arXiv subjects

Ahmet Keles

Publications and source records attributed to Ahmet Keles.

11 recordsLinked to original sources

arXiv2026

Fisher-Hartwig asymptotics for non-Hermitian random matrices

We prove the two-dimensional analogue of the asymptotics for Toeplitz determinants with Fisher-Hartwig singularities, for general real symbols. This formula has applications to random normal matrices with complex spectra: (i) the characteristic polynomial converges to a Gaussian multiplicative chaos random measure on the limiting droplet, in the subcritical phase; (ii) the electric potential converges pointwise to a logarithmically correlated field; (iii) the measure of its level sets (i.e. thick points) is identified; (iv) the associated free energy undergoes a freezing transition. This establishes emergence of the Liouville quantum gravity measure from free fermions in 2d, and universality with respect to the external potential.

math.PR↗

arXiv2025

Non-intersecting Brownian Motions and Gaussian Multiplicative Chaos

We obtain Fisher-Hartwig asymptotics with root and jump type singularities in space-time under the law of the stationary Hermitian Ornstein-Uhlenbeck process, which serve as a dynamical generalization of earlier static results obtained by Riemann-Hilbert methods. This extends previous asymptotics by [Krasovsky 2007], [Its, Krasovsky 2008], and [Charlier 2019]. As a consequence, fractional powers of the absolute value of the characteristic polynomial of this process (and the exponential eigenvalues counting process) converge to a two dimensional Gaussian multiplicative chaos measure on an infinite strip in the subcritical phase. The dynamical Fisher-Hartwig asymptotics also provide the leading order of the log-characteristic polynomial, together with optimal bulk rigidity for non-intersecting Brownian motions. These results offer (i) the second connection between random matrix theory and Liouville quantum gravity measures after [Bourgade, Falconet 2025], by proving a dynamical generalization of the single-time convergence to the GMC from [Berestycki, Webb, Wong 2018], (ii) a dynamical extension of the maximum of the log-characteristic polynomial [Lambert, Paquette 2019] and the optimal rigidity [Claeys, Fahs, Lambert, Webb 2021].

math.PR↗

arXiv2024

Pairing from repulsion in a two-dimensional Fermi gas with soft-core interactions

We investigate a model many-body system of spinless Fermi gas in two dimensions, where the bare two-body interaction is repulsive and takes the form of a soft-core disk potential. We obtain the zero temperature phase diagram of this model by numerical functional renormalization group (FRG), which retains the effective interaction vertices in all channels to provide a detailed picture of how Cooper pairing emerges under the renormalization flow. The repulsion drives the system to a series of superfluid states with higher angular momentum paring, for example in the $f$- and $h$-wave channels instead of the $p$-wave channel. This is in sharp contrast to the original Kohn-Luttinger mechanism where pairing of very large angular momenta and exponentially small transition temperature was predicted. We trace the stabilization and enhancement of $f$- and $h$-wave pairing back to the momentum dependence of the bare interaction. A perturbative calculation is carried out to show that while the second order Kohn-Luttinger diagrams provide a qualitative understanding of the onsets of the various superfluid phases, they are unable to accurately capture the phase boundaries predicted by FRG. Our findings suggest that tuning the shape of the interaction potential offers a promising route to achieve stronger ``pairing glue" and to realize nontrivial superfluid phases in repulsive Fermi gases beyond the scope of the original Kohn-Luttinger analysis.

cond-mat.quant-gas↗

arXiv2022

Rise and fall of plaquette order in Shastry-Sutherland magnet revealed by pseudo-fermion functional renormalization group

The Shastry-Sutherland model as a canonical example of frustrated magnetism has been extensively studied. The conventional wisdom has been that the transition from the plaquette valence bond order to the Neel order is direct and potentially realizes a deconfined quantum critical point beyond the Ginzburg-Landau paradigm. This scenario however was challenged recently by improved numerics from density matrix renormalization group which offers evidence for a narrow gapless spin liquid between the two phases. Prompted by this controversy and to shed light on this intricate parameter regime from a fresh perspective, we report high-resolution functional renormalization group analysis of the generalized Shastry-Sutherland model. The flows of over 50 million running couplings provide a detailed picture for the evolution of spin correlations as the frequency/energy scale is dialed from the ultraviolet to the infrared to yield the zero temperature phase diagram. The singlet dimer phase emerges as a fixed point, the Neel order is characterized by divergence in the vertex function, while the transition into and out of the plaquette order is accompanied by pronounced peaks in the plaquette susceptibility. The plaquette order is suppressed before the onset of the Neel order, lending evidence for a finite spin liquid region for $J_1/J_2\in (0.77,0.82)$, where the flow is continuous without any indication of divergence.

