arXiv subjects

Bilal Tanatar

Publications and source records attributed to Bilal Tanatar.

11 recordsLinked to original sources

arXiv2026

Sector-resolved non-Bloch topology and nonlocal entanglement dynamics in a bond-dissipative Kitaev chain

A core characteristic of dissipative non-Hermitian topology is that the relaxation dynamics tracks the non-Bloch bulk-boundary correspondence, rendering an algebraic decay in the gapless regime and an exponential falloff in the gapped phase, so that local observables directly diagnose the topology. We show that this correspondence breaks down in a dissipative topological superconductor, where the local observables turn blind to the very topology they are expected to decipher. Via a bond-dissipative dimerized Kitaev chain in a third-quantized rapidity-matrix formulation, we find that at zero chemical potential the Majorana rapidity matrix decomposes into two independent non-Hermitian sectors, each with its own generalized Brillouin zone and non-Bloch winding number, thereby revealing a sector-resolved non-Bloch bulk-boundary correspondence. The local density is a cross-sector covariance and relaxes at the sum of the two sector rates, so it remains sector-blind even when one sector is gapless and topological. For balanced gain and loss, the finite-time zero events of the entanglement spectrum under purely periodic-boundary Lindblad evolution recover this hidden edge content sector by sector, serving as a dynamical invariant that returns the open-boundary edge rapidities without physically opening the chain.

quant-ph↗

arXiv2026

Large nonlinear Hall effect in strained moir\'e structures hosting pseudospin-3/2 fermions

We investigate the linear and nonlinear Hall response of a moir\'e \emph{watermill lattice}, in which stacking and twisting generate a four-band manifold near the Fermi level with suppressed group velocities at discrete magic angles. Including an inversion symmetry breaking onsite mass breaks the interlayer symmetry, opening a gap in this manifold and driving the system into a non-trivial bulk topological phase. We map the resulting phase diagram as a function of the strength of the mass and twist angle $\theta$, revealing several sectors with high Chern numbers. We then introduce strain to break the residual $C_3$ symmetry of the lattice which activates a finite Berry curvature dipole and correspondingly, a nonlinear Hall response. The dipole reverses sign sharply across topological phase boundaries, producing butterfly like features when plotted against the relevant system parameters. Its magnitude substantially exceeds that reported for symmetry-broken transition metal dichalcogenides, consistent with the elevated Wilson-loop winding and enhanced quantum geometry associated with the lattice's pseudospin-$3/2$ character. We conclude by incorporating thermal effects on the Berry curvature dipole, asserting that it is an important tool for discerning topology at low temperatures.

cond-mat.mes-hall↗

arXiv2026

Chaos suppression via adaptive feedback control of intermittency: From exactly solvable ergodic maps to interacting microbubble clusters

Intermittency represents a fundamental route to chaos in nonlinear dynamical systems. In this work we introduce an adaptive control strategy in which the control parameter of an intermittent system is promoted to a dynamical variable that evolves autonomously under an auxiliary nonlinear map drawn from the same functional hierarchy as the system itself. The construction eliminates the need for orbit identification, local linearization, and trajectory-triggered perturbations, which are central ingredients of conventional feedback schemes. The theoretical framework is developed within a class of one-dimensional nonlinear ergodic maps with exactly known invariant (Sinai--Ruelle--Bowen) measures, for which we derive in closed form (i) the dynamics and invariant measure of the evolving control parameter, (ii) the invariant measure of the coupled system, and (iii) the $q$-generalized Lyapunov exponents before and after control. The generalized Lyapunov spectrum serves as an analytical order parameter for the control process: the collapse of its positive regions provides a quantitative and initial-condition-independent signature of chaos suppression, and yields the sensitivity to initial conditions in explicit form. To establish the physical relevance of the approach beyond low-dimensional maps, we apply the same construction to a cluster of three interacting ultrasound-driven microbubbles described by the Keller--Herring model, promoting the experimentally accessible acoustic driving frequency to a dynamical variable. Systematic bifurcation and Lyapunov analyses, performed over wide ranges of driving pressure, frequency, and equilibrium radii, demonstrate that intermittent chaotic radial oscillations are progressively suppressed and replaced by stable periodic motion.

nlin.CD↗

arXiv2026

Probing topological phase transitions via nonlinear Hall response in strained moir\'e dice lattice

