-n}$ carries no giant component: one-step branching and connectivity are inequivalent. We separate the fixed-pair matching law from the shell-averaged $q\ln(1/q)$ law of the bond ensemble and develop the comb into a mesoscopic shell theory; we map the fragmentation domain, with its support threshold $V_*(\alpha)$ and the boundary-healing recursion; and we treat the marginal case $\alpha=2$, where shell and matching marginalities compound into a double logarithm. Three long-range thresholds emerge with distinct meanings --- $\alpha=1/2$ (the exact variance threshold of the random Fock-space energy and the square-summability boundary of the leading LIOM-dressing estimate), $\alpha=2n$ (change of the local resonant objects), and $\alpha=2$ (marginality of the long-range shell sum) --- none of which is, by itself, a localization transition.

cond-mat.dis-nn↗

arXiv2026

Exact Gaussian pinning of a relative-phase mode and interaction-driven detuning from the pinned frequency

Hybridization between two identical fermionic layers or components produces a rigid bonding--antibonding splitting $2t_h$. We show that in a paired state this scale enters the collective dynamics exactly within Gaussian fluctuation theory: the copy-odd relative-phase kernel vanishes at $\omega=2t_h$, with the underlying parity-pair identity holding pointwise in momentum. Within a broad class of conventionally paired systems, the result is independent of chemical potential, band structure, orbital content, and dimensionality. It follows from copy-pseudospin Larmor precession generated by intercopy hopping together with the Goldstone--Ward condition imposed by superconducting self-consistency. Pairing also isolates $2t_h$ from quasiparticle excitations, with thermal scattering below and pair creation above it whenever the gap is finite. At particle-hole symmetry, where the copy-odd amplitude decouples, the kernel zero becomes an isolated relative-phase pole at $\Omega_L=2t_h$, and the layer-imbalance response is a single Gaussian mode exhausting its Gaussian first moment; the corresponding full-Hamiltonian first moment obeys an exact operator sum rule. This pinning is not protected beyond Gaussian order. An exact interaction torque destroys the Larmor closure, while an exactly solvable rung and exact diagonalization of the attractive Hubbard model on a periodic $N_s=12$, $z=3$ bilayer honeycomb cluster show strong detuning. At $|U|=4t$, the dominant layer-imbalance excitation occurs at $0.467(2t_h)$ while retaining $98.6\%$ of the zeroth-moment spectral weight but only $92.4\%$ of the exact first moment. Thus the Gaussian result provides an exact reference frequency whose many-body renormalization can be substantial while a dominant layer-odd excitation survives.

cond-mat.supr-con↗

arXiv2026

Optical Signatures and Quantum Geometry in Proximity-Induced Topological Superconductors

Topological-insulator-superconductor (TI-SC) heterostructures provide a promising platform for proximity-induced topological superconductivity, but diagnosing superconductivity at a buried interface remains challenging for conventional surface-sensitive probes. Here, we develop a quantitative theory of the longitudinal optical response of a TI-SC heterostructure and show that the complex sheet conductance provides an interface-selective route to isolating and diagnosing the buried proximitized interface state. Starting from a minimal model, we derive a low-energy description of the heterointerface in which the induced gap emerges directly from the TI-SC coupling. Combined with a slab-based thickness-extrapolation procedure, this framework yields a practical protocol for separating the buried interfacial sheet conductance from bulk and exposed-surface optical contributions. The extracted interface response exhibits a robust, thickness-independent coherence peak at an energy set by the proximity-induced gap, clearly distinguishable from both the pair-breaking scale of the parent superconductor and the Dirac cone on the exposed TI surface. At low energies, the heterointerface is described by an effective time-reversal-invariant topological-superconducting theory, while the associated low-frequency optical spectral weight admits a quantum-geometric interpretation through the optical sum rule. Our results establish terahertz/infrared spectroscopy of thickness-extracted sheet conductance as a noninvasive route to identifying and quantifying proximity-induced superconductivity at buried TI-SC interfaces.

cond-mat.mes-hall↗

arXiv2024

Single-particle excitations across the localization and many-body localization transition in quasi-periodic systems

We study localization and many-body localization transition in one dimensional systems in the presence of deterministic quasi-periodic potential. We use single-particle excitations obtained through single-particle Green's function in real space to characterize the localization to delocalization transition. A single parameter scaling analysis of the ratio of the typical to average value of the local density of states (LDOS) of single particle excitations shows that the critical exponent with which the correlation length $ξ$ diverges at the transition point $ξ\sim |h-h_c|^{-ν}$, coming from the localized side, satisfies the inequality $ν\ge 1$ for the non-interacting Aubry-Andre (AA) model. For the interacting system with AA potential, we study single particle excitations produced in highly excited many-body eigenstates across the MBL transition and found that the critical exponent obtained from finite-size scaling of the ratio of the typical to average value of the LDOS satisfies $ν\ge 1$ here as well. This analysis of local density of states shows that the localization and MBL transition in systems with quasi-periodic potential belong to a different universality class than the localization and MBL transition in systems with random disorder where $ν\ge 2$. In complete contrast to this, finite-size scaling of the level spacing ratio is known to support the same universality class for MBL transitions in systems with quasiperiodic as well as random disorder potentials. For the interacting systems with quasiperiodic potentials, though finite-size scaling of the level spacing ratio shows a transition at $h_c^{lsr}$ which is close to the transition point obtained from LDOS within numerical precision, the critical exponent obtained from finite-size scaling of level spacing ratio is $ν\sim 0.54$ in close similarity to the MBL systems with random disorder.