cond-mat.str-el↗

arXiv2020

$f$-wave superfluidity from repulsive interaction in Rydberg-dressed Fermi gas

Interacting Fermi gas provides an ideal model system to understand unconventional pairing and intertwined orders relevant to a large class of quantum materials. Rydberg-dressed Fermi gas is a recent experimental system where the sign, strength, and range of the interaction can be controlled. The interaction in momentum space has a negative minimum at $q_c$ inversely proportional to the characteristic length-scale in real space, the soft-core radius $r_c$. We show theoretically that single-component (spinless) Rydberg-dressed Fermi gas in two dimensions has a rich phase diagram with novel superfluid and density wave orders due to the interplay of the Fermi momentum $p_F$, interaction range $r_c$, and interaction strength $u_0$. For repulsive bare interactions $u_0>0$, the dominant instability is $f$-wave superfluid for $p_Fr_c\lesssim 2$, and density wave for $p_Fr_c\gtrsim 4$. The $f$-wave pairing in this repulsive Fermi gas is reminiscent of the conventional Kohn-Luttinger mechanism, but has a much higher $T_c$. For attractive bare interactions $u_0<0$, the leading instability is $p$-wave pairing. The phase diagram is obtained from functional renormalization group that treats all competing many-body instabilities in the particle-particle and particle-hole channels on equal footing.

cond-mat.quant-gas↗

arXiv2019

Scrambling dynamics and many-body chaos in a random dipolar spin model

Is there a quantum many-body system that scrambles information as fast as a black hole? The Sachev-Ye-Kitaev model can saturate the conjectured bound for chaos, but it requires random all-to-all couplings of Majorana fermions that are hard to realize in experiments. Here we examine a quantum spin model of randomly oriented dipoles where the spin exchange is governed by dipole-dipole interactions. The model is inspired by recent experiments on dipolar spin systems of magnetic atoms, dipolar molecules, and nitrogen-vacancy centers. We map out the phase diagram of this model by computing the energy level statistics, spectral form factor, and out-of-time-order correlation (OTOC) functions. We find a broad regime of many-body chaos where the energy levels obey Wigner-Dyson statistics and the OTOC shows distinctive behaviors at different times: Its early-time dynamics is characterized by an exponential growth, while the approach to its saturated value at late times obeys a power law. The temperature scaling of the Lyapunov exponent $λ_L$ shows that while it is well below the conjectured bound $2πT$ at high temperatures, $λ_L$ approaches the bound at low temperatures and for large number of spins.

cond-mat.quant-gas↗

arXiv2018

Weyl nodes in periodic structures of superconductors and spin active materials

Motivated by recent progress in epitaxial growth of proximity structures of s-wave superconductors (S) and spin-active materials (M), we show that the periodic structure of S and M can behave effectively as a superconductor with pairs of point nodes, near which the low energy excitations are Weyl fermions. A simple toy model, where M is described by a Kronig-Penney potential with both spin-orbit coupling and exchange field, is proposed and solved to obtain the phase diagram of the nodal structure, the spin texture of the Weyl fermions, as well as the zero energy surface states in the form of open Fermi lines ("Fermi arcs"). Going beyond the simple model, a lattice model with alternating layers of S and magnetic $Z_2$ topological insulators (M) is solved. The calculated spectrum confirms previous prediction of Weyl nodes based on tunneling Hamiltonian of Dirac electrons. Our results provide further evidence that periodic structures of S and M are well suited for engineering gapless topological superconductors.

cond-mat.supr-con↗

arXiv2018

Absence of long-range order in a triangular spin system with dipolar interactions