Valley polarized twisted bilayer dice lattice hosts topologically nontrivial flat bands far from charge neutrality due to broken time reversal symmetry, whereas the ones in the vicinity of it remain topologically trivial. However, when both valleys are taken into consideration, the time reversal symmetry is preserved, which poses a serious hindrance to enumerate the valley specific topological phases that rely on the detection of the Berry curvature. In this work, we demonstrate that such a twisted structure with an applied uniaxial strain exhibits a nonlinear Hall effect far from charge neutrality. We ascertain that the nonlinear anomalous Hall signals can serve as a probe for topological phase transitions associated with a specific energy state that is constrained to reside at the lower edge of the middle subband and controlled via a staggered mass. Specifically, we show that the nonlinear anomalous Hall response undergoes a sign reversal across the topological phase boundaries. By tuning the carrier density, we compute the nonlinear Hall response obtained from the Berry curvature dipole, both in the chiral limit, and also when the chiral symmetry is broken. It is further seen that the nonlinear Hall effect is significantly enhanced in the broken chiral symmetry regime.

cond-mat.mes-hall↗

arXiv2026

Floquet generation of hybrid-order topology and $\mathbb{Z}_2$-like bipolar localization

Periodic driving offers a powerful tool to engineer topological phases and even induce phase transitions that are inaccessible in static settings. In this work, we demonstrate that a suitable driving protocol applied to the Benalcazar-Bernevig-Hughes (BBH) model, a canonical quadrupolar insulator with a pi-flux-induced projective PT, gives rise to a hybrid-order topological phase in which the dispersive first-order edge states and localized higher-order corner modes are shown to coexist at distinct quasienergies. Further, extending the scenario to non-reciprocal hopping induced non-Hermiticity, we uncover a Z2-like skin effect characterized by a sharp transition from a unipolar to a bipolar eigenstate-localized phase. Remarkably, this phenomenon, which is established as a prerogative for spinful systems, emerges here purely from the interplay between the embedded gauge structure and Floquet-renormalized symmetry constraints, without invoking physical spin degrees of freedom. Further, the broken bulk-boundary correspondence in this driven non-Hermitian setting, can be restored via computing the two-dimensional generalized Brillouin zone (GBZ), which we construct through a symmetry-reduced mapping onto an effective one-dimensional problem. The resulting non-Bloch invariants faithfully capture both the higher-order topology and the unipolar to bipolar transition. These findings reveal periodic driving as a versatile and controllable handle for sculpting the interplay of higher-order topology, symmetry transmutation, and non-Hermitian skin physics in a single unified platform.

cond-mat.mes-hall↗

arXiv2022

Defining a critical temperature of a crossover from BEC to the normal phase in anisotropic quantum magnets

We address the problem of identifying the critical temperature in a crossover from the Bose-Einstein condensed (BEC) phase to the normal phase. For this purpose we study the temperature dependence of magnetization of spin-gapped quantum magnets described by BEC of triplons. We have calculated the heat capacity $C_H$ at constant field and fluctuations in magnetization in a spin-gapped quantum magnet using the Hartree-Fock-Bogouliubov approximation and found optimized parameters of the Hamiltonian of triplon gas. In the region of phase transition, the heat capacity $C_H$ is smeared out due to the Dzyaloshinsky-Moriya (DM) interaction. The sharp maximum of the fluctuations in the magnetization is identified as the critical temperature of the crossover.

cond-mat.quant-gas↗

arXiv2021

Effects of exchange and weak Dzyaloshinsky-Moriya anisotropies on thermodynamic characteristics of spin-gapped magnets

We study the modification of low temperature properties of quantum magnets such as magnetization, heat capacity, energy spectrum, and densities of condensed and noncondensed quasiparticles (triplons) due to anisotropies in the framework of mean-field based approach. We show that in contrast to exchange anisotropy (EA) interaction, Dzyaloshinsky-Moriya (DM) interaction modifies the physics dramatically. Particularly, it changes the sign of the anomalous density in the whole range of temperatures. Its critical behavior is slightly modified also by the EA. We have found that the shift of the critical temperature of phase transition (or crossover caused by DM interaction) is positive and significant. Using the experimental data on the magnetization of the compound TlCuCl$_3$, we have found optimal values for the strengths of EA and DM interactions. The spectrum of the energy of low lying excitations has also been investigated and found to develop a linear dispersion similar to Goldstone mode with a negligibly small anisotropy gap.

cond-mat.stat-mech↗

arXiv2021

Critical behavior of Tan's contact for bosonic systems with a fixed chemical potential