cond-mat.dis-nn↗

arXiv2023

Interplay of disorder and interactions in the bilayer band-insulator : A determinant quantum Monte Carlo study

In previous studies of the half-filled bilayer attractive Hubbard model [Prasad {\it et al.} Phys. Rev. A {\bf 89}, 043605 (2014); Prasad, Phys. Rev. B {\bf 106}, 184506 (2022)], it has been shown that the clean system has a band-insulator (BI) to superfluid (SF) quantum phase transition. In this paper, we append the effects of random on-site disorder on the kinetic energy, double occupancy, and the pair-pair correlations in the bilayer model. Using the determinant quantum Monte Carlo simulation, we observe that the on-site random disorder plays a significant role in the localization of on-site pairs, and hence in the reduction of the effective hopping. This results in an increase of the double occupancy, which is an effect that is similar to the attractive interaction. We find no change in the critical value of the interaction at which the model undergoes a transition from the BI to SF regime, even though the pair-pair correlations get suppressed for finite on-site disorder strengths $V_d/t=0.1-0.8$. We also confirm that the weak-disorder suppresses the SF phase largely in the strong-coupling limit. Hence the region of the SF phase reduces in the presence of random on-site disorder. Finally, through finite-size scaling, we have estimated the critical disorder strength $V_d^c/t\sim 1.44$ at $\abs{U}/t=5$.

cond-mat.supr-con↗

arXiv2022

Finite temperature study of correlations in bilayer band-insulator

We perform the finite-temperature determinant quantum Monte Carlo simulation for the attractive Hubbard model on the half-filled bilayer square lattice. Recent progress on optical lattice experiments lead us to investigate various single-particle properties such as momentum distribution and double occupancies which should be easily measured in cold-atom experiments. The pair-pair and the density-density correlations have been studied in detail, and through finite-size scaling, we show that there is no competing charge density wave order in the bilayer band-insulator model and that the superfluid phase is the stable phase for the interaction range $\abs{U}/t = 5-10$. We show the existence of two energy scales in the system as we increase the attractive interaction, one governing the phase coherence and the other one corresponding to the molecule formation. In the end, we map out the full $T-U$ phase diagram and compare the $T_c$ obtained through the mean-field analysis. We observe that the maximum $T_c/t(= 0.27)$ occurs for $\abs{U}/t = 6$, which is roughly twice the reported $T_c$ of the single-layer attractive Hubbard model.

cond-mat.str-el↗

arXiv2021

Many-body localization and enhanced non-ergodic sub-diffusive regime in the presence of random long-range interactions

We study many-body localization (MBL) in a one-dimensional system of spinless fermions with a deterministic aperiodic potential in the presence of long-range interactions decaying as power-law $V_{ij}/(r_i-r_j)^α$ with distance and having random coefficients $V_{ij}$. We demonstrate that MBL survives even for $α<1$ and is preceded by a broad non-ergodic sub-diffusive phase. Starting from parameters at which the short-range interacting system shows infinite temperature MBL phase, turning on random power-law interactions results in many-body mobility edges in the spectrum with a larger fraction of ergodic delocalized states for smaller values of $α$. Hence, the critical disorder $h_c^r$, at which ergodic to non-ergodic transition takes place increases with the range of interactions. Time evolution of the density imbalance $I(t)$, which has power-law decay $I(t) \sim t^{-γ}$ in the intermediate to large time regime, shows that the critical disorder $h_{c}^I$, above which the system becomes diffusion-less (with $γ\sim 0$) and transits into the MBL phase is much larger than $h_c^r$. In between $h_{c}^r$ and $h_{c}^I$ there is a broad non-ergodic sub-diffusive phase, which is characterized by the Poissonian statistics for the level spacing ratio, multifractal eigenfunctions and a non zero dynamical exponent $γ\ll 1/2$. The system continues to be sub-diffusive even on the ergodic side ($h < h_c^r$) of the MBL transition, where the eigenstates near the mobility edges are multifractal. For $h < h_{0} 1/2$. The rich phase diagram obtained here is unique to random nature of long-range interactions. We explain this in terms of the enhanced correlations among local energies of the effective Anderson model induced by random power-law interactions.

cond-mat.dis-nn↗

arXiv2012

Fermionic Superfluid from a Bilayer Band Insulator in an Optical Lattice

We propose a model to realize a fermionic superfluid state in an optical lattice circumventing the cooling problem. Our proposal exploits the idea of tuning the interaction in a characteristically low entropy state, a band-insulator in an optical bilayer system, to obtain a superfluid. By performing a detailed analysis of the model including fluctuations and augmented by a variational quantum Monte Carlo calculations of the ground state, we show that the superfluid state obtained has high transition temperature of the order of the hopping energy. Our system is designed to suppress other competing orders such as a charge density wave. We suggest a laboratory realization of this model via an orthogonally shaken optical lattice bilayer.

cond-mat.quant-gas↗