Antiferromagnetic Heisenberg model on the triangular lattice is perhaps the best known example of frustrated magnets, but it orders at low temperatures. Recent density matrix renormalization group (DMRG) calculations find that next nearest neighbor interaction $J_2$ enhances the frustration and leads to a spin liquid for $J_2/J_1\in (0.08,0.15)$. In addition, DMRG study of a dipolar Heisenberg model with longer range interactions gives evidence for a spin liquid at small dipole titling angle $θ\in[0,10^\circ)$. In both cases, the putative spin liquid region appears to be small. Here, we show that for the triangular lattice dipolar Heisenberg model, a robust quantum paramagnetic phase exists in a surprisingly wide region, $θ\in [0,54^\circ)$, for dipoles tilted along the lattice diagonal direction. We obtain the phase diagram of the model by functional renormalization group (RG) which treats all magnetic instabilities on equal footing. The quantum paramagnetic phase is characterized by a smooth continuous flow of vertex functions and spin susceptibility down to the lowest RG scale, in contrast to the apparent breakdown of RG flow in phases with stripe or spiral order. Our finding points to a promising direction to search for quantum spin liquids in ultracold dipolar molecules.

cond-mat.quant-gas↗

arXiv2018

Renormalization group analysis of dipolar Heisenberg model on square lattice

We present a detailed functional renormalization group analysis of spin-1/2 dipolar Heisenberg model on square lattice. This model is similar to the well known $J_1$-$J_2$ model and describes the pseudospin degrees of freedom of polar molecules confined in deep optical lattice with long-range anisotropic dipole-dipole interactions. Previous study of this model based on tensor network ansatz indicates a paramagnetic ground state for certain dipole tilting angles which can be tuned in experiments to control the exchange couplings. The tensor ansatz formulated on a small cluster unit cell is inadequate to describe the spiral order, and therefore the phase diagram at high azimuthal tilting angles remains undetermined. Here we obtain the full phase diagram of the model from numerical pseudofermion functional renormalization group calculations. We show that an extended quantum paramagnetic phase is realized between the Néel and stripe/spiral phase. In this region, the spin susceptibility flows smoothly down to the lowest numerical renormalization group scales with no sign of divergence or breakdown of the flow, in sharp contrast to the flow towards the long-range ordered phases. Our results provide further evidence that the dipolar Heisenberg model is a fertile ground for quantum spin liquids.

cond-mat.quant-gas↗

arXiv2017

Theory of interacting fermions in shaken square optical lattice

We develop a theory of weakly interacting fermionic atoms in shaken optical lattices based on the orbital mixing in the presence of time-periodic modulations. Specifically, we focus on fermionic atoms in circularly shaken square lattice with near resonance frequencies, i.e., tuned close to the energy separation between $s$-band and the $p$-bands. First, we derive a time-independent four-band effective Hamiltonian in the non-interacting limit. Diagonalization of the effective Hamiltonian yields a quasi-energy spectrum consistent with the full numerical Floquet solution that includes all higher bands. In particular, we find that the hybridized $s$-band develops multiple minima and therefore non-trivial Fermi surfaces at different fillings. We then obtain the effective interactions for atoms in the hybridized $s$-band analytically and show that they acquire momentum dependence on the Fermi surface even though the bare interaction is contact-like. We apply the theory to find the phase diagram of fermions with weak attractive interactions and demonstrate that the pairing symmetry is $s+d$-wave. Our theory is valid for a range of shaking frequencies near resonance, and it can be generalized to other phases of interacting fermions in shaken lattices.

cond-mat.quant-gas↗

arXiv2016

Competing many-body instabilities in two-dimensional dipolar Fermi gases

Experiments on quantum degenerate Fermi gases of magnetic atoms and dipolar molecules begin to probe their broken symmetry phases dominated by the long-range, anisotropic dipole-dipole interaction. Several candidate phases including the p-wave superfluid, the stripe density wave, and a supersolid have been proposed theoretically for two-dimensional spinless dipolar Fermi gases. Yet the phase boundaries predicted by different approximations vary greatly, and a definitive phase diagram is still lacking. Here we present a theory that treats all competing many-body instabilities in the particle-particle and particle-hole channel on equal footing. We obtain the low temperature phase diagram by numerically solving the functional renormalization-group flow equations and find a nontrivial density wave phase at small dipolar tilting angles and strong interactions, but no evidence of the supersolid phase. We also estimate the critical temperatures of the ordered phases.

cond-mat.quant-gas↗