arXiv subjects

Goksu Can Toga

Publications and source records attributed to Goksu Can Toga.

12 recordsLinked to original sources

arXiv2026

Fast Scrambling in the Hyperbolic Ising Model

We investigate many-body chaos and scrambling in the Hyperbolic Ising model, a mixed-field Ising model living in the background of AdS2. The effect of the curvature is captured by site-dependent couplings obtained from the AdS2 metric applied to a flat nearest-neighbor spin chain. Using a combination of out-of-time-ordered correlators (OTOCs), Krylov complexity, and spectral statistics, we present consistent evidence that this model exhibits faster scrambling behavior relative to its flat counterpart. In particular, we observe signatures consistent with fast scrambling dynamics emerging from purely local interactions. At the system sizes accessible to tensor network simulations, the OTOCs display short-lived exponential growth regimes, from which we extract effective Lyapunov exponents. These effective finite-size exponents exhibit a temperature dependence broadly compatible with the Maldacena-Shenker-Stanford (MSS) bound within numerical uncertainty. Our results indicate that increasing spatial curvature can significantly decrease scrambling time in systems with only nearest-neighbor interactions, providing a minimal and computationally accessible platform for studying quantum chaos. This makes the model a promising test-bed for exploring scrambling and operator growth in near-term quantum simulation architectures.

quant-ph↗

arXiv2026

Quantum Ising Model on $(2+1)-$Dimensional Anti$-$de Sitter Space using Tensor Networks

We study the quantum Ising model on (2+1)-dimensional anti-de Sitter space using Matrix Product States (MPS) and Matrix Product Operators (MPOs). We explore the bulk phase diagram of the theory on regular tessellations of hyperbolic space with coordination number seven and find disordered and ordered phases separated by a phase transition. We find that the boundary-boundary spin correlation function exhibits power law scaling deep in the disordered phase of the Ising model consistent with holography. At the critical point, we find the boundary entanglement entropy scales logarithmically with subsystem size but away from this, we see a linear scaling. In comparison, the full system exhibits a volume law scaling, which is expected in chaotic and/or highly connected systems. We also measure Out of time Ordered Correlators (OTOCs) to explore the scrambling behavior of the theory.

hep-lat↗

arXiv2026

Information Propagation in Rydberg Arrays via Analog OTOC Calculations

Out-of-time-order correlators (OTOCs) are the main tool for probing quantum chaos and scrambling, and have become crucial probes in many areas of quantum computing. However, the measurement of OTOCs is difficult to implement on analog quantum computers due to the requirement of backward time evolution. In this paper, we develop and implement a randomized measurement protocol to compute OTOCs on Aquila by QuEra Computing. Unlike traditional methods that require backward time evolution, our approach utilizes a sequence of global randomized quenches that approximates the unitary 2-design properties necessary for extracting infinite-temperature OTOCs from statistical correlations. We demonstrate the protocol's success by explicitly observing the lightcone of information propagation in 1D Rydberg chains, and compare hardware results to both state-vector simulations and matrix product state (MPS) tensor network calculations. This work establishes the first demonstration of fully analog randomized OTOC measurements in neutral-atom simulators, providing a scalable pathway to probe quantum chaos in complex many-body systems.

quant-ph↗

arXiv2025

Probing Bound State Relaxation Dynamics in Systems Out-of-Equilibrium on Quantum Computers

Pump-probe spectroscopy is a powerful tool for probing response dynamics of quantum many-body systems in and out-of-equilibrium. Quantum computers have proved useful in simulating such experiments by exciting the system, evolving, and then measuring observables to first order, all in one setting. Here, we use this approach to investigate the mixed-field Ising model, where the longitudinal field plays the role of a confining potential that prohibits the spread of the excitations, spinons, or domain walls into space. We study the discrete bound states that arise from such a setting and their evolution under different quench dynamics by initially pumping the chain out of equilibrium and then probing various non-equal time correlation functions. Finally, we study false vacuum decay, where initially one expects unhindered propagation of the ground state, or true vacuum, bubbles into the lattice, but instead sees the emergence of Bloch oscillations that are directly the reason for the long-lived oscillations in this finite-size model. Our work sets the stage for simulating systems out-of-equilibrium on classical and quantum computers using pump-probe experiments without needing ancillary qubits.

quant-ph↗

arXiv2024

Simulating Field Theories with Quantum Computers

In this study, we investigate Trotter evolution in the Gross-Neveu and hyperbolic Ising models in two spacetime dimensions, using quantum computers. We identify different sources of errors prevalent in various quantum processing units and discuss challenges to scale up the size of the computation. We present benchmark results obtained on a variety of platforms and employ a range of error mitigation techniques to address coherent and incoherent noise. By comparing these mitigated outcomes with exact diagonalization results and density matrix renormalization group calculations, we assess the effectiveness of our approaches. Moreover, we demonstrate the implementation of an out-of-time-ordered correlator (OTOC) protocol using IBM's quantum computers.

