arXiv subjects

Vinayak M. Kulkarni

Publications and source records attributed to Vinayak M. Kulkarni.

6 recordsLinked to original sources

arXiv2026

Emergent $\PT$ Symmetry and Exceptional Points in a Driven Dirac Impurity

Periodic driving can generate passive non-Hermitian impurity dynamics without microscopic gain. We derive this mechanism for an inversion-asymmetric spin--orbit-coupled Dirac impurity: off-shell angular harmonics produce a real spin-odd shift that the retarded bath converts into relative spin-dependent decay. After common damping is removed, the kernel contains the parity--time ($\mathcal{PT}$) core $Δ_{\rm eff}σ_x+iΓ_{\rm PT}σ_z$ and its causal Kramers--Kronig detuning. Full finite-band frequency dependence turns the constant-core benchmark into an avoided coalescence. In contrast, a stationary rotating drive, evaluated with the full momentum integral and both helicity cuts, supports a family of nonlinear causal pole exceptional points (EPs), certified by a double-zero condition, local winding, and pole exchange. Zero-temperature complete-basis calculations on four $z$-shifted $N=10$ and $12$ matrix block-Wilson chains continue a representative EP to $U=0.0025$. On a common contour both chains have the same winding and pole exchange, while a Rouch'e ratio $0.678<1$ preserves the enclosed zero count. This is a controlled finite-chain result, not a thermodynamic-limit numerical renormalization group or strong-coupling theorem. Divergent biorthogonal projectors cancel in complete propagators and in the particle--hole-symmetric finite-$U$ charge resolvent, precluding universal screening enhancement. On an equal-velocity branchwise-linearized submanifold, the exact finite-$U$ Anderson contact matrix is rational in a dressed rapidity and $GL(2,\mathbb{C})$ covariant; its Yang--Baxter structure survives the non-unitary similarity as a unipotent EP boundary twist. This does not extend to the full curved, frequency-dependent driven kernel.

cond-mat.str-el↗

arXiv2026

Jordan-Twist Bethe Ansatz and Many-Body Exceptional-Point Amplification in the Finite-$U$ Anderson Impurity

We construct an interacting integrable realization of many-body exceptional-point amplification in the static equal-velocity linearized finite-$U$ Anderson impurity. Two spin-orbit branches are linearized about counterpropagating Fermi points and folded into equal-velocity chiral components. The impurity carries the constant pseudo-Hermitian matrix $M=γσ_x+iβσ_z$, while the hybridization is a component scalar. A canonical $GL(2,\mathbb C)$ transformation preserves the Anderson interaction, and a position-dependent version maps the model to the conventional Anderson Hamiltonian plus a conserved complexified pseudospin charge with boundary twist $G=\exp(iML/v)$. The exact two-electron Anderson $R$-matrix is rational in the dressed rapidity $u(p)=p(p-2ε_d-U)/(2UΓ_A)$ and yields YBE, RLL, and twisted RTT relations for arbitrary particle number. At $β^2=γ^2$, $G$ is nontrivial unipotent. On every pseudospin-$S$ multiplet, the deformed Hamiltonian is similar to a single Jordan block of order $2S+1$; finite $U$ shifts its energy but does not split it. Approaching the unipotent point through a singularly conjugated diagonal twist, the descendant spin roots contract to $λ=\infty$ with scaled positions fixed by $L_r^{(-2S-1)}(2x)$. For the maximal descendant at large $S$, their normalized zeros converge to the Szego curve. Curvature, unequal velocities, and nonscalar channel couplings lie outside the theorem.

math-ph↗

arXiv2026

Quantum weight and low-loss EELS signatures of Wannier quantum geometry in black phosphorus

Quantum geometry is now experimentally accessible in crystalline solids, with black phosphorus providing a key platform through polarization-resolved angle-resolved photoemission spectroscopy. We develop a first-principles framework that connects the momentum-resolved quantum metric of black phosphorus to a complementary bulk observable: the direction-resolved quantum weight measurable through low-loss electron energy-loss spectroscopy (EELS). A 32-band DFT--Wannier Hamiltonian is used to compute both single-band and occupied-manifold geometric quantities from analytic momentum derivatives. We show that the raw single-band quantum metric of the top valence band is not globally meaningful in the conventional cell because folding degeneracies and intra-valence near degeneracies produce true isolated-band singularities; masked maps and occupied-manifold projectors are therefore essential. Because semilocal PBE produces near-gap semimetallic pockets and spurious subgap interpolation features, we introduce an experimentally motivated restricted quantum weight $K_{ii}(ω_c)$, which obeys the corresponding restricted Souza--Wilkens--Martin sum rule and is the appropriate quantity for low-loss EELS once the zero-loss region is excluded. The restricted in-plane quantum weight is nearly isotropic, $K_{zz}/K_{xx}=0.972\pm0.005$ (armchair/zigzag), despite the strong band-mass anisotropy and armchair-only absorption onset of black phosphorus. Orbital-resolved Hubbard--Hartree corrections leave the absolute quantum weights rigid at the sub-percent level while producing a small but resolved armchair-directed drift of $K_{zz}/K_{xx}$, approximately $+0.46\%$ per eV of $U$. These results identify low-loss EELS spectral moments as a practical probe of integrated quantum geometry in an anisotropic layered material.