The temperature dependence of Tan's contact parameter $C$ and its derivatives for spin gapped quantum magnets are investigated. We use the paradigm of Bose-Einstein condensation (BEC) to describe the low temperature properties of quasiparticles in the system known as triplons. Since the number of particles and the condensate fraction are not fixed we use the $μVT$ ensemble to calculate the thermodynamic quantities. The interactions are treated at the Hartree-Fock-Bogoliubov approximation level. We obtained the temperature dependence of $C$ and its derivative with respect to temperature and applied magnetic field both above and below $T_c$ of the phase transition from the normal phase to BEC. We have shown that $C$ is regular, while its derivatives are discontinuous at $T_c$ in accordance with Ehrenfest's classification of phase transitions. Moreover, we have found a sign change in $\partial C/\partial T$ close to the critical temperature. As to the quantum critical point, $C$ and its derivatives are regular as a function of the control parameter $r$, which induces the quantum phase transition. At very low temperatures, one may evaluate $C$ simply from the expression $C=m^2μ^2/{\bar a}^{4}$, where the only parameter effective mass of quasiparticles should be estimated. We propose a method for measuring of Tan's contact for spin gapped dimerized magnets.

cond-mat.quant-gas↗

arXiv2020

Characteristic temperatures of a triplon system of dimerized quantum magnets

Exploiting the analogy between ultracold atomic gases and the system of triplons, we study magneto-thermodynamic properties of dimerized quantum magnets in the framework of Bose -Einstein condensation (BEC). Particularly, introducing the inversion (or Joule - Thomson) temperature $T_{JT}$ as the point where Joule - Thomson coefficient of an isenthalpic process changes its sign, we show that for a simple paramagnet, this temperature is infinite, while for three-dimensional (3D) dimerized quantum magnets it is finite and always larger than the critical temperature $T_c$ of BEC. Below the inversion temperature $T<T_{JT}$ the system of triplons may be in a liquid phase, which undergoes a transition into a superfluid phase at $T\le T_c<T_{JT}$. The dependence of the inversion temperature on the external magnetic field $T_{JT} (H)$ has been calculated for quantum magnets of TlCuCl$_3$ and Sr$_3$Cr$_2$O$_8$.

cond-mat.quant-gas↗

arXiv2019

Generalized Aubry-André-Harper model with modulated hopping and $p$-wave pairing

We study an extended Aubry-Andr{é}-Harper model with simultaneous modulation of hopping, on-site potential, and $p$-wave superconducting pairing. For the case of commensurate modulation of $β= 1/2$ it is shown that the model hosts four different types of topological states: adiabatic cycles can be defined which pump particles, two types of Majorana fermions, or Cooper pairs. In the incommensurate case we calculate the phase diagram of the model in several regions. We characterize the phases by calculating the mean inverse participation ratio and perform multi-fractal analysis. In addition, we characterize whether the phases found are topologically trivial or not. We find an interesting critical extended phase when incommensurate hopping modulation is present. The rise between the inverse participation ratio in regions separating localized and extended states is gradual, rather than sharp. When, in addition, the on-site potential modulation is incommensurate, we find several sharp rises and falls in the inverse participation ratio. In these two cases all different phases exhibit topological edge states. For the commensurate case we calculate the evolution of the Hofstadter butterfly and the band Chern numbers upon variation of the pairing parameter for zero and finite on-site potential. For zero on-site potential the butterflies are triangular-like near zero pairing, when gap-closure occurs, they are square-like, and hexagonal-like for larger pairing, but with the Chern numbers switched compared to the triangular case. For the finite case gaps at quarter and three-quarters filling close and lead to a switch in Chern numbers.

cond-mat.dis-nn↗

arXiv2012

Bistable behavior of a two-mode Bose-Einstein condensate in an optical cavity

We consider a two-component Bose-Einstein condensate in a one-dimensional optical cavity. Specifically, the condensate atoms are taken to be in two degenerate modes due to their internal hyperfine spin degrees of freedom and they are coupled to the cavity field and an external transverse laser field in a Raman scheme. A parallel laser is also exciting the cavity mode. When the pump laser is far detuned from its resonance atomic transition frequency, an effective nonlinear optical model of the cavity-condensate system is developed under Discrete Mode Approximation (DMA), while matter-field coupling has been considered beyond the Rotating Wave Approximation. By analytical and numerical solutions of the nonlinear dynamical equations, we examine the mean cavity field and population difference (magnetization) of the condensate modes. The stationary solutions of both the mean cavity field and normalized magnetization demonstrate bistable behavior under certain conditions for the laser pump intensity and matter-field coupling strength.

cond-mat.quant-gas↗