quant-ph↗

arXiv2023

Tensor network representation of non-abelian gauge theory coupled to reduced staggered fermions

We show how to construct a tensor network representation of the path integral for reduced staggered fermions coupled to a non-abelian gauge field in two dimensions. The resulting formulation is both memory and computation efficient because reduced staggered fermions can be represented in terms of a minimal number of tensor indices while the gauge sector can be approximated using Gaussian quadrature with a truncation. Numerical results obtained using the Grassmann TRG algorithm are shown for the case of $SU(2)$ lattice gauge theory and compared to Monte Carlo results.

hep-lat↗

arXiv2023

Quantum Ising model on two dimensional anti-de Sitter space

This paper investigates the transverse Ising model on a discretization of two-dimensional anti-de Sitter space. We use classical and quantum algorithms to simulate real-time evolution and measure out-of-time-ordered correlators (OTOC). The latter can probe thermalization and scrambling of quantum information under time evolution. We compared tensor network-based methods both with simulation on gated-based superconducting quantum devices and analog quantum simulation using Rydberg arrays. While studying this system's thermalization properties, we observed different regimes depending on the radius of curvature of the space. In particular, we find a region of parameter space where the thermalization time depends only logarithmically on the number of degrees of freedom.

quant-ph↗

arXiv2023

Holography from lattice $N=4$ super Yang-Mills

In this paper we use lattice simulation to study four dimensional $N=4$ super Yang-Mills (SYM) theory. We have focused on the three color theory on lattices of size $12^4$ and for 't Hooft couplings up to $λ=40.0$. Our lattice action is based on a discretization of the Marcus or GL twist of $N=4$ SYM and retains one exact supersymmetry for non-zero lattice spacing. We show that lattice theory exists in a single non-Abelian Coulomb phase for all 't Hooft couplings. Furthermore the static potential we obtain from correlators of Polyakov lines is in good agreement with that obtained from holography - specifically the potential has a Coulombic form with a coefficent that varies as the square root of the 't Hooft coupling.

hep-th↗

arXiv2022

Quantum Simulation of the N flavor Gross-Neveu Model

We discuss the use of quantum simulation to study an $N$ flavor theory of interacting relativistic fermions in(1+1) dimensions on NISQ era machines. The case of two flavors is particularly interesting as it can be mapped to the Hubbard model. We derive the appropriate qubit Hamiltonians and associated quantum circuits. We compare classical simulation and DMRG/TEBD calculations with the results of quantum simulation on various platforms for $N$=2 and 4. We demonstrate that the four steps of the calculations of real-time scattering can actually be implemented using current NISQ devices.

hep-lat↗

arXiv2022

Improved coarse-graining methods on two dimensional tensor networks including fermions

We show how to apply renormalization group algorithms incorporating entanglement filtering methods and a loop optimization to a tensor network which includes Grassmann variables which represent fermions in an underlying lattice field theory. As a numerical test a variety of quantities are calculated for two dimensional Wilson--Majorana fermions and for the two flavor Gross--Neveu model. The improved algorithms show much better accuracy for quantities such as the free energy and the determination of Fisher's zeros.

hep-lat↗

arXiv2022

Anomalies and symmetric mass generation for Kaehler-Dirac fermions

We show that massless Kaehler-Dirac (KD) fermions exhibit a mixed gravitational anomaly involving an exact $U(1)$ symmetry which is unique to KD fields. Under this $U(1)$ symmetry the partition function transforms by a phase depending only on the Euler character of the background space. Compactifying flat space to a sphere we learn that the anomaly vanishes in odd dimensions but breaks the symmetry down to $Z_4$ in even dimensions. This $Z_4$ is sufficient to prohibit bilinear terms from arising in the fermionic effective action. Four fermion terms are allowed but require multiples of two flavors of KD field. In four dimensional flat space each KD field can be decomposed into four Dirac spinors and hence these anomaly constraints ensure that eight Dirac fermions or, for real representations, sixteen Majorana fermions are needed for a consistent interacting theory. These constraints on fermion number agree with known results for topological insulators and recent work on discrete anomalies rooted in the Dai-Freed theorem. Our work suggests that KD fermions may offer an independent path to understanding these constraints. Finally we point out that this anomaly survives intact under discretization and hence is relevant in understanding recent numerical results on lattice models possessing massive symmetric phases.

hep-th↗

arXiv2021

Symmetric Mass Generation in Lattice Gauge Theory

We construct a four dimensional lattice gauge theory in which fermions acquire mass without breaking symmetries as a result of gauge interactions. Our model consists of reduced staggered fermions transforming in the bifundamental representation of a $SU(2)\times SU(2)$ gauge symmetry. This fermion representation ensures that single site bilinear mass terms vanish identically. A symmetric four fermion operator is however allowed and we show numerical results that show that a condensate of this operator develops in the vacuum.

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