cond-mat.mtrl-sci↗

arXiv2026

Derivation of a $\PT$-Symmetric Sine-Gordon Model from a Nonequilibrium Spin-Boson System via Keldysh Functional Integrals

We present a microscopic derivation from a nonequilibrium spin-boson model to a $\PT$-symmetric non-Hermitian sine-Gordon (SG) effective theory, via the Keldysh functional-integral formalism, a Lang-Firsov polaron transformation, bosonization, and a Grassmann coherent-state spin trace.The spin trace yields the generic reduced vertex $g_r\cos(λΦ_1)+ig_i\sin(λΦ_1)$, where the imaginary part originates from the nonequilibrium Keldysh distribution asymmetry $δn(ω)=n_+(ω)-n_-(ω)$. We provide an explicit dictionary between the spin-boson microscopic parameters and the NH-SG couplings: $K=v_f/\tilde{J}_\parallel^2$ (Luttinger parameter from $J_\parallel$), $g_r\propto J_\perp^2/Γ$ (from the transverse coupling and impurity width), and $\mathcal{I}=g_i/g_r\proptoμ/v_f$ (bias ratio, an exact RG invariant).One-loop Wilson momentum-shell RG on the NH-SG action gives the closed equations $\diff K/\diff l=-g_r^2(1-\mathcal{I}^2)K^2$ and $\diff g_r/\diff l=(2-K)g_r$, identical to those of Ashida \textit{et al.}\ for the $\PT$-symmetric SG; the present work supplies the microscopic initial conditions from the spin-boson Keldysh reduction. The BKT separatrix $K=2$ (Toulouse line), the EP fixed manifold $\mathcal{I}=1$ ($μ=μ_c$), and the mass gap $m\simΛe^{-c/\sqrt{K_0-2}}$ all follow from this closed system.In the non-relativistic soliton sector near the EP, the effective coupling $\tilde{g}=g_r\sqrt{1-\mathcal{I}^2}$ reduces the S-matrix to the Lieb-Liniger rational form and the Bethe ansatz becomes exact for that auxiliary gas.Within this sector we derive $n$-string bound states with$E_n^{\rm bind}=-n(n^2-1)\tilde{g}^2/12$, identify the EP as the many-body bound-state threshold, and construct the Jordan-partner state from the $ε$-regularised dimer.

quant-ph↗

arXiv2025

Anderson Impurities In Edge States with Nonlinear and Dissipative Perturbations

We show that exceptional points (EPs) and non-Hermitian behavior can emerge dynamically in impurity models with Hermitian microscopic origins. Using perturbative renormalization group (RG) analysis, Fock-space diagonalization, and spin-spin relaxation time calculations, we demonstrate that nonlinear (NL) dispersion and anisotropic pseudochiral (PC) interactions generate complex fixed points and spectral defectiveness. The effective Kondo model features a square-root RG invariant linking planar and longitudinal Dzyaloshinskii--Moriya (DM) couplings, driving the onset of EPs. Our analysis reveals dissipative fixed points stabilized by an emergent Lie algebra structure and a scaling collapse in relaxation dynamics. Across both single- and two-impurity extensions, we identify a universal ``sign-reversion'' (SR) regime near critical NL coupling, where anisotropy preserves PC symmetry and SR serves as a signature of non-Hermitian flow. These results establish a new class of non-Hermitian criticality generated through RG evolution in otherwise Hermitian systems.

cond-mat.str-el↗

arXiv2024

Emergent soft-gap Anderson models at quantum criticality in a lattice Hamiltonian within dynamical mean field theory

Local quantum criticality in itinerant fermion systems has been extensively investigated through the soft-gap Anderson impurity model, wherein a localized, correlated impurity, hybridizes with a broad conduction band with a singular, $|ω|^r$, density of states. However, lattice models hosting quantum critical points (QCPs), do not appear to have such a spectrum emerging at the QCP. In this work, we report the emergence of such a singular form of the density of states in a three-orbital lattice model, within dynamical mean field theory, precisely at a quantum critical point, separating a gapless, Fermi liquid, metallic phase from a gapped, Mott insulating phase. A temperature-dependent exponent, $α$, defined using the corresponding Matsubara self-energy, is found to vary from $+1$ deep in the FL regime, to $-1$ in the Mott insulator regime. Interestingly, we find that $α$ becomes temperature independent, and hence isosbestic, precisely at the QCP. The isosbestic exponent is shown to lead to an emergent soft-gap spectrum, $|ω|^r$ at the QCP, where $r = |α_{\rm iso}|$. We discuss the implications of our findings for non-Fermi liquid behaviour in the quantum critical region of the phase diagram.

cond-mat.str-el↗